Python User Interface#


This page is a listing of the functions exposed by the Python interface. For a gentler introduction, see Tutorial/Basics. Note that this page is not a complete listing of all functions. In particular, because of the SWIG wrappers, every function in the C++ interface is accessible from the Python module, but not all of these functions are documented or intended for end users. See also the instructions for Parallel Meep.

The Python API functions and classes can be found in the meep module, which should be installed in your Python system by Meep's make install script. If you installed into a nonstandard location (e.g. your home directory), you may need to set the PYTHONPATH environment variable as documented in Building From Source. You typically import the meep module in Python via import meep as mp.

Table of Contents

Predefined Variables#

These are available directly via the meep package.

air, vacuum [Medium class ] — Two aliases for a predefined material type with a dielectric constant of 1.

perfect_electric_conductor or metal [Medium class ] — A predefined material type corresponding to a perfect electric conductor at the boundary of which the parallel electric field is zero. Technically, .

perfect_magnetic_conductor [Medium class ] — A predefined material type corresponding to a perfect magnetic conductor at the boundary of which the parallel magnetic field is zero. Technically, .

inf [number] — A big number (1020) to use for "infinite" dimensions of objects.

Constants (Enumerated Types)#

Several of the functions/classes in Meep ask you to specify e.g. a field component or a direction in the grid. These should be one of the following constants (which are available directly via the meep package):

direction constants — Specify a direction in the grid. One of X, Y, Z, R, P for , , , , , respectively.

side constants — Specify particular boundary in the positive High (e.g., +X) or negative Low (e.g., -X) direction.

boundary_condition constantsMetallic (i.e., zero electric field) or Magnetic (i.e., zero magnetic field).

component constants — Specify a particular field or other component. One of Ex, Ey, Ez, Er, Ep, Hx, Hy, Hz, Hy, Hp, Hz, Bx, By, Bz, By, Bp, Bz, Dx, Dy, Dz, Dr, Dp, Dielectric, Permeability, for , , , , , , , , , , , , , , , , , , , , ε, μ, respectively.

There are two convenience functions meep.component_name and meep.direction_name which, given a component/derived_component and direction argument respectively, return the equivalent string representation (e.g., meep.component_name(meep.Ex) returns ex and meep.direction_name(meep.R) returns r, etc.).

derived_component constants — These are additional components which are not actually stored by Meep but are computed as needed, mainly for use in output functions. One of Sx, Sy, Sz, Sr, Sp, EnergyDensity, D_EnergyDensity, H_EnergyDensity for , , , , (components of the Poynting vector ), , , , respectively.

There are two convenience functions meep.component_name and meep.direction_name which, given a component/derived_component and direction argument respectively, return the equivalent string representation (e.g., meep.component_name(meep.Ex) returns ex and meep.direction_name(meep.R) returns r, etc.).

The Simulation Class#

The Simulation class is the primary abstraction of the high-level interface. Minimally, a simulation script amounts to passing the desired keyword arguments to the Simulation constructor and calling the run method on the resulting instance.


Simulation#

class Simulation(object):

The Simulation class contains all the attributes that you can set to control various parameters of the Meep computation.

def __init__(self,
             cell_size: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
             resolution: float = None,
             geometry: Optional[List[meep.geom.GeometricObject]] = None,
             sources: Optional[List[meep.source.Source]] = None,
             eps_averaging: bool = True,
             dimensions: int = 3,
             boundary_layers: Optional[List[meep.simulation.PML]] = None,
             symmetries: Optional[List[meep.simulation.Symmetry]] = None,
             force_complex_fields: bool = False,
             default_material: meep.geom.Medium = Medium(),
             m: float = 0,
             k_point: Union[meep.geom.Vector3, Tuple[float, ...], bool] = False,
             kz_2d: str = 'complex',
             extra_materials: Optional[List[meep.geom.Medium]] = None,
             material_function: Optional[Callable[[Union[meep.geom.Vector3, Tuple[float, ...]]], meep.geom.Medium]] = None,
             epsilon_func: Optional[Callable[[Union[meep.geom.Vector3, Tuple[float, ...]]], float]] = None,
             epsilon_input_file: str = '',
             progress_interval: float = 4,
             subpixel_tol: float = 0.0001,
             subpixel_maxeval: int = 100000,
             loop_tile_base_db: int = 0,
             loop_tile_base_eh: int = 0,
             ensure_periodicity: bool = True,
             num_chunks: int = 0,
             Courant: float = 0.5,
             accurate_fields_near_cylorigin: bool = False,
             filename_prefix: Optional[str] = None,
             output_volume: Optional[meep.simulation.Volume] = None,
             output_single_precision: bool = False,
             geometry_center: Union[meep.geom.Vector3, Tuple[float, ...]] = Vector3<0.0, 0.0, 0.0>,
             force_all_components: bool = False,
             split_chunks_evenly: bool = True,
             chunk_layout=None,
             collect_stats: bool = False):

All Simulation attributes are described in further detail below. In brackets after each variable is the type of value that it should hold. The classes, complex datatypes like GeometricObject, are described in a later subsection. The basic datatypes, like integer, boolean, complex, and string are defined by Python. Vector3 is a meep class.

  • geometry [ list of GeometricObject class ] — Specifies the geometric objects making up the structure being simulated. When objects overlap, later objects in the list take precedence. Defaults to no objects (empty list).

  • geometry_center [ Vector3 class ] — Specifies the coordinates of the center of the cell. Defaults to (0, 0, 0), but changing this allows you to shift the coordinate system used in Meep (for example, to put the origin at the corner). Passing geometry_center=c is equivalent to adding the c vector to the coordinates of every other object in the simulation, i.e. c becomes the new origin that other objects are defined with respect to.

  • sources [ list of Source class ] — Specifies the current sources to be present in the simulation. Defaults to none (empty list).

  • symmetries [ list of Symmetry class ] — Specifies the spatial symmetries (mirror or rotation) to exploit in the simulation. Defaults to none (empty list). The symmetries must be obeyed by both the structure and the sources. See also Exploiting Symmetry.

  • boundary_layers [ list of PML class ] — Specifies the PML absorbing boundary layers to use. Defaults to none (empty list).

  • cell_size [ Vector3 ] — Specifies the size of the cell which is centered on the origin of the coordinate system. Any sizes of 0 imply a reduced-dimensionality calculation. Strictly speaking, the dielectric function is taken to be uniform along that dimension. A 2d calculation is especially optimized. See dimensions below. Note: because Maxwell's equations are scale invariant, you can use any units of distance you want to specify the cell size: nanometers, microns, centimeters, etc. However, it is usually convenient to pick some characteristic lengthscale of your problem and set that length to 1. See also Units. Required argument (no default).

  • default_material [Medium class ] — Holds the default material that is used for points not in any object of the geometry list. Defaults to air (ε=1). This can also be a NumPy array that defines a dielectric function much like epsilon_input_file below (see below). If you want to use a material function as the default material, use the material_function keyword argument (below).

  • material_function [ function ] — A Python function that takes a Vector3 and returns a Medium. See also Material Function. Defaults to None.

  • epsilon_func [ function ] — A Python function that takes a Vector3 and returns the dielectric constant at that point. See also Material Function. Defaults to None.

  • epsilon_input_file [string] — If this string is not empty (the default), then it should be the name of an HDF5 file whose first/only dataset defines a scalar, real-valued, frequency-independent dielectric function over some discrete grid. Alternatively, the dataset name can be specified explicitly if the string is in the form "filename:dataset". This dielectric function is then used in place of the ε property of default_material (i.e. where there are no geometry objects). The grid of the epsilon file dataset need not match the computational grid; it is scaled and/or linearly interpolated as needed to map the file onto the cell. The structure is warped if the proportions of the grids do not match. Note: the file contents only override the ε property of the default_material, whereas other properties (μ, susceptibilities, nonlinearities, etc.) of default_material are still used.

  • dimensions [integer] — Explicitly specifies the dimensionality of the simulation, if the value is less than 3. If the value is 3 (the default), then the dimensions are automatically reduced to 2 if possible when cell_size in the direction is 0. If dimensions is the special value of CYLINDRICAL, then cylindrical coordinates are used and the and dimensions are interpreted as and , respectively. If dimensions is 1, then the cell must be along the direction and only and field components are permitted. If dimensions is 2, then the cell must be in the plane.

  • m [number] — For CYLINDRICAL simulations, specifies that the angular dependence of the fields is of the form (default is m=0). If the simulation cell includes the origin , then m must be an integer.

  • accurate_fields_near_cylorigin [boolean] — For CYLINDRICAL simulations with |m| > 1, compute more accurate fields near the origin at the expense of requiring a smaller Courant factor. Empirically, when this option is set to True, a Courant factor of roughly or smaller seems to be needed. Default is False, in which case the , , and fields within |m| pixels of the origin are forced to zero, which usually ensures stability with the default Courant factor of 0.5, at the expense of slowing convergence of the fields near .

  • resolution [number] — Specifies the computational grid resolution in pixels per distance unit. Required argument. No default.

  • k_point [False or Vector3] — If False (the default), then the boundaries are perfect metallic (zero electric field). If a Vector3, then the boundaries are Bloch-periodic: the fields at one side are times the fields at the other side, separated by the lattice vector . A non-zero Vector3 will produce complex fields. The k_point vector is specified in Cartesian coordinates in units of 2π/distance. Note: this is different from MPB, equivalent to taking MPB's k_points through its function reciprocal->cartesian.

  • kz_2d ["complex", "real/imag", or "3d"] — A 2d cell (i.e., dimensions=2) combined with a k_point that has a non-zero component in would normally result in a 3d simulation with complex fields. However, by default (kz_2d="complex"), Meep will use a 2d computational cell in which is incorporated as an additional term in Maxwell's equations, which still results in complex fields but greatly improved performance. Setting kz_2d="3d" will instead use a 3d cell that is one pixel thick (with Bloch-periodic boundary conditions), which is considerably more expensive. The third possibility, kz_2d="real/imag", saves an additional factor of two by storing some field components as purely real and some as purely imaginary in a "real" field, but this option requires some care to use. See 2d Cell with Out-of-Plane Wavevector.

  • ensure_periodicity [boolean] — If True (the default) and if the boundary conditions are periodic (k_point is not False), then the geometric objects are automatically repeated periodically according to the lattice vectors which define the size of the cell.

  • eps_averaging [boolean] — If True (the default), then subpixel averaging is used when initializing the dielectric function. For simulations involving a material function, eps_averaging is False (the default) and must be enabled in which case the input variables subpixel_maxeval (default 104) and subpixel_tol (default 10-4) specify the maximum number of function evaluations and the integration tolerance for the adaptive numerical integration. Increasing/decreasing these, respectively, will cause a more accurate but slower computation of the average ε with diminishing returns for the actual FDTD error. Disabling subpixel averaging will lead to staircasing effects and irregular convergence.

  • force_complex_fields [boolean] — By default, Meep runs its simulations with purely real fields whenever possible. It uses complex fields which require twice the memory and computation if the k_point is non-zero or if m is non-zero. However, by setting force_complex_fields to True, Meep will always use complex fields.

  • force_all_components [boolean] — By default, in a 2d simulation Meep uses only the field components that might excited by your current sources: either the in-plane or out-of-plane polarization, depending on the source. (Both polarizations are excited if you use multiple source polarizations, or if an anisotropic medium is present that couples the two polarizations.) In rare cases (primarily for combining results of multiple simulations with differing polarizations), you might want to force it to simulate all fields, even those that remain zero throughout the simulation, by setting force_all_components to True.

  • filename_prefix [string] — A string prepended to all output filenames (e.g., for HDF5 files). If None (the default), then Meep constructs a default prefix based on the current Python filename ".py" replaced by "-" (e.g. foo.py uses a "foo-" prefix). You can get this prefix by calling get_filename_prefix.

  • Courant [number] — Specify the Courant factor which relates the time step size to the spatial discretization: . Default is 0.5. For numerical stability, the Courant factor must be at most , where is the minimum refractive index (usually 1), and in practice should be slightly smaller.

  • loop_tile_base_db, loop_tile_base_eh [number] — To improve the memory locality of the field updates, Meep has an experimental feature to "tile" the loops over the Yee grid voxels. The splitting of the update loops for step-curl and update-eh into tiles or subdomains involves a recursive-bisection method in which the base case for the number of voxels is specified using these two parameters, respectively. The default value is 0 or no tiling; a typical nonzero value to try would be 10000.

  • output_volume [Volume class ] — Specifies the default region of space that is output by the HDF5 output functions (below); see also the Volume class which manages meep::volume* objects. Default is None, which means that the whole cell is output. Normally, you should use the in_volume(...) function to modify the output volume instead of setting output_volume directly.

  • output_single_precision [boolean] — Meep performs its computations in double-precision floating point, and by default its output HDF5 files are in the same format. However, by setting this variable to True (default is False) you can instead output in single precision which saves a factor of two in space.

  • progress_interval [number] — Time interval (seconds) after which Meep prints a progress message. Default is 4 seconds.

  • extra_materials [ list of Medium class ] — By default, Meep turns off support for material dispersion (susceptibilities or conductivity) or nonlinearities if none of the objects in geometry have materials with these properties — since they are not needed, it is faster to omit their calculation. This doesn't work, however, if you use a material_function: materials via a user-specified function of position instead of just geometric objects. If your material function only returns a nonlinear material, for example, Meep won't notice this unless you tell it explicitly via extra_materials. extra_materials is a list of materials that Meep should look for in the cell in addition to any materials that are specified by geometric objects. You should list any materials other than scalar dielectrics that are returned by material_function here.

  • chunk_layout [string or Simulation instance or BinaryPartition class] — This will cause the Simulation to use the chunk layout described by either (1) an .h5 file (created using Simulation.dump_chunk_layout), (2) another Simulation instance, or (3) a BinaryPartition class object. For more information, see Load and Dump Structure and Parallel Meep/User-Specified Cell Partition.

The following require a bit more understanding of the inner workings of Meep to use. See also SWIG Wrappers.

  • structure [meep::structure*] — Pointer to the current structure being simulated; initialized by _init_structure which is called automatically by init_sim() which is called automatically by any of the run functions. The structure initialization is handled by the Simulation class, and most users will not need to call _init_structure.

  • fields [meep::fields*] — Pointer to the current fields being simulated; initialized by init_sim() which is called automatically by any of the run functions.

  • num_chunks [integer] — Minimum number of "chunks" (subregions) to divide the structure/fields into. Overrides the default value determined by the number of processors, PML layers, etcetera. Mainly useful for debugging.

  • split_chunks_evenly [boolean] — When True (the default), the work per chunk is not taken into account when splitting chunks up for multiple processors. The cell is simply split up into equal chunks (with the exception of PML regions, which must be on their own chunk). When False, Meep attempts to allocate an equal amount of work to each processor, which can increase the performance of parallel simulations.

def run(self, *step_funcs, **kwargs):
def run(step_functions..., until=condition/time):
def run(step_functions..., until_after_sources=condition/time):

run(step_functions..., until=condition/time)

Run the simulation until a certain time or condition, calling the given step functions (if any) at each timestep. The keyword argument until is either a number, in which case it is an additional time (in Meep units) to run for, or it is a function (of no arguments) which returns True when the simulation should stop. until can also be a list of stopping conditions which may include a number of additional functions.

run(step_functions..., until_after_sources=condition/time)

Run the simulation until all sources have turned off, calling the given step functions (if any) at each timestep. The keyword argument until_after_sources is either a number, in which case it is an additional time (in Meep units) to run for after the sources are off, or it is a function (of no arguments). In the latter case, the simulation runs until the sources are off and condition returns True. Like until above, until_after_sources can take a list of stopping conditions.

Output File Names#

The output filenames used by Meep, e.g. for HDF5 files, are automatically prefixed by the input variable filename_prefix. If filename_prefix is None (the default), however, then Meep constructs a default prefix based on the current Python filename with ".py" replaced by "-": e.g. test.py implies a prefix of "test-". You can get this prefix, or set the output folder, with these methods of the Simulation class:

def get_filename_prefix(self):

Return the current prefix string that is prepended, by default, to all file names.

If you don't want to use any prefix, then you should set filename_prefix to the empty string ''.

In addition to the filename prefix, you can also specify that all the output files be written into a newly-created directory (if it does not yet exist). This is done by calling Simulation.use_output_directory([dirname])

def use_output_directory(self, dname: str = ''):

Output all files into a subdirectory, which is created if necessary. If the optional argument dname is specified, that is the name of the directory. If dname is omitted and filename_prefix is None, the directory name is the current Python filename with ".py" replaced by "-out": e.g. test.py implies a directory of "test-out". If dname is omitted and filename_prefix has been set, the directory name is set to filename_prefix + "-out" and filename_prefix is then reset to None.

Simulation Time#

The Simulation class provides the following time-related methods:

def meep_time(self):

Return the current simulation time in simulation time units (e.g. during a run function). This is not the wall-clock time.

Occasionally, e.g. for termination conditions of the form , it is desirable to round the time to single precision in order to avoid small differences in roundoff error from making your results different by one timestep from machine to machine (a difference much bigger than roundoff error); in this case you can call Simulation.round_time() instead, which returns the time rounded to single precision.

def timestep(self):

Return the number of elapsed timesteps.

def print_times(self):

Call after running a simulation to print the times spent on various types of work. Example output:

Field time usage:
        connecting chunks: 0.0156826 s +/- 0.002525 s
            time stepping: 0.996411 s +/- 0.232147 s
       copying boundaries: 0.148588 s +/- 0.0390397 s
    all-all communication: 1.39423 s +/- 0.581098 s
        1-1 communication: 0.136174 s +/- 0.0107685 s
     Fourier transforming: 0.0321625 s +/- 0.0614168 s
          MPB mode solver: 0.348019 s +/- 0.370068 s
          everything else: 0.207387 s +/- 0.0164821 s

def time_spent_on(self, time_sink):

Return a list of times spent by each process for a type of work time_sink which is the same as for mean_time_spent_on.

def mean_time_spent_on(self, time_sink):

Return the mean time spent by all processes for a type of work time_sink which can be one of the following integer constants: 0: "time stepping", 1: "connecting chunks", 2: "copying boundaries", 3: "all-all communication", 4: "1-1 communication", 5: "outputting fields", 6: "Fourier transforming", 7: "MPB mode solver", 8: "near-to-far-field transform", 9: "updating B field", 10: "updating H field", 11: "updating D field", 12: "updating E field", 13: "boundary stepping B", 14: "boundary stepping WH", 15: "boundary stepping PH", 16: "boundary stepping H", 17: "boundary stepping D", 18: "boundary stepping WE", 19: "boundary stepping PE", 20: "boundary stepping E", 21: "everything else".

def output_times(self, fname):

Call after running a simulation to output to a file with filename fname the times spent on various types of work as CSV (comma separated values) with headers for each column and one row per process.

Field Computations#

Meep supports a large number of functions to perform computations on the fields. Most of them are accessed via the lower-level C++/SWIG interface. Some of them are based on the following simpler, higher-level versions. They are accessible as methods of a Simulation instance.

def set_boundary(self, side, direction, condition):

Sets the condition of the boundary on the specified side in the specified direction. See the Constants (Enumerated Types) section for valid side, direction, and boundary_condition values.

def phase_in_material(self, structure, time):

newstructure should be the structure field of another Simulation object with the same cell size and resolution. Over the next time period phasetime (in the current simulation's time units), the current structure (, , and conductivity ) will be gradually changed to newstructure. In particular, at each timestep it linearly interpolates between the old structure and the new structure. After phasetime has elapsed, the structure will remain equal to newstructure. This is demonstrated in the following image for two Cylinder objects (the simulation script is in examples/phase_in_material.py).

def get_field_point(self,
                    c: int = None,
                    pt: Union[meep.geom.Vector3, Tuple[float, ...]] = None):

Given a component or derived_component constant c and a Vector3 pt, returns the value of that component at that point.

def get_epsilon_point(self,
                      pt: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
                      frequency: float = 0.0):

Given a frequency frequency and a Vector3 pt, returns the average eigenvalue of the permittivity tensor at that location and frequency. If frequency is non-zero, the result is complex valued; otherwise it is the real, frequency-independent part of (the limit).

def get_mu_point(self,
                 pt: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
                 frequency: float = 0.0):

Given a frequency frequency and a Vector3 pt, returns the average eigenvalue of the permeability tensor at that location and frequency. If frequency is non-zero, the result is complex valued; otherwise it is the real, frequency-independent part of (the limit).

def get_epsilon_grid(self,
                     xtics: numpy.ndarray = None,
                     ytics: numpy.ndarray = None,
                     ztics: numpy.ndarray = None,
                     frequency: float = 0.0):

Given three 1d NumPy arrays (xtics,ytics,ztics) which define the coordinates of a Cartesian grid anywhere within the cell volume, compute the trace of the tensor at frequency (in Meep units) from the geometry exactly at each grid point. frequency defaults to 0 which is the instantaneous . (For MaterialGrids, the at each grid point is computed using bilinear interpolation from the nearest MaterialGrid points and possibly also projected to form a level set.) Note that this is different from get_epsilon_point which computes by bilinearly interpolating from the nearest Yee grid points. This function is useful for sampling the material geometry to any arbitrary resolution. The return value is a NumPy array with shape equivalent to numpy.meshgrid(xtics,ytics,ztics). Empty dimensions are collapsed.

def initialize_field(self,
                     cmpnt: int = None,
                     amp_func: Callable[[Union[meep.geom.Vector3, Tuple[float, ...]]], Union[float, complex]] = None):

Initialize the component c fields using the function func which has a single argument, a Vector3 giving a position and returns a complex number for the value of the field at that point.

def add_dft_fields(self, *args, **kwargs):
def add_dft_fields(cs, fcen, df, nfreq, freq, where=None, center=None, size=None, yee_grid=False, decimation_factor=0, persist=False):

Given a list of field components cs, compute the Fourier transform of these fields for nfreq equally spaced frequencies covering the frequency range fcen-df/2 to fcen+df/2 or an array/list freq for arbitrarily spaced frequencies over the Volume specified by where (default to the entire cell). The volume can also be specified via the center and size arguments. The default routine interpolates the Fourier-transformed fields at the center of each voxel within the specified volume. Alternatively, the exact Fourier-transformed fields evaluated at each corresponding Yee grid point is available by setting yee_grid to True. To reduce the memory-bandwidth burden of accumulating DFT fields, an integer decimation_factor can be specified for updating the DFT fields at every decimation_factor timesteps. If decimation_factor is 0 (the default), this value is automatically determined from the Nyquist rate of the bandwidth-limited sources and this DFT monitor. It can be turned off by setting it to 1. Use this feature with care, as the decimated timeseries may be corrupted by aliasing of high frequencies.

def flux_in_box(self, d, box=None, center=None, size=None):

Given a direction constant, and a mp.Volume, returns the flux (the integral of ) in that volume. Most commonly, you specify a volume that is a plane or a line, and a direction perpendicular to it, e.g.

flux_in_box(d=mp.X,mp.Volume(center=mp.Vector3(0,0,0),size=mp.Vector3(0,1,1)))

If the center and size arguments are provided instead of box, Meep will construct the appropriate volume for you.

def electric_energy_in_box(self, box=None, center=None, size=None):

Given a mp.Volume, returns the integral of the electric-field energy in the given volume. If the volume has zero size along a dimension, a lower-dimensional integral is used. If the center and size arguments are provided instead of box, Meep will construct the appropriate volume for you. Note: in cylindrical coordinates , the integrand is multiplied by the circumference , or equivalently the integral is over an annular volume.

def magnetic_energy_in_box(self, box=None, center=None, size=None):

Given a mp.Volume, returns the integral of the magnetic-field energy in the given volume. If the volume has zero size along a dimension, a lower-dimensional integral is used. If the center and size arguments are provided instead of box, Meep will construct the appropriate volume for you. Note: in cylindrical coordinates , the integrand is multiplied by the circumference , or equivalently the integral is over an annular volume.

def field_energy_in_box(self, box=None, center=None, size=None):

Given a mp.Volume, returns the integral of the electric- and magnetic-field energy in the given volume. If the volume has zero size along a dimension, a lower-dimensional integral is used. If the center and size arguments are provided instead of box, Meep will construct the appropriate volume for you. Note: in cylindrical coordinates , the integrand is multiplied by the circumference , or equivalently the integral is over an annular volume.

def modal_volume_in_box(self, box=None, center=None, size=None):

Given a mp.Volume, returns the instantaneous modal volume according to the Purcell-effect definition: . If no volume argument is provided, the entire cell is used by default. If the center and size arguments are provided instead of box, Meep will construct the appropriate volume for you.

Note that if you are at a fixed frequency and you use complex fields (via Bloch-periodic boundary conditions or fields_complex=True), then one half of the flux or energy integrals above corresponds to the time average of the flux or energy for a simulation with real fields.

Often, you want the integration box to be the entire cell. A useful function to return this box, which you can then use for the box arguments above, is Simulation.total_volume().

One versatile feature is that you can supply an arbitrary function of position and various field components and ask Meep to integrate it over a given volume, find its maximum, or output it (via output_field_function, described later). This is done via the functions:

def integrate_field_function(self,
                             cs,
                             func,
                             where=None,
                             center=None,
                             size=None):

Returns the integral of the complex-valued function func over the Volume specified by where (defaults to entire cell) for the meep::fields contained in the Simulation instance that calls this method. func is a function of position (a Vector3, its first argument) and zero or more field components specified by cs: a list of component constants. func can be real- or complex-valued. The volume can optionally be specified via the center and size arguments.

If any dimension of where is zero, that dimension is not integrated over. In this way you can specify 1d, 2d, or 3d integrals.

Note: in cylindrical coordinates , the integrand is multiplied by the circumference , or equivalently the integral is over an annular volume.

def max_abs_field_function(self,
                           cs,
                           func,
                           where=None,
                           center=None,
                           size=None):

As integrate_field_function, but returns the maximum absolute value of func in the volume where instead of its integral.

The integration is performed by summing over the grid points with a simple trapezoidal rule, and the maximum is similarly over the grid points. See Field Functions for examples of how to call integrate_field_function and max_abs_field_function. See Synchronizing the Magnetic and Electric Fields if you want to do computations combining the electric and magnetic fields. The volume can optionally be specified via the center and size arguments.

Occasionally, one wants to compute an integral that combines fields from two separate simulations (e.g. for nonlinear coupled-mode calculations). This functionality is supported in Meep, as long as the two simulations have the same cell, the same resolution, the same boundary conditions and symmetries (if any), and the same PML layers (if any).

def integrate2_field_function(self,
                              fields2,
                              cs1,
                              cs2,
                              func,
                              where=None,
                              center=None,
                              size=None):

Similar to integrate_field_function, but takes additional parameters fields2 and cs2. fields2 is a meep::fields* object similar to the global fields variable (see below) specifying the fields from another simulation. cs1 is a list of components to integrate with from the meep::fields instance in Simulation.fields, as for integrate_field_function, while cs2 is a list of components to integrate from fields2. Similar to integrate_field_function, func is a function that returns an number given arguments consisting of: the position vector, followed by the values of the components specified by cs1 (in order), followed by the values of the components specified by cs2 (in order). The volume can optionally be specified via the center and size arguments.

To get two fields in memory at once for integrate2_field_function, the easiest way is to run one simulation within a given Python file, then save the results in another fields variable, then run a second simulation. This would look something like:

...set up and run first simulation...
fields2 = sim.fields # save the fields in a variable
sim.fields = None    # prevent the fields from getting deallocated by reset-meep
sim.reset_meep()
...set up and run second simulation...

It is also possible to timestep both fields simultaneously (e.g. doing one timestep of one simulation then one timestep of another simulation, and so on, but this requires you to call much lower-level functions like fields_step().

Reloading Parameters#

Once the fields/simulation have been initialized, you can change the values of various parameters by using the following functions (which are members of the Simulation class):

def reset_meep(self):

Reset all of Meep's parameters, deleting the fields, structures, etcetera, from memory as if you had not run any computations. If the num_chunks or chunk_layout attributes have been modified internally, they are reset to their original values passed in at instantiation.

def restart_fields(self):

Restart the fields at time zero, with zero fields. Does not reset the Fourier transforms of the flux planes, which continue to be accumulated.

def change_k_point(self, k):

Change the k_point (the Bloch periodicity).

def change_sources(self, new_sources):

Change the list of sources in Simulation.sources to new_sources, and changes the sources used for the current simulation. new_sources must be a list of Source objects.

def set_materials(self,
                  geometry: List[meep.geom.GeometricObject] = None,
                  default_material: meep.geom.Medium = None):

This can be called in a step function, and is useful for changing the geometry or default material as a function of time.

Flux Spectra#

Given a bunch of FluxRegion objects, you can tell Meep to accumulate the Fourier transforms of the fields in those regions in order to compute the Poynting flux spectra. (Note: as a matter of convention, the "intensity" of the electromagnetic fields refers to the Poynting flux, not to the energy density.) See also Introduction/Transmittance/Reflectance Spectra and Tutorial/Basics/Transmittance Spectrum of a Waveguide Bend. These are attributes of the Simulation class. The most important function is:

def add_flux(self, *args, **kwargs):
def add_flux(fcen, df, nfreq, freq, FluxRegions, decimation_factor=0):

Add a bunch of FluxRegions to the current simulation (initializing the fields if they have not yet been initialized), telling Meep to accumulate the appropriate field Fourier transforms for nfreq equally spaced frequencies covering the frequency range fcen-df/2 to fcen+df/2 or an array/list freq for arbitrarily spaced frequencies. Return a flux object, which you can pass to the functions below to get the flux spectrum, etcetera. To reduce the memory-bandwidth burden of accumulating DFT fields, an integer decimation_factor can be specified for updating the DFT fields at every decimation_factor timesteps. If decimation_factor is 0 (the default), this value is automatically determined from the Nyquist rate of the bandwidth-limited sources and this DFT monitor. It can be turned off by setting it to 1. Use this feature with care, as the decimated timeseries may be corrupted by aliasing of high frequencies. The choice of decimation factor should take into account the properties of all sources in the simulation as well as the frequency range of the DFT field monitor.

As described in the tutorial, you normally use add_flux via statements like:

transmission = sim.add_flux(...)

to store the flux object in a variable. You can create as many flux objects as you want, e.g. to look at powers flowing in different regions or in different frequency ranges. Note, however, that Meep has to store (and update at every time step) a number of Fourier components equal to the number of grid points intersecting the flux region multiplied by the number of electric and magnetic field components required to get the Poynting vector multiplied by nfreq, so this can get quite expensive (in both memory and time) if you want a lot of frequency points over large regions of space.

Once you have called add_flux, the Fourier transforms of the fields are accumulated automatically during time-stepping by the run functions. At any time, you can ask for Meep to print out the current flux spectrum via the display_fluxes method.

def display_fluxes(self, *fluxes):

Given a number of flux objects, this displays a comma-separated table of frequencies and flux spectra, prefixed by "flux1:" or similar (where the number is incremented after each run). All of the fluxes should be for the same fcen/df/nfreq or freq. The first column are the frequencies, and subsequent columns are the flux spectra.

You might have to do something lower-level if you have multiple flux regions corresponding to different frequency ranges, or have other special needs. display_fluxes(f1, f2, f3) is actually equivalent to meep.display_csv("flux", meep.get_flux_freqs(f1), meep.get_fluxes(f1), meep.get_fluxes(f2), meep.get_fluxes(f3)), where display_csv takes a bunch of lists of numbers and prints them as a comma-separated table; this involves calling two lower-level functions:

def get_flux_freqs(f):

Given a flux object, returns a list of the frequencies that it is computing the spectrum for.

def get_fluxes(f):

Given a flux object, returns a list of the current flux spectrum that it has accumulated.

As described in Introduction/Transmittance/Reflectance Spectra and Tutorial/Basics/Transmittance Spectrum of a Waveguide Bend, for a reflection spectrum you often want to save the Fourier-transformed fields from a "normalization" run and then load them into another run to be subtracted. This can be done via:

def save_flux(self, fname, flux):

Save the Fourier-transformed fields corresponding to the given flux object in an HDF5 file of the given filename without the .h5 suffix (the current filename-prefix is prepended automatically).

def load_flux(self, fname, flux):

Load the Fourier-transformed fields into the given flux object (replacing any values currently there) from an HDF5 file of the given filename without the .h5 suffix (the current filename-prefix is prepended automatically). You must load from a file that was saved by save_flux in a simulation of the same dimensions (for both the cell and the flux regions) with the same number of processors and chunk layout.

def load_minus_flux(self, fname, flux):

As load_flux, but negates the Fourier-transformed fields after they are loaded. This means that they will be subtracted from any future field Fourier transforms that are accumulated.

Sometimes it is more convenient to keep the Fourier-transformed fields in memory rather than writing them to a file and immediately loading them back again. To that end, the Simulation class exposes the following three methods:

def get_flux_data(self, flux):

Get the Fourier-transformed fields corresponding to the given flux object as a FluxData, which is just a named tuple of NumPy arrays. Note that this object is only useful for passing to load_flux_data below and should be considered opaque.

def load_flux_data(self, flux, fdata):

Load the Fourier-transformed fields into the given flux object (replacing any values currently there) from the FluxData object fdata. You must load from an object that was created by get_flux_data in a simulation of the same dimensions (for both the cell and the flux regions) with the same number of processors and chunk layout.

def load_minus_flux_data(self, flux, fdata):

As load_flux_data, but negates the Fourier-transformed fields after they are loaded. This means that they will be subtracted from any future field Fourier transforms that are accumulated.

The Simulation class also provides some aliases for the corresponding "flux" methods.

  • save_mode
  • load_mode
  • load_minus_mode
  • get_mode_data
  • load_mode_data
  • load_minus_mode_data

Mode Decomposition#

Given a structure, Meep can decompose the Fourier-transformed fields into a superposition of its harmonic modes. For a theoretical background, see Features/Mode Decomposition.

def get_eigenmode_coefficients(self,
                               flux,
                               bands,
                               eig_parity=mp.NO_PARITY,
                               eig_vol=None,
                               eig_resolution=0,
                               eig_tolerance=1e-12,
                               kpoint_func=None,
                               direction=mp.AUTOMATIC):

Given a flux object and list of band indices bands or DiffractedPlanewave, return a namedtuple with the following fields:

  • alpha: the complex eigenmode coefficients as a 3d NumPy array of size (len(bands), flux.nfreqs, 2). The last/third dimension refers to modes propagating in the forward (+) or backward (-) directions defined relative to the sign of the propagation constant β of the mode (the wavevector component in the direction perpendicular to the mode-monitor plane).
  • vgrp: the group velocity as a NumPy array.
  • kpoints: a list of mp.Vector3s of the kpoint used in the mode calculation.
  • kdom: a list of mp.Vector3s of the mode's dominant wavevector.
  • cscale: a NumPy array of each mode's scaling coefficient. Useful for adjoint calculations.

The flux object should be created using add_mode_monitor. (You could also use add_flux, but with add_flux you need to be more careful about symmetries that bisect the flux plane: the add_flux object should only be used with get_eigenmode_coefficients for modes of the same symmetry, e.g. constrained via eig_parity. On the other hand, the performance of add_flux planes benefits more from symmetry.) eig_vol is the volume passed to MPB for the eigenmode calculation (based on interpolating the discretized materials from the Yee grid); in most cases this will simply be the volume over which the frequency-domain fields are tabulated, which is the default (i.e. flux.where). eig_parity should be one of [mp.NO_PARITY (default), mp.EVEN_Z, mp.ODD_Z, mp.EVEN_Y, mp.ODD_Y]. It is the parity (= polarization in 2d) of the mode to calculate, assuming the structure has and/or mirror symmetry in the source region, just as for EigenModeSource above. If the structure has both and mirror symmetry, you can combine more than one of these, e.g. EVEN_Z+ODD_Y. Default is NO_PARITY, in which case MPB computes all of the bands which will still be even or odd if the structure has mirror symmetry, of course. This is especially useful in 2d simulations to restrict yourself to a desired polarization. eig_resolution is the spatial resolution to use in MPB for the eigenmode calculations. This defaults to twice the Meep resolution in which case the structure is linearly interpolated from the Meep pixels. eig_tolerance is the tolerance to use in the MPB eigensolver. MPB terminates when the eigenvalues stop changing to less than this fractional tolerance. Defaults to 1e-12. (Note that this is the tolerance for the frequency eigenvalue ; the tolerance for the mode profile is effectively the square root of this.) For examples, see Tutorial/Mode Decomposition.

Technically, MPB computes and then inverts it with Newton's method to find the wavevector normal to eig_vol and mode for a given frequency; in rare cases (primarily waveguides with nonmonotonic dispersion relations, which doesn't usually happen in simple dielectric waveguides), MPB may need you to supply an initial "guess" for in order for this Newton iteration to converge. You can supply this initial guess with kpoint_func, which is a function kpoint_func(f, n) that supplies a rough initial guess for the of band number at frequency . (By default, the components in the plane of the eig_vol region are zero. However, if this region spans the entire cell in some directions, and the cell has Bloch-periodic boundary conditions via the k_point parameter, then the mode's components in those directions will match k_point so that the mode satisfies the Meep boundary conditions, regardless of kpoint_func.) If direction is set to mp.NO_DIRECTION, then kpoint_func is not only the initial guess and the search direction of the vectors, but is also taken to be the direction of the waveguide, allowing you to detect modes in oblique waveguides (not perpendicular to the flux plane).

Note: for planewaves in homogeneous media, the kpoints may not necessarily be equivalent to the actual wavevector of the mode. This quantity is given by kdom.

Note that Meep's MPB interface only supports dispersionless non-magnetic materials but it does support anisotropic . Any nonlinearities, magnetic responses conductivities , or dispersive polarizations in your materials will be ignored when computing the mode decomposition. PML will also be ignored.

def add_mode_monitor(self, *args, **kwargs):
def add_mode_monitor(fcen, df, nfreq, freq, ModeRegions, decimation_factor=0):

Similar to add_flux, but for use with get_eigenmode_coefficients.

add_mode_monitor works properly with arbitrary symmetries, but may be suboptimal because the Fourier-transformed region does not exploit the symmetry. As an optimization, if you have a mirror plane that bisects the mode monitor, you can instead use add_flux to gain a factor of two, but in that case you must also pass the corresponding eig_parity to get_eigenmode_coefficients in order to only compute eigenmodes with the corresponding mirror symmetry.

def get_eigenmode(self,
                  frequency,
                  direction,
                  where,
                  band_num,
                  kpoint,
                  eig_vol=None,
                  match_frequency=True,
                  parity=mp.NO_PARITY,
                  resolution=0,
                  eigensolver_tol=1e-12):

The parameters of this routine are the same as that of get_eigenmode_coefficients or EigenModeSource, but this function returns an object that can be used to inspect the computed mode. In particular, it returns an EigenmodeData instance with the following fields:

  • band_num: same as a single element of the bands parameter
  • freq: the computed frequency, same as the frequency input parameter if match_frequency=True
  • group_velocity: the group velocity of the mode in direction
  • k: the Bloch wavevector of the mode in direction
  • kdom: the dominant planewave of mode band_num
  • amplitude(point, component): the (complex) value of the given or field component (Ex, Hy, etcetera) at a particular point (a Vector3) in space (interpreted with Bloch-periodic boundary conditions if you give a point outside the original eig_vol).

If match_frequency=False or kpoint is not zero in the given direction, the frequency input parameter is ignored.

The following top-level function is also available:

def get_eigenmode_freqs(f):

Given a flux object, returns a list of the frequencies that it is computing the spectrum for.


DiffractedPlanewave#

class DiffractedPlanewave(object):

For mode decomposition or eigenmode source, specify a diffracted planewave in homogeneous media. Should be passed as the bands argument of get_eigenmode_coefficients, band_num of get_eigenmode, or eig_band of EigenModeSource.

def __init__(self,
             g: List[int] = None,
             axis: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
             s: complex = None,
             p: complex = None):

Construct a DiffractedPlanewave.

  • g [ list of 3 integers ] — The diffraction order corresponding to the wavevector . is the k_point (wavevector specifying the Bloch-periodic boundaries) of the Simulation class object. The diffraction order should be non-zero only in the -1 periodic directions of a dimensional cell of size (e.g., a plane in 3d) in which the mode monitor or source extends the entire length of the cell.

  • axis [ Vector3 ] — The plane of incidence for each planewave (used to define the and polarizations below) is defined to be the plane that contains the axis vector and the planewave's wavevector. If None, axis defaults to the first direction that lies in the plane of the monitor or source (e.g., direction for a plane in 3d, either or in 2d).

  • s [ complex ] — The complex amplitude of the polarziation (i.e., electric field perpendicular to the plane of incidence).

  • p [ complex ] — The complex amplitude of the polarziation (i.e., electric field parallel to the plane of incidence).

Energy Density Spectra#

Very similar to flux spectra, you can also compute energy density spectra: the energy density of the electromagnetic fields as a function of frequency, computed by Fourier transforming the fields and integrating the energy density:

The usage is similar to the flux spectra: you define a set of EnergyRegion objects telling Meep where it should compute the Fourier-transformed fields and energy densities, and call add_energy to add these regions to the current simulation over a specified frequency bandwidth, and then use display_electric_energy, display_magnetic_energy, or display_total_energy to display the energy density spectra at the end. There are also save_energy, load_energy, and load_minus_energy functions that you can use to subtract the fields from two simulation, e.g. in order to compute just the energy from scattered fields, similar to the flux spectra. The function used to add an EnergyRegion is as follows:

def add_energy(self, *args, **kwargs):
def add_energy(fcen, df, nfreq, freq, EnergyRegions, decimation_factor=0):

Add a bunch of EnergyRegions to the current simulation (initializing the fields if they have not yet been initialized), telling Meep to accumulate the appropriate field Fourier transforms for nfreq equally spaced frequencies covering the frequency range fcen-df/2 to fcen+df/2 or an array/list freq for arbitrarily spaced frequencies. Return an energy object, which you can pass to the functions below to get the energy spectrum, etcetera. To reduce the memory-bandwidth burden of accumulating DFT fields, an integer decimation_factor can be specified for updating the DFT fields at every decimation_factor timesteps. If decimation_factor is 0 (the default), this value is automatically determined from the Nyquist rate of the bandwidth-limited sources and this DFT monitor. It can be turned off by setting it to 1. Use this feature with care, as the decimated timeseries may be corrupted by aliasing of high frequencies.

As for flux regions, you normally use add_energy via statements like:

En = sim.add_energy(...)

to store the energy object in a variable. You can create as many energy objects as you want, e.g. to look at the energy densities in different objects or in different frequency ranges. Note, however, that Meep has to store (and update at every time step) a number of Fourier components equal to the number of grid points intersecting the energy region multiplied by nfreq, so this can get quite expensive (in both memory and time) if you want a lot of frequency points over large regions of space.

Once you have called add_energy, the Fourier transforms of the fields are accumulated automatically during time-stepping by the run functions. At any time, you can ask for Meep to print out the current energy density spectrum via:

def display_electric_energy(self, *energys):

Given a number of energy objects, this displays a comma-separated table of frequencies and energy density spectra for the electric fields prefixed by "electric_energy1:" or similar (where the number is incremented after each run). All of the energy should be for the same fcen/df/nfreq or freq. The first column are the frequencies, and subsequent columns are the energy density spectra.

def display_magnetic_energy(self, *energys):

Given a number of energy objects, this displays a comma-separated table of frequencies and energy density spectra for the magnetic fields prefixed by "magnetic_energy1:" or similar (where the number is incremented after each run). All of the energy should be for the same fcen/df/nfreq or freq. The first column are the frequencies, and subsequent columns are the energy density spectra.

def display_total_energy(self, *energys):

Given a number of energy objects, this displays a comma-separated table of frequencies and energy density spectra for the total fields "total_energy1:" or similar (where the number is incremented after each run). All of the energy should be for the same fcen/df/nfreq or freq. The first column are the frequencies, and subsequent columns are the energy density spectra.

You might have to do something lower-level if you have multiple energy regions corresponding to different frequency ranges, or have other special needs. display_electric_energy(e1, e2, e3) is actually equivalent to meep.display_csv("electric_energy", meep.get_energy_freqs(e1), meep.get_electric_energy(e1), meep.get_electric_energy(e2), meep.get_electric_energy(e3)), where display_csv takes a bunch of lists of numbers and prints them as a comma-separated table; this involves calling lower-level functions:

def get_energy_freqs(f):

Given an energy object, returns a list of the frequencies that it is computing the spectrum for.

def get_electric_energy(f):

Given an energy object, returns a list of the current energy density spectrum for the electric fields that it has accumulated.

def get_magnetic_energy(f):

Given an energy object, returns a list of the current energy density spectrum for the magnetic fields that it has accumulated.

def get_total_energy(f):

Given an energy object, returns a list of the current energy density spectrum for the total fields that it has accumulated.

As described in Introduction/Transmittance/Reflectance Spectra and Tutorial/Basics/Transmittance Spectrum of a Waveguide Bend for flux computations, to compute the energy density from the scattered fields you often want to save the Fourier-transformed fields from a "normalization" run and then load them into another run to be subtracted. This can be done via:

def save_energy(self,
                fname: str,
                energy: meep.simulation.DftEnergy):

Save the Fourier-transformed fields corresponding to the given energy object in an HDF5 file of the given filename without the .h5 suffix (the current filename-prefix is prepended automatically).

def load_energy(self,
                fname: str,
                energy: meep.simulation.DftEnergy):

Load the Fourier-transformed fields into the given energy object (replacing any values currently there) from an HDF5 file of the given filename without the .h5 suffix (the current filename-prefix is prepended automatically). You must load from a file that was saved by save_energy in a simulation of the same dimensions for both the cell and the energy regions with the same number of processors and chunk layout.

def load_minus_energy(self,
                      fname: str,
                      energy: meep.simulation.DftEnergy):

As load_energy, but negates the Fourier-transformed fields after they are loaded. This means that they will be subtracted from any future field Fourier transforms that are accumulated.

Force Spectra#

Very similar to flux spectra, you can also compute force spectra: forces on an object as a function of frequency, computed by Fourier transforming the fields and integrating the vacuum Maxwell stress tensor:

over a surface via . You should normally only evaluate the stress tensor over a surface lying in vacuum, as the interpretation and definition of the stress tensor in arbitrary media is often problematic (the subject of extensive and controversial literature). It is fine if the surface encloses an object made of arbitrary materials, as long as the surface itself is in vacuum.

See also Tutorial/Optical Forces.

Most commonly, you will want to normalize the force spectrum in some way, just as for flux spectra. Most simply, you could divide two different force spectra to compute the ratio of forces on two objects. Often, you will divide a force spectrum by a flux spectrum, to divide the force by the incident power on an object, in order to compute the useful dimensionless ratio / where in Meep units. For example, it is a simple exercise to show that the force on a perfectly reflecting mirror with normal-incident power satisfies /, and for a perfectly absorbing (black) surface /.

The usage is similar to the flux spectra: you define a set of ForceRegion objects telling Meep where it should compute the Fourier-transformed fields and stress tensors, and call add_force to add these regions to the current simulation over a specified frequency bandwidth, and then use display_forces to display the force spectra at the end. There are also save_force, load_force, and load_minus_force functions that you can use to subtract the fields from two simulation, e.g. in order to compute just the force from scattered fields, similar to the flux spectra. The function used to add a ForceRegion object is defined as follows:

def add_force(self, *args, **kwargs):
def add_force(fcen, df, nfreq, freq, ForceRegions, decimation_factor=0):

Add a bunch of ForceRegions to the current simulation (initializing the fields if they have not yet been initialized), telling Meep to accumulate the appropriate field Fourier transforms for nfreq equally spaced frequencies covering the frequency range fcen-df/2 to fcen+df/2 or an array/list freq for arbitrarily spaced frequencies. Return a forceobject, which you can pass to the functions below to get the force spectrum, etcetera. To reduce the memory-bandwidth burden of accumulating DFT fields, an integer decimation_factor can be specified for updating the DFT fields at every decimation_factor timesteps. If decimation_factor is 0 (the default), this value is automatically determined from the Nyquist rate of the bandwidth-limited sources and this DFT monitor. It can be turned off by setting it to 1. Use this feature with care, as the decimated timeseries may be corrupted by aliasing of high frequencies.

As for flux regions, you normally use add_force via statements like:

Fx = sim.add_force(...)

to store the force object in a variable. You can create as many force objects as you want, e.g. to look at forces on different objects, in different directions, or in different frequency ranges. Note, however, that Meep has to store (and update at every time step) a number of Fourier components equal to the number of grid points intersecting the force region, multiplied by the number of electric and magnetic field components required to get the stress vector, multiplied by nfreq, so this can get quite expensive (in both memory and time) if you want a lot of frequency points over large regions of space.

Once you have called add_force, the Fourier transforms of the fields are accumulated automatically during time-stepping by the run functions. At any time, you can ask for Meep to print out the current force spectrum via:

def display_forces(self, *forces):

Given a number of force objects, this displays a comma-separated table of frequencies and force spectra, prefixed by "force1:" or similar (where the number is incremented after each run). All of the forces should be for the same fcen/df/nfreq or freq. The first column are the frequencies, and subsequent columns are the force spectra.

You might have to do something lower-level if you have multiple force regions corresponding to different frequency ranges, or have other special needs. display_forces(f1, f2, f3) is actually equivalent to meep.display_csv("force", meep.get_force_freqs(f1), meep.get_forces(f1), meep.get_forces(f2), meep.get_forces(f3)), where display_csv takes a bunch of lists of numbers and prints them as a comma-separated table; this involves calling two lower-level functions:

def get_force_freqs(f):

Given a force object, returns a list of the frequencies that it is computing the spectrum for.

def get_forces(f):

Given a force object, returns a list of the current force spectrum that it has accumulated.

As described in Introduction/Transmittance/Reflectance Spectra and Tutorial/Basics/Transmittance Spectrum of a Waveguide Bend for flux computations, to compute the force from the scattered fields often requires saving the Fourier-transformed fields from a "normalization" run and then loading them into another run to be subtracted. This can be done via these Simulation methods:

def save_force(self, fname, force):

Save the Fourier-transformed fields corresponding to the given force object in an HDF5 file of the given filename without the .h5 suffix (the current filename-prefix is prepended automatically).

def load_force(self, fname, force):

Load the Fourier-transformed fields into the given force object (replacing any values currently there) from an HDF5 file of the given filename without the .h5 suffix (the current filename-prefix is prepended automatically). You must load from a file that was saved by save_force in a simulation of the same dimensions for both the cell and the force regions with the same number of processors and chunk layout.

def load_minus_force(self, fname, force):

As load_force, but negates the Fourier-transformed fields after they are loaded. This means that they will be subtracted from any future field Fourier transforms that are accumulated.

To keep the fields in memory and avoid writing to and reading from a file, use the following three Simulation methods:

def get_force_data(self, force):

Get the Fourier-transformed fields corresponding to the given force object as a ForceData, which is just a named tuple of NumPy arrays. Note that this object is only useful for passing to load_force_data below and should be considered opaque.

def load_force_data(self, force, fdata):

Load the Fourier-transformed fields into the given force object (replacing any values currently there) from the ForceData object fdata. You must load from an object that was created by get_force_data in a simulation of the same dimensions (for both the cell and the flux regions) with the same number of processors and chunk layout.

def load_minus_force_data(self, force, fdata):

As load_force_data, but negates the Fourier-transformed fields after they are loaded. This means that they will be subtracted from any future field Fourier transforms that are accumulated.

LDOS spectra#

Meep can also calculate the LDOS (local density of states) spectrum, as described in Tutorial/Local Density of States. To do this, you simply pass the following step function to your run command:

def Ldos(*args):
def Ldos(fcen, df, nfreq, freq):

Create an LDOS object with either frequency bandwidth df centered at fcen and nfreq equally spaced frequency points or an array/list freq for arbitrarily spaced frequencies. This can be passed to the dft_ldos step function below as a keyword argument.

def get_ldos_freqs(l):

Given an LDOS object, returns a list of the frequencies that it is computing the spectrum for.

def dft_ldos(*args, **kwargs):
def dft_ldos(fcen=None, df=None, nfreq=None, freq=None, ldos=None):

Compute the power spectrum of the sources (usually a single point dipole source), normalized to correspond to the LDOS, in either a frequency bandwidth df centered at fcen and nfreq equally spaced frequency points or an array/list freq for arbitrarily spaced frequencies. One can also pass in an Ldos object as dft_ldos(ldos=my_Ldos).

The resulting spectrum is outputted as comma-delimited text, prefixed by ldos:,, and is also stored in the ldos_data variable of the Simulation object after the run is complete. The Fourier-transformed electric field and current source are stored in the ldos_Fdata and ldos_Jdata of the Simulation object, respectively.

Analytically, the per-polarization LDOS is exactly proportional to the power radiated by an -oriented point-dipole current, , at a given position in space. For a more mathematical treatment of the theory behind the LDOS, refer to the relevant discussion in Section 4.4 ("Currents and Fields: The Local Density of States") in Chapter 4 ("Electromagnetic Wave Source Conditions") of the book Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, but for now it is defined as:

where the normalization is necessary for obtaining the power exerted by a unit-amplitude dipole (assuming linear materials), and hats denote Fourier transforms. It is this quantity that is computed by the dft_ldos command for a single dipole source. For a volumetric source, the numerator and denominator are both integrated over the current volume, but "LDOS" computation is less meaningful in this case.

Near-to-Far-Field Spectra#

Meep can compute a near-to-far-field transformation in the frequency domain as described in Tutorial/Near-to-Far Field Spectra: given the fields on a "near" bounding surface inside the cell, it can compute the fields arbitrarily far away using an analytical transformation, assuming that the "near" surface and the "far" region lie in a single homogeneous non-periodic 2d, 3d, or cylindrical region. That is, in a simulation surrounded by PML that absorbs outgoing waves, the near-to-far-field feature can compute the fields outside the cell as if the outgoing waves had not been absorbed (i.e. in the fictitious infinite open volume). Moreover, this operation is performed on the Fourier-transformed fields: like the flux and force spectra above, you specify a set of desired frequencies, Meep accumulates the Fourier transforms, and then Meep computes the fields at each frequency for the desired far-field points.

This is based on the principle of equivalence: given the Fourier-transformed tangential fields on the "near" surface, Meep computes equivalent currents and convolves them with the analytical Green's functions in order to compute the fields at any desired point in the "far" region. For details, see Section 4.2.1 ("The Principle of Equivalence") in Chapter 4 ("Electromagnetic Wave Source Conditions") of the book Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology. Since the "far" fields are computed using the full Green's functions, they should be able to be computed anywhere outside of the near-field surface monitor. The only limiting factor should be discretization errors but for any given distance, the "far" fields should converge to the actual DFT fields at that location with resolution (assuming the distance separation is >> resolution).

There are three steps to using the near-to-far-field feature: first, define the "near" surface(s) as a set of surfaces capturing all outgoing radiation in the desired direction(s); second, run the simulation, typically with a pulsed source, to allow Meep to accumulate the Fourier transforms on the near surface(s); third, tell Meep to compute the far fields at any desired points (optionally saving the far fields from a grid of points to an HDF5 file). To define the near surfaces, use this Simulation method:

def add_near2far(self, *args, **kwargs):
def add_near2far(fcen, df, nfreq, freq, Near2FarRegions, nperiods=1, decimation_factor=0):

Add a bunch of Near2FarRegions to the current simulation (initializing the fields if they have not yet been initialized), telling Meep to accumulate the appropriate field Fourier transforms for nfreq equally spaced frequencies covering the frequency range fcen-df/2 to fcen+df/2 or an array/list freq for arbitrarily spaced frequencies. Return a near2far object, which you can pass to the functions below to get the far fields. To reduce the memory-bandwidth burden of accumulating DFT fields, an integer decimation_factor can be specified for updating the DFT fields at every decimation_factor timesteps. If decimation_factor is 0 (the default), this value is automatically determined from the Nyquist rate of the bandwidth-limited sources and this DFT monitor. It can be turned off by setting it to 1. Use this feature with care, as the decimated timeseries may be corrupted by aliasing of high frequencies.

Each Near2FarRegion is identical to FluxRegion except for the name: in 3d, these give a set of planes (important: all these "near surfaces" must lie in a single homogeneous material with isotropic ε and μ — and they should not lie in the PML regions) surrounding the source(s) of outgoing radiation that you want to capture and convert to a far field. Ideally, these should form a closed surface, but in practice it is sufficient for the Near2FarRegions to capture all of the radiation in the direction of the far-field points. Important: as for flux computations, each Near2FarRegion should be assigned a weight of ±1 indicating the direction of the outward normal relative to the +coordinate direction. So, for example, if you have six regions defining the six faces of a cube, i.e. the faces in the , , , , , and directions, then they should have weights +1, -1, +1, -1, +1, and -1 respectively. Note that, neglecting discretization errors, all near-field surfaces that enclose the same outgoing fields are equivalent and will yield the same far fields with a discretization-induced difference that vanishes with increasing resolution etc.

After the simulation run is complete, you can compute the far fields. This is usually for a pulsed source so that the fields have decayed away and the Fourier transforms have finished accumulating.

If you have Bloch-periodic boundary conditions, then the corresponding near-to-far transformation actually needs to perform a "lattice sum" of infinitely many periodic copies of the near fields. This doesn't happen by default, which means the default near2far calculation may not be what you want for periodic boundary conditions. However, if the Near2FarRegion spans the entire cell along the periodic directions, you can turn on an approximate lattice sum by passing nperiods > 1. In particular, it then sums 2*nperiods+1 Bloch-periodic copies of the near fields whenever a far field is requested. You can repeatedly double nperiods until the answer converges to your satisfaction; in general, if the far field is at a distance , and the period is , then you want nperiods to be much larger than . (Future versions of Meep may use fancier techniques like Ewald summation to compute the lattice sum more rapidly at large distances.)

def get_farfield(self, near2far, x):

Given a Vector3 point x which can lie anywhere outside the near-field surface, including outside the cell and a near2far object, returns the computed (Fourier-transformed) "far" fields at x as list of length 6nfreq, consisting of fields in Cartesian coordinates and in cylindrical coordinates for the frequencies 1,2,...,nfreq.

def output_farfields(self,
                     near2far,
                     fname: str = None,
                     resolution: float = None,
                     where: meep.simulation.Volume = None,
                     center: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
                     size: Union[meep.geom.Vector3, Tuple[float, ...]] = None):

Given an HDF5 file name fname (does not include the .h5 suffix), a Volume given by where (may be 0d, 1d, 2d, or 3d), and a resolution (in grid points / distance unit), outputs the far fields in where (which may lie outside the cell) in a grid with the given resolution (which may differ from the FDTD grid resolution) to the HDF5 file as a set of twelve array datasets ex.r, ex.i, ..., hz.r, hz.i, giving the real and imaginary parts of the Fourier-transformed and fields on this grid. Each dataset is an 4d array of although dimensions that are equal to one are omitted. The volume can optionally be specified via center and size.

def get_farfields(self,
                  near2far,
                  resolution: float = None,
                  where: meep.simulation.Volume = None,
                  center: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
                  size: Union[meep.geom.Vector3, Tuple[float, ...]] = None):

Like output_farfields but returns a dictionary of NumPy arrays instead of writing to a file. The dictionary keys are Ex, Ey, Ez, Hx, Hy, Hz. Each array has the same shape as described in output_farfields.

Note that far fields have the same units and scaling as the Fourier transforms of the fields, and hence cannot be directly compared to time-domain fields. In practice, it is easiest to use the far fields in computations where overall scaling (units) cancel out or are irrelevant, e.g. to compute the fraction of the far fields in one region vs. another region.

This lower-level function is also available:

def get_near2far_freqs(f):

Given a near2far object, returns a list of the frequencies that it is computing the spectrum for.

(Multi-frequency get_farfields and output_farfields can be accelerated by compiling Meep with --with-openmp and using the OMP_NUM_THREADS environment variable to specify multiple threads.)

For a scattered-field computation, you often want to separate the scattered and incident fields. As described in Introduction/Transmittance/Reflectance Spectra and Tutorial/Basics/Transmittance Spectrum of a Waveguide Bend for flux computations, you can do this by saving the Fourier-transformed incident from a "normalization" run and then load them into another run to be subtracted. This can be done via these Simulation methods:

def save_near2far(self, fname, near2far):

Save the Fourier-transformed fields corresponding to the given near2far object in an HDF5 file of the given filename (without the .h5 suffix). The current filename-prefix is prepended automatically.

def load_near2far(self, fname, near2far):

Load the Fourier-transformed fields into the given near2far object (replacing any values currently there) from an HDF5 file of the given filename without the .h5 suffix (the current filename-prefix is prepended automatically). You must load from a file that was saved by save_near2far in a simulation of the same dimensions for both the cell and the near2far regions with the same number of processors and chunk layout.

def load_minus_near2far(self, fname, near2far):

As load_near2far, but negates the Fourier-transformed fields after they are loaded. This means that they will be subtracted from any future field Fourier transforms that are accumulated.

To keep the fields in memory and avoid writing to and reading from a file, use the following three methods:

def get_near2far_data(self, near2far):

Get the Fourier-transformed fields corresponding to the given near2far object as a NearToFarData, which is just a named tuple of NumPy arrays. Note that this object is only useful for passing to load_near2far_data below and should be considered opaque.

def load_near2far_data(self, near2far, n2fdata):

Load the Fourier-transformed fields into the near2far object (replacing any values currently there) from the NearToFarData object n2fdata. You must load from an object that was created by get_near2far_data in a simulation of the same dimensions (for both the cell and the flux regions) with the same number of processors and chunk layout.

def load_minus_near2far_data(self, near2far, n2fdata):

As load_near2far_data, but negates the Fourier-transformed fields after they are loaded. This means that they will be subtracted from any future field Fourier transforms that are accumulated.

See also this lower-level function:

def scale_near2far_fields(s, near2far):

Scale the Fourier-transformed fields in near2far by the complex number s. e.g. load_minus_near2far is equivalent to load_near2far followed by scale_near2far_fields with s=-1.

And this DftNear2Far method:

def flux(self,
         direction: int = None,
         where: meep.simulation.Volume = None,
         resolution: float = None):

Given a Volume where (may be 0d, 1d, 2d, or 3d) and a resolution (in grid points / distance unit), compute the far fields in where (which may lie outside the cell) in a grid with the given resolution (which may differ from the FDTD solution) and return its Poynting flux in direction as a list. The dataset is a 1d array of nfreq dimensions.

Load and Dump Simulation State#

These functions add support for saving and restoring parts of the Simulation state.

For all functions listed below, when dumping/loading state to/from a distributed file system (using say, parallel HDF5) and running in an MPI environment, setting single_parallel_file=True (the default) will result in all processes writing/reading to/from the same/single file after computing their respective offsets into this file. When set to False, each process writes/reads data for the chunks it owns to/from a separate, process unique file.

Load and Dump Structure#

These functions dump the raw ε and μ data to disk and load it back for doing multiple simulations with the same materials but different sources etc. The only prerequisite is that the dump/load simulations have the same chunks (i.e. the same grid, number of processors, symmetries, and PML). When using split_chunks_evenly=False, you must also dump the original chunk layout using dump_chunk_layout and load it into the new Simulation using the chunk_layout parameter. Currently only stores dispersive and non-dispersive and but not nonlinearities. Note that loading data from a file in this way overwrites any geometry data passed to the Simulation constructor.

def dump_structure(self,
                   fname: str = None,
                   single_parallel_file: bool = True):

Dumps the structure to the file fname.

def load_structure(self,
                   fname: str = None,
                   single_parallel_file: bool = True):

Loads a structure from the file fname.

Load and Dump Chunk Layout#

def dump_chunk_layout(self, fname: str = None):

Dumps the chunk layout to file fname.

To load a chunk layout into a Simulation, use the chunk_layout argument to the constructor, passing either a file obtained from dump_chunk_layout or another Simulation instance. Note that when using split_chunks_evenly=False this parameter is required when saving and loading flux spectra, force spectra, or near-to-far spectra so that the two runs have the same chunk layout. Just pass the Simulation object from the first run to the second run:

# Split chunks based on amount of work instead of size
sim1 = mp.Simulation(..., split_chunks_evenly=False)
norm_flux = sim1.add_flux(...)
sim1.run(...)
sim1.save_flux(...)

# Make sure the second run uses the same chunk layout as the first
sim2 = mp.Simulation(..., chunk_layout=sim1)
flux = sim2.add_flux(...)
sim2.load_minus_flux(...)
sim2.run(...)

Load and Dump Fields#

These functions can be used to dump (and later load) the time-domain fields and the DFT fields at a certain timestamp. Polarization fields for dispersive materials are not supported. The timestamp at which the dump happens is also saved so that the simulation can continue from where it was saved. The one prerequisite of this feature is that it needs the Simulation object to have been setup exactly the same as the one it was dumped from.

def dump_fields(self,
                fname: str = None,
                single_parallel_file: bool = True):

Dumps the fields to the file fname.

def load_fields(self,
                fname: str = None,
                single_parallel_file: bool = True):

Loads a fields from the file fname.

Checkpoint and Restore#

The above dump/load related functions can be used to implement a checkpoint/restore like feature. The caveat of this feature is that it does not store all the state required to re-create the Simulation object itself. Instead, it expects the user to create and set up the new Simulation object to be exactly the same as the one the state was dumped from.

def dump(self,
         dirname: str = None,
         dump_structure: bool = True,
         dump_fields: bool = True,
         single_parallel_file: bool = True):

Dumps simulation state.

def load(self,
         dirname: str,
         load_structure: bool = True,
         load_fields: bool = True,
         single_parallel_file: bool = True):

Loads simulation state.

This should called right after the Simulation object has been created but before 'init_sim' is called.

Example usage:

# Setup, run and dump the simulation.
sim1 = mp.Simulation(...)
sim1.run(..., until=xx)
sim1.dump(dirname, dump_structure=True, dump_fields=True, ...)

...

# Later in the same or a new process/run
sim2 = mp.Simulation(<same setup as sim1>)
sim2.load(dirname, load_structure=True, load_fields=True, ...)
sim2.run(...)  # continues from t=xx

Frequency-Domain Solver#

Meep contains a frequency-domain solver that computes the fields produced in a geometry in response to a continuous-wave (CW) source. This is based on an iterative linear solver instead of time-stepping. For details, see Section 5.3 ("Frequency-domain solver") of Computer Physics Communications, Vol. 181, pp. 687-702 (2010). Benchmarking results have shown that in many instances, such as cavities (e.g., ring resonators) with long-lived resonant modes, this solver converges much faster than simply running an equivalent time-domain simulation with a CW source (using the default width of zero for no transient turn-on), time-stepping until all transient effects from the source turn-on have disappeared, especially if the fields are desired to a very high accuracy.

To use the frequency-domain solver, simply define a ContinuousSource with the desired frequency and initialize the fields and geometry via init_sim():

sim = mp.Simulation(...)
sim.init_sim()
sim.solve_cw(tol, maxiters, L)

The first two parameters to the frequency-domain solver are the tolerance tol for the iterative solver (10−8, by default) and a maximum number of iterations maxiters (104, by default). Finally, there is a parameter that determines a tradeoff between memory and work per step and convergence rate of the iterative algorithm, biconjugate gradient stabilized (BiCGSTAB-L), that is used; larger values of will often lead to faster convergence at the expense of more memory and more work per iteration. Default is , and normally a value ≥ 2 should be used.

The frequency-domain solver supports arbitrary geometries, PML, boundary conditions, symmetries, parallelism, conductors, and arbitrary nondispersive materials. Lorentz-Drude dispersive materials are not currently supported in the frequency-domain solver, but since you are solving at a known fixed frequency rather than timestepping, you should be able to pick conductivities etcetera in order to obtain any desired complex ε and μ at that frequency.

The frequency-domain solver requires you to use complex-valued fields, via force_complex_fields=True.

After solve_cw completes, it should be as if you had just run the simulation for an infinite time with the source at that frequency. You can call the various field-output functions and so on as usual at this point. For examples, see Tutorial/Frequency Domain Solver and Tutorial/Mode Decomposition/Reflectance and Transmittance Spectra for Planewave at Oblique Incidence.

Note: The convergence of the iterative solver can sometimes encounter difficulties. For example, increasing the diameter of a ring resonator relative to the wavelength increases the condition number, which worsens the convergence of iterative solvers. The general way to improve this is to implement a more sophisticated iterative solver that employs preconditioners. Preconditioning wave equations (Helmholtz-like equations) is notoriously difficult to do well, but some possible strategies are discussed in Issue #548. In the meantime, a simpler way improving convergence (at the expense of computational cost) is to increase the parameter and the number of iterations.

Frequency-Domain Eigensolver#

Building on the frequency-domain solver above, Meep also includes a frequency-domain eigensolver that computes resonant frequencies and modes in the frequency domain. The usage is very similar to solve_cw:

sim = mp.Simulation(...)
sim.init_sim()
eigfreq = sim.solve_eigfreq(tol, maxiters, guessfreq, cwtol, cwmaxiters, L)

The solve_eig routine performs repeated calls to solve_cw in a way that converges to the resonant mode whose frequency is closest to the source frequency. The complex resonant-mode frequency is returned, and the mode Q can be computed from eigfreq.real / (-2*eigfreq.imag). Upon return, the fields should be the corresponding resonant mode (with an arbitrary scaling).

The resonant mode is converged to a relative error of roughly tol, which defaults to 1e-7. A maximum of maxiters (defaults to 100) calls to solve_cw are performed. The tolerance for each solve_cw call is cwtol (defaults to tol*1e-3) and the maximum iterations is cwmaxiters (104, by default); the L parameter (defaults to 10) is also passed through to solve_cw.

The closer the input frequency is to the resonant-mode frequency, the faster solve_eig should converge. Instead of using the source frequency, you can instead pass a guessfreq argument to solve_eigfreq specifying an input frequency (which may even be complex).

Technically, solve_eig is using a shift-and-invert power iteration to compute the resonant mode, as reviewed in Frequency-Domain Eigensolver.

As for solve_cw above, you are required to set force_complex_fields=True to use solve_eigfreq.

GDSII Support#

This feature is only available if Meep is built with libGDSII. It so, then the following functions are available:

def GDSII_layers(fname):

Returns a list of integer-valued layer indices for the layers present in the specified GDSII file.

mp.GDSII_layers('python/examples/coupler.gds')
Out[2]: [0, 1, 2, 3, 4, 5, 31, 32]

def GDSII_prisms(material, fname, layer=-1, zmin=0.0, zmax=0.0):

Returns a list of GeometricObjects with material (mp.Medium) on layer number layer of a GDSII file fname with zmin and zmax (default 0).

def GDSII_vol(fname, layer, zmin, zmax):

Returns a mp.Volume read from a GDSII file fname on layer number layer with zmin and zmax (default 0). This function is useful for creating a FluxRegion from a GDSII file as follows:

fr = mp.FluxRegion(volume=mp.GDSII_vol(fname, layer, zmin, zmax))

Data Visualization#

This module provides basic visualization functionality for the simulation domain. The intent of the module is to provide functions that can be called with no customization options whatsoever and will do useful relevant things by default, but which can also be customized in cases where you do want to take the time to spruce up the output. The Simulation class provides the following methods:

def plot2D(self,
           ax: Optional[matplotlib.axes._axes.Axes] = None,
           output_plane: Optional[meep.simulation.Volume] = None,
           fields: Optional = None,
           labels: bool = False,
           eps_parameters: Optional[dict] = None,
           boundary_parameters: Optional[dict] = None,
           source_parameters: Optional[dict] = None,
           monitor_parameters: Optional[dict] = None,
           field_parameters: Optional[dict] = None,
           colorbar_parameters: Optional[dict] = None,
           frequency: Optional[float] = None,
           plot_eps_flag: bool = True,
           plot_sources_flag: bool = True,
           plot_monitors_flag: bool = True,
           plot_boundaries_flag: bool = True,
           nb: bool = False,
           **kwargs):

Plots a 2D cross section of the simulation domain using matplotlib. The plot includes the geometry, boundary layers, sources, and monitors. Fields can also be superimposed on a 2D slice. Requires matplotlib. Calling this function would look something like:

sim = mp.Simulation(...)
sim.run(...)
field_func = lambda x: 20*np.log10(np.abs(x))
import matplotlib.pyplot as plt
sim.plot2D(fields=mp.Ez,
           field_parameters={'alpha':0.8, 'cmap':'RdBu', 'interpolation':'none', 'post_process':field_func},
           boundary_parameters={'hatch':'o', 'linewidth':1.5, 'facecolor':'y', 'edgecolor':'b', 'alpha':0.3})
plt.show()
plt.savefig('sim_domain.png')

If you just want to quickly visualize the simulation domain without the fields (i.e., when setting up your simulation), there is no need to invoke the run function prior to calling plot2D. Just define the Simulation object followed by any DFT monitors and then invoke plot2D.

Note: When running a parallel simulation, the plot2D function expects to be called on all processes, but only generates a plot on the master process.

Parameters:

  • ax: a matplotlib axis object. plot2D() will add plot objects, like lines, patches, and scatter plots, to this object. If no ax is supplied, then the routine will create a new figure and grab its axis.
  • output_plane: a Volume object that specifies the plane over which to plot. Must be 2D and a subset of the grid volume (i.e., it should not extend beyond the cell).
  • fields: the field component (mp.Ex, mp.Ey, mp.Ez, mp.Hx, mp.Hy, mp.Hz) to superimpose over the simulation geometry. Default is None, where no fields are superimposed.
  • labels: if True, then labels will appear over each of the simulation elements. Defaults to False.
  • eps_parameters: a dict of optional plotting parameters that override the default parameters for the geometry.
    • interpolation='spline36': interpolation algorithm used to upsample the pixels.
    • cmap='binary': the color map of the geometry
    • alpha=1.0: transparency of geometry
    • contour=False: if True, plot a contour of the geometry rather than its image
    • contour_linewidth=1: line width of the contour lines if contour=True
    • frequency=None: for materials with a frequency-dependent permittivity , specifies the frequency (in Meep units) of the real part of the permittivity to use in the plot. Defaults to the frequency parameter of the Source object.
    • resolution=None: the resolution of the grid. Defaults to the resolution of the Simulation object.
    • colorbar=False: whether to add a colorbar to the plot's parent Figure based on epsilon values.
  • boundary_parameters: a dict of optional plotting parameters that override the default parameters for the boundary layers.
    • alpha=1.0: transparency of boundary layers
    • facecolor='g': color of polygon face
    • edgecolor='g': color of outline stroke
    • linewidth=1: line width of outline stroke
    • hatch='\': hatching pattern
  • source_parameters: a dict of optional plotting parameters that override the default parameters for the sources.
    • color='r': color of line and pt sources
    • alpha=1.0: transparency of source
    • facecolor='none': color of polygon face for planar sources
    • edgecolor='r': color of outline stroke for planar sources
    • linewidth=1: line width of outline stroke
    • hatch='\': hatching pattern
    • label_color='r': color of source labels
    • label_alpha=0.3: transparency of source label box
    • offset=20: distance from source center and label box
  • monitor_parameters: a dict of optional plotting parameters that override the default parameters for the monitors.
    • color='g': color of line and point monitors
    • alpha=1.0: transparency of monitors
    • facecolor='none': color of polygon face for planar monitors
    • edgecolor='r': color of outline stroke for planar monitors
    • linewidth=1: line width of outline stroke
    • hatch='\': hatching pattern
    • label_color='g': color of source labels
    • label_alpha=0.3: transparency of monitor label box
    • offset=20: distance from monitor center and label box
  • field_parameters: a dict of optional plotting parameters that override the default parameters for the fields.
    • interpolation='spline36': interpolation function used to upsample field pixels
    • cmap='RdBu': color map for field pixels
    • alpha=0.6: transparency of fields
    • post_process=np.real: post processing function to apply to fields (must be a function object)
    • colorbar=False: whether to add a colorbar to the plot's parent Figure based on field values.
  • colorbar_parameters: a dict of optional plotting parameters that override the default parameters for the colorbar.
    • label=None: an optional label for the colorbar, defaults to '' for epsilon and 'field values' for fields.
    • orientation='vertical': the orientation of the colorbar gradient
    • extend=None: make pointed end(s) for out-of-range values. Allowed values are: ['neither', 'both', 'min', 'max']
    • format=None: formatter for tick labels. Can be an fstring (i.e. "{x:.2e}") or a matplotlib.ticker.ScalarFormatter.
    • position='right': position of the colorbar with respect to the Axes
    • size='5%': size of the colorbar in the dimension perpendicular to its orientation
    • pad='2%': fraction of original axes between colorbar and image axes
  • nb: set this to True if plotting in a Jupyter notebook to use ipympl for plotting. Note: this requires ipympl to be installed.

def plot3D(self,
           save_to_image: bool = False,
           image_name: str = 'sim.png',
           **kwargs):

Uses vispy to render a 3D scene of the simulation object. The simulation object must be 3D. Can also be embedded in Jupyter notebooks.

Args: save_to_image: if True, saves the image to a file image_name: the name of the image file to save to

kwargs: Camera settings. scale_factor: float, camera zoom factor azimuth: float, azimuthal angle in degrees elevation: float, elevation angle in degrees

def visualize_chunks(self):

Displays an interactive image of how the cell is divided into chunks. Each rectangular region is a chunk, and each color represents a different processor. Requires matplotlib.

An animated visualization is also possible via the Animate2D class.

Run and Step Functions#

The actual work in Meep is performed by run functions, which time-step the simulation for a given amount of time or until a given condition is satisfied. These are attributes of the Simulation class.

The run functions, in turn, can be modified by use of step functions: these are called at every time step and can perform any arbitrary computation on the fields, do outputs and I/O, or even modify the simulation. The step functions can be transformed by many modifier functions, like at_beginning, during_sources, etcetera which cause them to only be called at certain times, etcetera, instead of at every time step.

A common point of confusion is described in The Run Function Is Not A Loop. Read this article if you want to make Meep do some customized action on each time step, as many users make the same mistake. What you really want to in that case is to write a step function, as described below.

def run(self, *step_funcs, **kwargs):
def run(step_functions..., until=condition/time):
def run(step_functions..., until_after_sources=condition/time):

run(step_functions..., until=condition/time)

Run the simulation until a certain time or condition, calling the given step functions (if any) at each timestep. The keyword argument until is either a number, in which case it is an additional time (in Meep units) to run for, or it is a function (of no arguments) which returns True when the simulation should stop. until can also be a list of stopping conditions which may include a number of additional functions.

run(step_functions..., until_after_sources=condition/time)

Run the simulation until all sources have turned off, calling the given step functions (if any) at each timestep. The keyword argument until_after_sources is either a number, in which case it is an additional time (in Meep units) to run for after the sources are off, or it is a function (of no arguments). In the latter case, the simulation runs until the sources are off and condition returns True. Like until above, until_after_sources can take a list of stopping conditions.

In particular, a useful value for until_after_sources or until is often stop_when_fields_decayed, which is demonstrated in Tutorial/Basics. These top-level functions are available:

def stop_when_fields_decayed(dt=None, c=None, pt=None, decay_by=None):

Return a condition function, suitable for passing to Simulation.run as the until or until_after_sources parameter, that examines the component c (e.g. meep.Ex, etc.) at the point pt (a Vector3) and keeps running until its absolute value squared has decayed by at least decay_by from its maximum previous value. In particular, it keeps incrementing the run time by dt (in Meep units) and checks the maximum value over that time period — in this way, it won't be fooled just because the field happens to go through zero at some instant.

Note that, if you make decay_by very small, you may need to increase the cutoff property of your source(s), to decrease the amplitude of the small high-frequency components that are excited when the source turns off. High frequencies near the Nyquist frequency of the grid have slow group velocities and are absorbed poorly by PML.

def stop_when_energy_decayed(dt=None, decay_by=None):

Return a condition function, suitable for passing to Simulation.run as the until or until_after_sources parameter, that examines the field energy over the entire cell volume at every dt time units and keeps incrementing the run time by dt until its absolute value has decayed by at least decay_by from its maximum recorded value.

Note that, if you make decay_by very small, you may need to increase the cutoff property of your source(s), to decrease the amplitude of the small high-frequency field components that are excited when the source turns off. High frequencies near the Nyquist frequency of the grid have slow group velocities and are absorbed poorly by PML.

def stop_when_dft_decayed(tol=1e-11,
                      minimum_run_time=0,
                      maximum_run_time=None):

Return a condition function, suitable for passing to Simulation.run as the until or until_after_sources parameter, that checks the Simulation's DFT objects every timesteps, and stops the simulation once all the field components and frequencies of every DFT object have decayed by at least some tolerance tol (default is 1e-11). The time interval is determined automatically based on the frequency content in the DFT monitors. There are two optional parameters: a minimum run time minimum_run_time (default: 0) or a maximum run time maximum_run_time (no default).

def stop_after_walltime(t):

Return a condition function, suitable for passing to Simulation.run as the until parameter. Stops the simulation after t seconds of wall time have passed.

def stop_on_interrupt():

Return a condition function, suitable for passing to Simulation.run as the until parameter. Instead of terminating when receiving a SIGINT or SIGTERM signal from the system, the simulation will abort time stepping and continue executing any code that follows the run function (e.g., outputting fields).

Finally, another run function, useful for computing band diagrams, is available via these Simulation methods:

def run_k_points(self,
                 t: float = None,
                 k_points: List[Union[meep.geom.Vector3, Tuple[float, ...]]] = None):

Given a list of Vector3, k_points of k vectors, runs a simulation for each k point (i.e. specifying Bloch-periodic boundary conditions) and extracts the eigen-frequencies, and returns a list of the complex frequencies. In particular, you should have specified one or more Gaussian sources. It will run the simulation until the sources are turned off plus an additional time units. It will run Harminv at the same point/component as the first Gaussian source and look for modes in the union of the frequency ranges for all sources. Returns a list of lists of frequencies (one list of frequencies for each k). Also prints out a comma-delimited list of frequencies, prefixed by freqs:, and their imaginary parts, prefixed by freqs-im:. See Tutorial/Resonant Modes and Transmission in a Waveguide Cavity.

def run_k_point(self,
                t: float = None,
                k: Union[meep.geom.Vector3, Tuple[float, ...]] = None):

Lower level function called by run_k_points that runs a simulation for a single k point k_point and returns a Harminv instance. Useful when you need to access more Harminv data than just the frequencies.

Predefined Step Functions#

Several useful step functions are predefined by Meep. These are available directly via the meep package but require a Simulation instance as an argument.

Output Functions#

The most common step function is an output function, which outputs some field component to an HDF5 file. Normally, you will want to modify this by one of the at_* functions, below, as outputting a field at every time step can get quite time- and storage-consuming.

Note that although the various field components are stored at different places in the Yee lattice, when they are outputted they are all linearly interpolated to the same grid: to the points at the centers of the Yee cells, i.e. in 3d.

def output_dft(self,
               dft_fields: meep.simulation.DftFields,
               fname: str):

Output the Fourier-transformed fields in dft_fields (created by add_dft_fields) to an HDF5 file with name fname (does not include the .h5 suffix).

def output_epsilon(sim=None, *step_func_args, **kwargs):

Given a frequency frequency, (provided as a keyword argument) output (relative permittivity); for an anisotropic tensor the output is the harmonic mean of the eigenvalues. If frequency is non-zero, the output is complex; otherwise it is the real, frequency-independent part of (the limit). When called as part of a step function, the sim argument specifying the Simulation object can be omitted, e.g., sim.run(mp.at_beginning(mp.output_epsilon(frequency=1/0.7)),until=10).

def output_mu(sim=None, *step_func_args, **kwargs):

Given a frequency frequency, (provided as a keyword argument) output (relative permeability); for an anisotropic tensor the output is the harmonic mean of the eigenvalues. If frequency is non-zero, the output is complex; otherwise it is the real, frequency-independent part of (the limit). When called as part of a step function, the sim argument specifying the Simulation object can be omitted, e.g., sim.run(mp.at_beginning(mp.output_mu(frequency=1/0.7)),until=10).

def output_poynting(sim):

Output the Poynting flux . Note that you might want to wrap this step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_hpwr(sim):

Output the magnetic-field energy density

def output_dpwr(sim):

Output the electric-field energy density

def output_tot_pwr(sim):

Output the total electric and magnetic energy density. Note that you might want to wrap this step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_png(compnt, options, rm_h5=True):

Output the given field component (e.g. Ex, etc.) as a PNG image, by first outputting the HDF5 file, then converting to PNG via h5topng, then deleting the HDF5 file. The second argument is a string giving options to pass to h5topng (e.g. "-Zc bluered"). See also Tutorial/Basics/Output Tips and Tricks.

It is often useful to use the h5topng -C or -A options to overlay the dielectric function when outputting fields. To do this, you need to know the name of the dielectric-function .h5 file which must have been previously output by output_epsilon. To make this easier, a built-in shell variable $EPS is provided which refers to the last-output dielectric-function .h5 file. So, for example output_png(mp.Ez,"-C $EPS") will output the field and overlay the dielectric contours.

By default, output_png deletes the .h5 file when it is done. To preserve the .h5 file requires output_png(component, h5topng_options, rm_h5=False).

def output_hfield(sim):

Outputs all the components of the field h, (magnetic) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_hfield_x(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_y(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_z(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_r(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_p(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield(sim):

Outputs all the components of the field b, (magnetic) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_bfield_x(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_y(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_z(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_r(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_p(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_efield(sim):

Outputs all the components of the field e, (electric) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_efield_x(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_y(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_z(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_r(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_p(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_dfield(sim):

Outputs all the components of the field d, (displacement) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_dfield_x(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_y(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_z(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_r(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_p(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_sfield(sim):

Outputs all the components of the field s, (poynting flux) to an HDF5 file. That is, the different components are stored as different datasets within the same file. Note that you might want to wrap this step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_sfield_x(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_y(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_z(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_r(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_p(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

More generally, it is possible to output an arbitrary function of position and zero or more field components, similar to the Simulation.integrate_field_function method, described above. This is done by:

def output_field_function(self,
                          name,
                          cs,
                          func,
                          real_only=False,
                          h5file=None):

Output the field function func to an HDF5 file in the datasets named name*.r and name*.i for the real and imaginary parts. Similar to integrate_field_function, func is a function of position (a Vector3) and the field components corresponding to cs: a list of component constants. If real_only is True, only outputs the real part of func.

See also Field Functions, and Synchronizing the Magnetic and Electric Fields if you want to do computations combining the electric and magnetic fields.

Array Slices#

The output functions described above write the data for the fields and materials for the entire cell to an HDF5 file. This is useful for post-processing large datasets which may not fit into memory as you can later read in the HDF5 file to obtain field/material data as a NumPy array. However, in some cases it is convenient to bypass the disk altogether to obtain the data directly in the form of a NumPy array without writing/reading HDF5 files. Additionally, you may want the field/material data on just a subregion (or slice) of the entire volume. This functionality is provided by the get_array method which takes as input a subregion of the cell and the field/material component. The method returns a NumPy array containing values of the field/material at the current simulation time.

def get_array(self,
              component: int = None,
              vol: meep.simulation.Volume = None,
              center: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
              size: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
              cmplx: bool = None,
              arr: Optional[numpy.ndarray] = None,
              frequency: float = 0,
              snap: bool = False):

Returns a slice of the materials or time-domain fields over a subregion of the cell at the current simulation time as a NumPy array. The materials/fields are centered on the Yee-grid voxels using a bilinear interpolation of the nearest Yee-grid points.

  • component [ component constant ] — The field or material component (e.g., meep.Ex, meep.Hy, meep.Sz, meep.Dielectric, etc) of the array data. No default.

  • vol [ Volume ] — The rectilinear subregion/slice of the cell volume. The return value of get_array has the same dimensions as the Volume's size attribute. If None (default), then a size and center must be specified.

  • center, size [ Vector3 ] — If both are specified, the method will construct an appropriate Volume. This is a convenience feature and alternative to supplying a Volume.

  • cmplx [ boolean ] — If True, return complex-valued data otherwise return real-valued data (default).

  • arr [ numpy.ndarray ] — Optional parameter to pass a pre-allocated NumPy array of the correct size and type (either numpy.float32 or numpy.float64 depending on the floating-point precision of the fields and materials) which will be overwritten with the field/material data instead of allocating a new array. Normally, this will be the array returned from a previous call to get_array for a similar slice, allowing one to re-use arr (e.g., when fetching the same slice repeatedly at different times).

  • frequency [ number ] — The frequency at which the average eigenvalue of the and tensors are evaluated. Defaults to 0 which is the instantaneous .

  • snap [ boolean ] — Empty dimensions of the grid slice are "collapsed" into a single element. However, if snap is set to True, this interpolation behavior is disabled and the grid slice is instead "snapped" everywhere to the nearest grid point. (Empty slice dimensions are still of size one.) This feature is mainly useful for comparing results with the output_ routines (e.g., output_epsilon, output_efield_z, etc.).

For convenience, the following wrappers for get_array over the entire cell are available: get_epsilon(), get_mu(), get_hpwr(), get_dpwr(), get_tot_pwr(), get_Xfield(), get_Xfield_x(), get_Xfield_y(), get_Xfield_z(), get_Xfield_r(), get_Xfield_p() where X is one of h, b, e, d, or s. The routines get_Xfield_* all return an array type consistent with the fields (real or complex). The routines get_epsilon() and get_mu() accept the optional argument frequency (defaults to 0) and all routines accept snap (defaults to False).

Note on array-slice dimensions: The routines get_epsilon, get_Xfield_z, etc. use as default size=meep.Simulation.fields.total_volume() which for simulations involving Bloch-periodic boundaries (via k_point) will result in arrays that have slightly different dimensions than e.g. get_array(center=meep.Vector3(), size=cell_size, component=meep.Dielectric, etc. (i.e., the slice spans the entire cell volume cell_size). Neither of these approaches is "wrong", they are just slightly different methods of fetching the boundaries. The key point is that if you pass the same value for the size parameter, or use the default, the slicing routines always give you the same-size array for all components. You should not try to predict the exact size of these arrays; rather, you should simply rely on Meep's output.

def get_dft_array(self,
                  dft_obj: meep.simulation.DftObj = None,
                  component: int = None,
                  num_freq: int = None):

Returns the Fourier-transformed fields as a NumPy array. The type is either numpy.complex64 or numpy.complex128 depending on the floating-point precision of the fields. The DFT fields are centered on the Yee-grid voxels using bilinear interpolation of the nearest Yee-grid points.

  • dft_obj [ DftObj class ] — A dft_flux, dft_force, dft_fields, or dft_near2far object obtained from calling the appropriate add function (e.g., mp.add_flux).

  • component [ component constant ]— The field component (e.g., meep.Ez).

  • num_freq [ int ] — The index of the frequency. An integer in the range 0...nfreq-1, where nfreq is the number of frequencies stored in dft_obj as set by the nfreq parameter to add_dft_fields, add_flux, etc.

Array Metadata#

def get_array_metadata(self,
                       vol=None,
                       center=None,
                       size=None,
                       dft_cell=None,
                       return_pw=False):

This routine provides geometric information useful for interpreting the arrays returned by get_array or get_dft_array for the spatial region defined by vol or center/size. In both cases, the return value is a tuple (x,y,z,w), where:

  • x,y,z are 1d NumPy arrays storing the coordinates of the points in the grid slice
  • w is a NumPy array of the same dimensions as the array returned by get_array/get_dft_array, whose entries are the weights in a cubature rule for integrating over the spatial region (with the points in the cubature rule being just the grid points contained in the region). Thus, if is some spatially-varying quantity whose value at the th grid point is , the integral of over the region may be approximated by the sum:

This is a 1-, 2-, or 3-dimensional integral depending on the number of dimensions in which has zero extent. If the samples are stored in an array Q of the same dimensions as w, then evaluating the sum on the RHS is just one line: np.sum(w*Q).

A convenience parameter dft_cell is provided as an alternative to vol or center/size. Set dft_cell to a dft_flux or dft_fields object to define the region covered by the array. If the dft_cell argument is provided then all other arguments related to the spatial region (vol, center, and size) are ignored. If no arguments are provided, then the entire cell is used.

For empty dimensions of the grid slice get_array_metadata will collapse the two elements corresponding to the nearest Yee grid points into a single element using linear interpolation.

If return_pw=True, the return value is a 2-tuple (p,w) where p (points) is a list of mp.Vector3s with the same dimensions as w (weights). Otherwise, by default the return value is a 4-tuple (x,y,z,w).

The following are some examples of how array metadata can be used.

Labeling Axes in Plots of Grid Quantities

# using the geometry from the bend-flux tutorial example
import matplotlib.pyplot as plt
import numpy as np

eps_array=sim.get_epsilon()
(x,y,z,w)=sim.get_array_metadata()
plt.figure()
ax = plt.subplot(111)
plt.pcolormesh(x,y,np.transpose(eps_array),shading='gouraud')
ax.set_aspect('equal')
plt.show()

Computing Quantities Defined by Integrals of Field-Dependent Functions Over Grid Regions

  • energy stored in the -field in a region :

  • Poynting flux through a surface :

  import numpy as np

  # E-field modal volume in box from time-domain fields
  box            = mp.Volume(center=box_center, size=box_size)
  (Ex,Ey,Ez)     = [sim.get_array(vol=box, component=c, cmplx=True) for c in [mp.Ex, mp.Ey, mp.Ez]]
  eps            = sim.get_array(vol=box, component=mp.Dielectric)
  (x,y,z,w)      = sim.get_array_metadata(vol=box)
  energy_density = np.real(eps*(np.conj(Ex)*Ex + np.conj(Ey)*Ey + np.conj(Ez)*Ez)) # array
  energy         = np.sum(w*energy_density)                                        # scalar

  # x-directed Poynting flux through monitor from frequency-domain fields
  monitor        = mp.FluxRegion(center=mon_center, size=mon_size)
  dft_cell       = sim.add_flux(freq, 0, 1, monitor)
  sim.run(...)    # timestep until DFTs converged
  (Ey,Ez,Hy,Hz)  = [sim.get_dft_array(dft_cell,c,0) for c in [mp.Ey, mp.Ez, mp.Hy, mp.Hz]]
  (x,y,z,w)      = sim.get_array_metadata(dft=dft_cell)
  flux_density   = np.real( np.conj(Ey)*Hz - np.conj(Ez)*Hy )    # array
  flux           = np.sum(w*flux_density)                        # scalar

Source Slices#

def get_source(self,
               component,
               vol=None,
               center=None,
               size=None):

Return an array of complex values of the source amplitude for component over the given vol or center/size. The array has the same dimensions as that returned by get_array. Not supported for cylindrical coordinates.

Harminv Step Function#

The following step function collects field data from a given point and runs Harminv on that data to extract the frequencies, decay rates, and other information.

PadeDFT Step Function#

The following step function collects field data from a given point or volume and performs spectral extrapolation by computing the Padé approximant of the DFT at every specified spatial point.

Step-Function Modifiers#

Rather than writing a brand-new step function every time something a bit different is required, the following "modifier" functions take a bunch of step functions and produce new step functions with modified behavior. See also Tutorial/Basics for examples.

Miscellaneous Step-Function Modifiers#

def combine_step_funcs(*step_funcs):

Given zero or more step functions, return a new step function that on each step calls all of the passed step functions.

def synchronized_magnetic(*step_funcs):

Given zero or more step functions, return a new step function that on each step calls all of the passed step functions with the magnetic field synchronized in time with the electric field. See Synchronizing the Magnetic and Electric Fields.

Controlling When a Step Function Executes#

def when_true(cond, *step_funcs):

Given zero or more step functions and a condition function condition (a function of no arguments), evaluate the step functions whenever condition returns True.

def when_false(cond, *step_funcs):

Given zero or more step functions and a condition function condition (a function of no arguments), evaluate the step functions whenever condition returns False.

def at_every(dt, *step_funcs):

Given zero or more step functions, evaluates them at every time interval of units (rounded up to the next time step).

def after_time(t, *step_funcs):

Given zero or more step functions, evaluates them only for times after a time units have elapsed from the start of the run.

def before_time(t, *step_funcs):

Given zero or more step functions, evaluates them only for times before a time units have elapsed from the start of the run.

def at_time(t, *step_funcs):

Given zero or more step functions, evaluates them only once, after a time units have elapsed from the start of the run.

def after_sources(*step_funcs):

Given zero or more step functions, evaluates them only for times after all of the sources have turned off.

def after_sources_and_time(t, *step_funcs):

Given zero or more step functions, evaluates them only for times after all of the sources have turned off, plus an additional time units have elapsed.

def during_sources(*step_funcs):

Given zero or more step functions, evaluates them only for times before all of the sources have turned off.

def at_beginning(*step_funcs):

Given zero or more step functions, evaluates them only once, at the beginning of the run.

def at_end(*step_funcs):

Given zero or more step functions, evaluates them only once, at the end of the run.

Modifying HDF5 Output#

def in_volume(v, *step_funcs):

Given zero or more step functions, modifies any output functions among them to only output a subset (or a superset) of the cell, corresponding to the meep::volume* v (created by the Volume function).

def in_point(pt, *step_funcs):

Given zero or more step functions, modifies any output functions among them to only output a single point of data, at pt (a Vector3).

def to_appended(fname, *step_funcs):

Given zero or more step functions, modifies any output functions among them to append their data to datasets in a single newly-created file named filename (plus an .h5 suffix and the current filename prefix). They append by adding an extra dimension to their datasets, corresponding to time.

def with_prefix(pre, *step_funcs):

Given zero or more step functions, modifies any output functions among them to prepend the string prefix to the file names (much like filename_prefix, above).

Writing Your Own Step Functions#

A step function can take two forms. The simplest is just a function with one argument (the simulation instance), which is called at every time step unless modified by one of the modifier functions above. e.g.

def my_step(sim):
    print("Hello world!")

If one then does sim.run(my_step, until=100), Meep will run for 100 time units and print "Hello world!" at every time step.

This suffices for most purposes. However, sometimes you need a step function that opens a file, or accumulates some computation, and you need to clean up (e.g. close the file or print the results) at the end of the run. For this case, you can write a step function of two arguments: the second argument will either be step when it is called during time-stepping, or finish when it is called at the end of the run:

def my_step(sim, todo):
    if todo == 'step':
       # do something
    elif todo == 'finish':
       # do something else

    # access simulation attributes
    sim.fields ...etc.

Low-Level Functions#

By default, Meep initializes C++ objects like meep::structure and meep::fields in the Simulation object based on attributes like sources and geometry. Theses objects are then accessible via simulation_instance.structure and simulation_instance.fields. Given these, you can then call essentially any function in the C++ interface, because all of the C++ functions are automatically made accessible to Python by the wrapper-generator program SWIG.

Initializing the Structure and Fields#

The structure and fields variables are automatically initialized when any of the run functions is called, or by various other functions such as add_flux. To initialize them separately, you can call Simulation.init_sim() manually, or Simulation._init_structure(k_point) to just initialize the structure.

If you want to time step more than one field simultaneously, the easiest way is probably to do something like:

sim = Simulation(cell_size, resolution).init_sim()
my_fields = sim.fields
sim.fields = None
sim.reset_meep()

and then change the geometry etc. and re-run sim.init_sim(). Then you'll have two field objects in memory.

SWIG Wrappers#

If you look at a function in the C++ interface, then there are a few simple rules to infer the name of the corresponding Python function.

  • First, all functions in the meep:: namespace are available in the Meep Python module from the top-level meep package.
  • Second, any method of a class is accessible via the standard Python class interface. For example, meep::fields::step, which is the function that performs a time-step, is exposed to Python as fields_instance.step() where a fields instance is usually accessible from Simulation.fields.
  • C++ constructors are called using the normal Python class instantiation. E.g., fields = mp.fields(...) returns a new meep::fields object. Calling destructors is not necessary because objects are automatically garbage collected.

Some argument type conversion is performed automatically, e.g. types like complex numbers are converted to complex<double>, etcetera. Vector3 vectors are converted to meep::vec, but to do this it is necessary to know the dimensionality of the problem in C++. The problem dimensions are automatically initialized by Simulation._init_structure, but if you want to pass vector arguments to C++ before that time you should call Simulation.require_dimensions(), which infers the dimensions from the cell_size, k_point, and dimensions variables.

Class Reference#

Classes are complex datatypes with various properties which may have default values. Classes can be "subclasses" of other classes. Subclasses inherit all the properties of their superclass and can be used in any place the superclass is expected.

The meep package defines several types of classes. The most important of these is the Simulation class. Classes which are available directly from the meep package are constructed with:

mp.ClassName(prop1=val1, prop2=val2, ...)

The most numerous are the geometric object classes which are the same as those used in MPB. You can get a list of the available classes (and constants) in the Python interpreter with:

import meep
[x for x in dir(meep) if x[0].isupper()]

More information, including their property types and default values, is available with the standard python help function: help(mp.ClassName).

The following classes are available directly via the meep package.


Medium#

class Medium(object):

This class is used to specify the materials that geometric objects are made of. It represents an electromagnetic medium which is possibly nonlinear and/or dispersive. See also Materials. To model a perfectly-conducting metal, use the predefined metal object, above. To model imperfect conductors, use a dispersive dielectric material. See also the Predefined Variables: metal, perfect_electric_conductor, and perfect_magnetic_conductor.

Material Function

Any function that accepts a Medium instance can also accept a user-defined Python function. This allows you to specify the material as an arbitrary function of position. The function must have one argument, the position Vector3, and return the material at that point, which should be a Python Medium instance. This is accomplished by passing a function to the material_function keyword argument in the Simulation constructor, or the material keyword argument in any GeometricObject constructor. For an example, see Subpixel Smoothing/Enabling Averaging for Material Function.

Instead of the material or material_function arguments, you can also use the epsilon_func keyword argument to Simulation and GeometricObject, which takes a function of position that returns the dielectric constant at that point.

Important: If your material function returns nonlinear, dispersive (Lorentzian or conducting), or magnetic materials, you should also include a list of these materials in the extra_materials input variable (above) to let Meep know that it needs to support these material types in your simulation. For dispersive materials, you need to include a material with the same values of and , so you can only have a finite number of these, whereas can vary continuously and a matching need not be specified in extra_materials. For nonlinear or conductivity materials, your extra_materials list need not match the actual values of or returned by your material function, which can vary continuously.

Complex and : you cannot specify a frequency-independent complex or in Meep where the imaginary part is a frequency-independent loss but there is an alternative. That is because there are only two important physical situations. First, if you only care about the loss in a narrow bandwidth around some frequency, you can set the loss at that frequency via the conductivity. Second, if you care about a broad bandwidth, then all physical materials have a frequency-dependent complex and/or , and you need to specify that frequency dependence by fitting to Lorentzian and/or Drude resonances via the LorentzianSusceptibility or DrudeSusceptibility classes below.

Dispersive dielectric and magnetic materials, above, are specified via a list of objects that are subclasses of type Susceptibility.

def __init__(self,
             epsilon_diag=Vector3<1.0, 1.0, 1.0>,
             epsilon_offdiag=Vector3<0.0, 0.0, 0.0>,
             mu_diag=Vector3<1.0, 1.0, 1.0>,
             mu_offdiag=Vector3<0.0, 0.0, 0.0>,
             E_susceptibilities=None,
             H_susceptibilities=None,
             E_chi2_diag=Vector3<0.0, 0.0, 0.0>,
             E_chi3_diag=Vector3<0.0, 0.0, 0.0>,
             H_chi2_diag=Vector3<0.0, 0.0, 0.0>,
             H_chi3_diag=Vector3<0.0, 0.0, 0.0>,
             D_conductivity_diag=Vector3<0.0, 0.0, 0.0>,
             D_conductivity_offdiag=Vector3<0.0, 0.0, 0.0>,
             B_conductivity_diag=Vector3<0.0, 0.0, 0.0>,
             B_conductivity_offdiag=Vector3<0.0, 0.0, 0.0>,
             epsilon=None,
             index=None,
             mu=None,
             chi2=None,
             chi3=None,
             D_conductivity=None,
             B_conductivity=None,
             E_chi2=None,
             E_chi3=None,
             H_chi2=None,
             H_chi3=None,
             valid_freq_range=FreqRange(min=-1e+20, max=1e+20)):

Creates a Medium object.

  • epsilon [number] The frequency-independent isotropic relative permittivity or dielectric constant. Default is 1. You can also use index=n as a synonym for epsilon=n*n; note that this is not really the refractive index if you also specify μ, since the true index is . Using epsilon=ep is actually a synonym for epsilon_diag=mp.Vector3(ep, ep, ep).

  • epsilon_diag and epsilon_offdiag [Vector3] — These properties allow you to specify ε as an arbitrary real-symmetric tensor by giving the diagonal and offdiagonal parts. Specifying epsilon_diag=Vector3(a, b, c) and/or epsilon_offdiag=Vector3(u, v, w) corresponds to a relative permittivity ε tensor Default is the identity matrix ( and ).

  • mu [number] — The frequency-independent isotropic relative permeability μ. Default is 1. Using mu=pm is actually a synonym for mu_diag=mp.Vector3(pm, pm, pm).

  • mu_diag and mu_offdiag [Vector3] — These properties allow you to specify μ as an arbitrary real-symmetric tensor by giving the diagonal and offdiagonal parts exactly as for ε above. Default is the identity matrix.

  • D_conductivity [number] — The frequency-independent electric conductivity . Default is 0. You can also specify a diagonal anisotropic conductivity tensor by using the property D_conductivity_diag which takes a Vector3 to give the tensor diagonal. See also Conductivity.

  • B_conductivity [number] — The frequency-independent magnetic conductivity . Default is 0. You can also specify a diagonal anisotropic conductivity tensor by using the property B_conductivity_diag which takes a Vector3 to give the tensor diagonal. See also Conductivity.

  • chi2 [number] — The nonlinear electric Pockels susceptibility (quadratic nonlinearity). Default is 0. See also Nonlinearity. This is equivalent to setting E_chi2; alternatively, an analogous magnetic nonlinearity can be specified using H_chi2. These are isotropic nonlinearities, but diagonal anisotropic polarizations of the form can be specified with E_chi2_diag (which defaults to [E_chi2,E_chi2,E_chi2]).

  • chi3 [number] — The nonlinear electric Kerr susceptibility (cubic nonlinearity). Default is 0. See also Nonlinearity. This is equivalent to setting E_chi3; alternatively, an analogous magnetic nonlinearity can be specified using H_chi3. These are isotropic nonlinearities, but diagonal anisotropic polarizations of the form can be specified with E_chi3_diag (which defaults to [E_chi3,E_chi3,E_chi3]).

  • E_susceptibilities [ list of Susceptibility class ] — List of dispersive susceptibilities (see below) added to the dielectric constant ε in order to model material dispersion. Defaults to none (empty list). See also Material Dispersion.

  • H_susceptibilities [ list of Susceptibility class ] — List of dispersive susceptibilities (see below) added to the permeability μ in order to model material dispersion. Defaults to none (empty list). See also Material Dispersion.

def __repr__(self):

Return repr(self).

def epsilon(self, freq):

Returns the medium's permittivity tensor as a 3x3 Numpy array at the specified frequency freq which can be either a scalar, list, or Numpy array. In the case of a list/array of N frequency points, a Numpy array of size Nx3x3 is returned.

def mu(self, freq):

Returns the medium's permeability tensor as a 3x3 Numpy array at the specified frequency freq which can be either a scalar, list, or Numpy array. In the case of a list/array of N frequency points, a Numpy array of size Nx3x3 is returned.

def transform(self, m):

Transforms epsilon, mu, and sigma of any susceptibilities by the 3×3 matrix m. If m is a rotation matrix, then the principal axes of the susceptibilities are rotated by m. More generally, the susceptibilities χ are transformed to MχMᵀ/|det M|, which corresponds to transformation optics for an arbitrary curvilinear coordinate transformation with Jacobian matrix M. The absolute value of the determinant is to prevent inadvertent construction of left-handed materials, which are problematic in nondispersive media.


MaterialGrid#

class MaterialGrid(object):

This class is used to specify materials on a rectilinear grid. A class object is passed as the material argument of a Block geometric object or the default_material argument of the Simulation constructor (similar to a material function).

def __init__(self,
             grid_size: Union[meep.geom.Vector3, Tuple[float, ...]],
             medium1: meep.geom.Medium,
             medium2: meep.geom.Medium,
             weights: numpy.ndarray = None,
             grid_type: str = 'U_DEFAULT',
             do_averaging: bool = False,
             beta: float = 0,
             eta: float = 0.5,
             damping: float = 0):

Creates a MaterialGrid object.

The input are two materials medium1 and medium2 along with a weight function which is defined on a rectilinear grid by the NumPy array weights of size grid_size (a 3-tuple or Vector3 of integers ,,). The resolution of the grid may be nonuniform depending on the size property of the Block object as shown in the following example for a 2d MaterialGrid with and . implies that the MaterialGrid is extruded in the direction. The grid points are defined at the corners of the voxels.

Elements of the weights array must be in the range [0,1] where 0 is medium1 and 1 is medium2. An array of boolean values False and True will be converted to 0 and 1, respectively. The weights array is used to define a linear interpolation from medium1 to medium2. Two material types are supported: (1) frequency-independent isotropic (epsilon_diag and epsilon_offdiag are interpolated) and (2) LorentzianSusceptibility (sigma and sigma_offdiag are interpolated). medium1 and medium2 must both be the same type. The materials are bilinearly interpolated from the rectilinear grid to Meep's Yee grid.

For improving accuracy, subpixel smoothing can be enabled by specifying do_averaging=True. If you want to use a material grid to define a (nearly) discontinuous, piecewise-constant material that is either medium1 or medium2 almost everywhere, you can optionally enable a (smoothed) projection feature by setting the parameter beta to a positive value. The default is no projection (beta=0). When the projection feature is enabled, the weights can be thought of as a level-set function defining an interface at with a smoothing factor where gives an unsmoothed, discontinuous interface. The projection operator is involving the parameters beta (: bias or "smoothness" of the turn on) and eta (: offset for erosion/dilation). The level set provides a general approach for defining a discontinuous function from otherwise continuously varying (via the bilinear interpolation) grid values. Subpixel smoothing is fast and accurate because it exploits an analytic formulation for level-set functions. Note that when subpixel smoothing is enabled via do_averaging=True, projecting the weights is done internally using the beta parameter. It is therefore not necessary to manually project the weights outside of MaterialGrid. However, visualizing the weights used to define the structure does require manually projecting the weights yourself. (Alternatively, you can output the actual structure using plot2D or output_epsilon.)

A nonzero damping term creates an artificial conductivity damping, which acts as dissipation loss that penalizes intermediate pixel values of non-binarized structures. The value of damping should be proportional to times the typical frequency of the problem.

It is possible to overlap any number of different MaterialGrids. This can be useful for defining grids which are symmetric (e.g., mirror, rotation). One way to set this up is by overlapping a given MaterialGrid object with a symmetrized copy of itself. In the case of spatially overlapping MaterialGrid objects (with no intervening objects), any overlapping points are computed using the method grid_type which is one of "U_MIN" (minimum of the overlapping grid values), "U_PROD" (product), "U_MEAN" (mean), "U_DEFAULT" (topmost material grid). In general, these "U_*" options allow you to combine any material grids that overlap in space with no intervening objects.

def update_weights(self, x: numpy.ndarray):

Reset the weights to x.


Susceptibility#

class Susceptibility(object):

Parent class for various dispersive susceptibility terms, parameterized by an anisotropic amplitude . See Material Dispersion.

def __init__(self,
             sigma_diag=Vector3<0.0, 0.0, 0.0>,
             sigma_offdiag=Vector3<0.0, 0.0, 0.0>,
             sigma=None):
  • sigma [number] — The scale factor .

You can also specify an anisotropic tensor by using the property sigma_diag which takes three numbers or a Vector3 to give the tensor diagonal, and sigma_offdiag which specifies the offdiagonal elements (defaults to 0). That is, sigma_diag=mp.Vector3(a, b, c) and sigma_offdiag=mp.Vector3(u, v, w) corresponds to a tensor


LorentzianSusceptibility#

class LorentzianSusceptibility(Susceptibility):

Specifies a single dispersive susceptibility of Lorentzian (damped harmonic oscillator) form. See Material Dispersion, with the parameters (in addition to ):

def __init__(self, frequency=0.0, gamma=0.0, **kwargs):
  • frequency [number] — The resonance frequency .

  • gamma [number] — The resonance loss rate .

Note: multiple objects with identical values for the frequency and gamma but different sigma will appear as a single Lorentzian susceptibility term in the preliminary simulation info output.


DrudeSusceptibility#

class DrudeSusceptibility(Susceptibility):

Specifies a single dispersive susceptibility of Drude form. See Material Dispersion, with the parameters (in addition to ):

def __init__(self, frequency=0.0, gamma=0.0, **kwargs):
  • frequency [number] — The frequency scale factor which multiplies (not a resonance frequency).

  • gamma [number] — The loss rate .


MultilevelAtom#

class MultilevelAtom(Susceptibility):

Specifies a multievel atomic susceptibility for modeling saturable gain and absorption. This is a subclass of E_susceptibilities which contains two objects: (1) transitions: a list of atomic Transitions (defined below), and (2) initial_populations: a list of numbers defining the initial population of each atomic level. See Materials/Saturable Gain and Absorption.

def __init__(self,
             initial_populations=None,
             transitions=None,
             **kwargs):
  • sigma [number] — The scale factor .

You can also specify an anisotropic tensor by using the property sigma_diag which takes three numbers or a Vector3 to give the tensor diagonal, and sigma_offdiag which specifies the offdiagonal elements (defaults to 0). That is, sigma_diag=mp.Vector3(a, b, c) and sigma_offdiag=mp.Vector3(u, v, w) corresponds to a tensor


Transition#

class Transition(object):

def __init__(self,
             from_level,
             to_level,
             transition_rate=0,
             frequency=0,
             sigma_diag=Vector3<1.0, 1.0, 1.0>,
             gamma=0,
             pumping_rate=0):

Construct a Transition.

  • frequency [number] — The radiative transition frequency .

  • gamma [number] — The loss rate .

  • sigma_diag [Vector3] — The per-polarization coupling strength .

  • from_level [number] — The atomic level from which the transition occurs.

  • to_level [number] — The atomic level to which the transition occurs.

  • transition_rate [number] — The non-radiative transition rate . Default is 0.

  • pumping_rate [number] — The pumping rate . Default is 0.


NoisyLorentzianSusceptibility#

class NoisyLorentzianSusceptibility(LorentzianSusceptibility):

Specifies a single dispersive susceptibility of Lorentzian (damped harmonic oscillator) or Drude form. See Material Dispersion, with the same sigma, frequency, and gamma parameters, but with an additional Gaussian random noise term (uncorrelated in space and time, zero mean) added to the P damped-oscillator equation.

def __init__(self, noise_amp=0.0, **kwargs):
  • noise_amp [number] — The noise has root-mean square amplitude σ noise_amp.

This is a somewhat unusual polarizable medium, a Lorentzian susceptibility with a random noise term added into the damped-oscillator equation at each point. This can be used to directly model thermal radiation in both the far field and the near field. Note, however that it is more efficient to compute far-field thermal radiation using Kirchhoff's law of radiation, which states that emissivity equals absorptivity. Near-field thermal radiation can usually be computed more efficiently using frequency-domain methods, e.g. via SCUFF-EM, as described e.g. here or here.


NoisyDrudeSusceptibility#

class NoisyDrudeSusceptibility(DrudeSusceptibility):

Specifies a single dispersive susceptibility of Lorentzian (damped harmonic oscillator) or Drude form. See Material Dispersion, with the same sigma, frequency, and gamma parameters, but with an additional Gaussian random noise term (uncorrelated in space and time, zero mean) added to the P damped-oscillator equation.

def __init__(self, noise_amp=0.0, **kwargs):
  • noise_amp [number] — The noise has root-mean square amplitude σ noise_amp.

This is a somewhat unusual polarizable medium, a Lorentzian susceptibility with a random noise term added into the damped-oscillator equation at each point. This can be used to directly model thermal radiation in both the far field and the near field. Note, however that it is more efficient to compute far-field thermal radiation using Kirchhoff's law of radiation, which states that emissivity equals absorptivity. Near-field thermal radiation can usually be computed more efficiently using frequency-domain methods, e.g. via SCUFF-EM, as described e.g. here or here.


GyrotropicLorentzianSusceptibility#

class GyrotropicLorentzianSusceptibility(LorentzianSusceptibility):

(Experimental feature) Specifies a single dispersive gyrotropic susceptibility of Lorentzian (damped harmonic oscillator) or Drude form. Its parameters are sigma, frequency, and gamma, which have the usual meanings, and an additional 3-vector bias:

def __init__(self, bias=Vector3<0.0, 0.0, 0.0>, **kwargs):
  • bias [Vector3] — The gyrotropy vector. Its direction determines the orientation of the gyrotropic response, and the magnitude is the precession frequency .

GyrotropicDrudeSusceptibility#

class GyrotropicDrudeSusceptibility(DrudeSusceptibility):

(Experimental feature) Specifies a single dispersive gyrotropic susceptibility of Lorentzian (damped harmonic oscillator) or Drude form. Its parameters are sigma, frequency, and gamma, which have the usual meanings, and an additional 3-vector bias:

def __init__(self, bias=Vector3<0.0, 0.0, 0.0>, **kwargs):
  • bias [Vector3] — The gyrotropy vector. Its direction determines the orientation of the gyrotropic response, and the magnitude is the precession frequency .

GyrotropicSaturatedSusceptibility#

class GyrotropicSaturatedSusceptibility(Susceptibility):

(Experimental feature) Specifies a single dispersive gyrotropic susceptibility governed by a linearized Landau-Lifshitz-Gilbert equation. This class takes parameters sigma, frequency, and gamma, whose meanings are different from the Lorentzian and Drude case. It also takes a 3-vector bias parameter and an alpha parameter:

def __init__(self,
             bias=Vector3<0.0, 0.0, 0.0>,
             frequency=0.0,
             gamma=0.0,
             alpha=0.0,
             **kwargs):
  • sigma [number] — The coupling factor between the polarization and the driving field. In magnetic ferrites, this is the Larmor precession frequency at the saturation field.

  • frequency [number] — The Larmor precession frequency, .

  • gamma [number] — The loss rate in the off-diagonal response.

  • alpha [number] — The loss factor in the diagonal response. Note that this parameter is dimensionless and contains no 2π factor.

  • bias [Vector3] — Vector specifying the orientation of the gyrotropic response. Unlike the similarly-named bias parameter for the gyrotropic Lorentzian/Drude susceptibilities, the magnitude is ignored; instead, the relevant precession frequencies are determined by the sigma and frequency parameters.


Vector3#

class Vector3(object):

Properties:

x, y, z [float or complex] — The x, y, and z components of the vector. Generally, functions that take a Vector3 as an argument will accept an iterable (e.g., a tuple or list) and automatically convert to a Vector3.

def __add__(self, other):

Return the sum of the two vectors.

v3 = v1 + v2

def __eq__(self, other):

Returns whether or not the two vectors are numerically equal. Beware of using this function after operations that may have some error due to the finite precision of floating-point numbers; use close instead.

v1 == v2

def __init__(self,
             x: float = 0.0,
             y: float = 0.0,
             z: float = 0.0):

Create a new Vector3 with the given components. All three components default to zero. This can also be represented simply as (x,y,z) or [x,y,z].

def __mul__(self, other):

If other is a Vector3, returns the dot product of v1 and other. If other is a number, then v1 is scaled by the number.

c = v1 * other

def __ne__(self, other):

Returns whether or not the two vectors are numerically unequal. Beware of using this function after operations that may have some error due to the finite precision of floating-point numbers; use close instead.

v1 != v2

def __repr__(self):

Return repr(self).

def __rmul__(self, other):

If other is a Vector3, returns the dot product of v1 and other. If other is a number, then v1 is scaled by the number.

c = other * v1

def __sub__(self, other):

Return the difference of the two vectors.

v3 = v1 - v2

def cdot(self, v):

Returns the conjugated dot product: conj(self) dot v.

def close(self, v, tol=1e-07):

Returns whether or not the corresponding components of the self and v vectors are within tol of each other. Defaults to 1e-7.

v1.close(v2, [tol])

def cross(self, v):

Return the cross product of self and v.

v3 = v1.cross(v2)

def dot(self, v):

Returns the dot product of self and v.

v3 = v1.dot(v2)

def norm(self):

Returns the length math.sqrt(abs(self.dot(self))) of the given vector.

v2 = v1.norm()

def rotate(self, axis, theta):

Returns the vector rotated by an angle theta (in radians) in the right-hand direction around the axis vector (whose length is ignored). You may find the python functions math.degrees and math.radians useful to convert angles between degrees and radians.

v2 = v1.rotate(axis, theta)

def unit(self):

Returns a unit vector in the direction of the vector.

v2 = v1.unit()

GeometricObject#

class GeometricObject(object):

This class, and its descendants, are used to specify the solid geometric objects that form the dielectric structure being simulated.

In a 2d calculation, only the intersections of the objects with the plane are considered.

Geometry Utilities

See the MPB documentation for utility functions to help manipulate geometric objects.

Examples

These are some examples of geometric objects created using some GeometricObject subclasses:

# A cylinder of infinite radius and height 0.25 pointing along the x axis,
# centered at the origin:
cyl = mp.Cylinder(center=mp.Vector3(0,0,0), height=0.25, radius=mp.inf,
                axis=mp.Vector3(1,0,0), material=mp.Medium(index=3.5))
# An ellipsoid with its long axis pointing along (1,1,1), centered on
# the origin (the other two axes are orthogonal and have equal semi-axis lengths):
ell = mp.Ellipsoid(center=mp.Vector3(0,0,0), size=mp.Vector3(0.8,0.2,0.2),
                e1=Vector3(1,1,1), e2=Vector3(0,1,-1), e3=Vector3(-2,1,1),
                material=mp.Medium(epsilon=13))
# A unit cube of material metal with a spherical air hole of radius 0.2 at
# its center, the whole thing centered at (1,2,3):
geometry=[mp.Block(center=Vector3(1,2,3), size=Vector3(1,1,1), material=mp.metal),
        mp.Sphere(center=Vector3(1,2,3), radius=0.2, material=mp.air)]
# A hexagonal prism defined by six vertices centered on the origin
# of material crystalline silicon (from the materials library)
vertices = [mp.Vector3(-1,0),
            mp.Vector3(-0.5,math.sqrt(3)/2),
            mp.Vector3(0.5,math.sqrt(3)/2),
            mp.Vector3(1,0),
            mp.Vector3(0.5,-math.sqrt(3)/2),
            mp.Vector3(-0.5,-math.sqrt(3)/2)]

geometry = [mp.Prism(vertices, height=1.5, center=mp.Vector3(), material=cSi)]

def __init__(self,
             material=Medium(),
             center=Vector3<0.0, 0.0, 0.0>,
             epsilon_func=None):

Construct a GeometricObject.

  • material [Medium class or function ] — The material that the object is made of (usually some sort of dielectric). Uses default Medium. If a function is supplied, it must take one argument and return a Python Medium.

  • epsilon_func [ function ] — A function that takes one argument (a Vector3) and returns the dielectric constant at that point. Can be used instead of material. Default is None.

  • center [Vector3] — Center point of the object. Defaults to (0,0,0).

One normally does not create objects of type GeometricObject directly, however; instead, you use one of the following subclasses. Recall that subclasses inherit the properties of their superclass, so these subclasses automatically have the material and center properties and can be specified in a subclass's constructor via keyword arguments.

def info(self, indent_by=0):

Displays all properties and current values of a GeometricObject, indented by indent_by spaces (default is 0).

def shift(self, vec):

Shifts the object's center by vec (Vector3), returning a new object. This can also be accomplished via the + operator:

geometric_obj + Vector3(10,10,10)

Using += will shift the object in place.


Sphere#

class Sphere(GeometricObject):

Represents a sphere.

Properties:

  • radius [number] — Radius of the sphere. No default value.

def __init__(self, radius, **kwargs):

Constructs a Sphere


Cylinder#

class Cylinder(GeometricObject):

A cylinder, with circular cross-section and finite height.

Properties:

  • radius [number] — Radius of the cylinder's cross-section. No default value.

  • height [number] — Length of the cylinder along its axis. No default value.

  • axis [Vector3] — Direction of the cylinder's axis; the length of this vector is ignored. Defaults to Vector3(x=0, y=0, z=1).

def __init__(self,
             radius,
             axis=Vector3<0.0, 0.0, 1.0>,
             height=1e+20,
             **kwargs):

Constructs a Cylinder.


Wedge#

class Wedge(Cylinder):

Represents a cylindrical wedge.

def __init__(self,
             radius,
             wedge_angle=6.283185307179586,
             wedge_start=Vector3<1.0, 0.0, 0.0>,
             **kwargs):

Constructs a Wedge.


Cone#

class Cone(Cylinder):

A cone, or possibly a truncated cone. This is actually a subclass of Cylinder, and inherits all of the same properties, with one additional property. The radius of the base of the cone is given by the radius property inherited from Cylinder, while the radius of the tip is given by the new property, radius2. The center of a cone is halfway between the two circular ends.

def __init__(self, radius, radius2=0, **kwargs):

Construct a Cone.

radius2 [number] — Radius of the tip of the cone (i.e. the end of the cone pointed to by the axis vector). Defaults to zero (a "sharp" cone).


Block#

class Block(GeometricObject):

A parallelepiped (i.e., a brick, possibly with non-orthogonal axes).

def __init__(self,
             size,
             e1=Vector3<1.0, 0.0, 0.0>,
             e2=Vector3<0.0, 1.0, 0.0>,
             e3=Vector3<0.0, 0.0, 1.0>,
             **kwargs):

Construct a Block.

  • size [Vector3] — The lengths of the block edges along each of its three axes. Not really a 3-vector, but it has three components, each of which should be nonzero. No default value.

  • e1, e2, e3 [Vector3] — The directions of the axes of the block; the lengths of these vectors are ignored. Must be linearly independent. They default to the three lattice directions.


Ellipsoid#

class Ellipsoid(Block):

An ellipsoid. This is actually a subclass of Block, and inherits all the same properties, but defines an ellipsoid inscribed inside the block.

def __init__(self, **kwargs):

Construct an Ellipsoid.


Prism#

class Prism(GeometricObject):

Polygonal prism type.

def __init__(self,
             vertices,
             height,
             axis=Vector3<0.0, 0.0, 1.0>,
             center=None,
             sidewall_angle=0,
             **kwargs):

Construct a Prism.

  • vertices [list of Vector3] — The vertices that make up the prism. They must lie in a plane that's perpendicular to the axis. Note that infinite lengths are not supported. To simulate infinite geometry, just extend the edge of the prism beyond the cell.

  • height [number] — The prism thickness, extruded in the direction of axis. mp.inf can be used for infinite height. No default value.

  • axis [Vector3] — The axis perpendicular to the prism. Defaults to Vector3(0,0,1).

  • center [Vector3] — If center is not specified, then the coordinates of the vertices define the bottom of the prism with the top of the prism being at the same coordinates shifted by height*axis. If center is specified, then center is the coordinates of the centroid of all the vertices (top and bottom) of the resulting 3d prism so that the coordinates of the vertices are shifted accordingly.

  • sidewall_angle [number] — The sidewall angle of the prism in units of radians. Default is 0.


Matrix#

class Matrix(object):

The Matrix class represents a 3x3 matrix with c1, c2, and c3 as its columns.

m.transpose()
m.getH() or m.H
m.determinant()
m.inverse()

Return the transpose, adjoint (conjugate transpose), determinant, or inverse of the given matrix.

m1 + m2
m1 - m2
m1 * m2

Return the sum, difference, or product of the given matrices.

v * m
m * v

Returns the Vector3 product of the matrix m by the vector v, with the vector multiplied on the left or the right respectively.

s * m
m * s

Scales the matrix m by the number s.

def __init__(self,
             c1=Vector3<0.0, 0.0, 0.0>,
             c2=Vector3<0.0, 0.0, 0.0>,
             c3=Vector3<0.0, 0.0, 0.0>,
             diag=Vector3<0.0, 0.0, 0.0>,
             offdiag=Vector3<0.0, 0.0, 0.0>):

Constructs a Matrix.

def __repr__(self):

Return repr(self).

Related function:

def get_rotation_matrix(axis, theta):

Like Vector3.rotate, except returns the (unitary) rotation matrix that performs the given rotation. i.e., get_rotation_matrix(axis, theta) * v produces the same result as v.rotate(axis, theta).

  • axis [Vector3] — The vector around which the rotation is applied in the right-hand direction.

  • theta [number] — The rotation angle (in radians).


Symmetry#

class Symmetry(object):

This class is used for the symmetries input variable to specify symmetries which must preserve both the structure and the sources. Any number of symmetries can be exploited simultaneously but there is no point in specifying redundant symmetries: the cell can be reduced by at most a factor of 4 in 2d and 8 in 3d. See also Exploiting Symmetry. This is the base class of the specific symmetries below, so normally you don't create it directly. However, it has two properties which are shared by all symmetries:

The specific symmetry sub-classes are:

Mirror — A mirror symmetry plane. direction is the direction normal to the mirror plane.

Rotate2 — A 180° (twofold) rotational symmetry (a.k.a. ). direction is the axis of the rotation.

Rotate4 — A 90° (fourfold) rotational symmetry (a.k.a. ). direction is the axis of the rotation.

def __init__(self,
             direction: int = None,
             phase: complex = (1+0j)):

Construct a Symmetry.

  • direction [direction constant ] — The direction of the symmetry (the normal to a mirror plane or the axis for a rotational symmetry). e.g. X, Y, or Z (only Cartesian/grid directions are allowed). No default value.

  • phase [complex] — An additional phase to multiply the fields by when operating the symmetry on them. Default is +1, e.g. a phase of -1 for a mirror plane corresponds to an odd mirror. Technically, you are essentially specifying the representation of the symmetry group that your fields and sources transform under.


Rotate2#

class Rotate2(Symmetry):

A 180° (twofold) rotational symmetry (a.k.a. ). direction is the axis of the rotation.


Rotate4#

class Rotate4(Symmetry):

A 90° (fourfold) rotational symmetry (a.k.a. ). direction is the axis of the rotation.


Mirror#

class Mirror(Symmetry):

A mirror symmetry plane. direction is the direction normal to the mirror plane.


Identity#

class Identity(Symmetry):

PML#

class PML(object):

This class is used for specifying the PML absorbing boundary layers around the cell, if any, via the boundary_layers input variable. See also Perfectly Matched Layers. boundary_layers can be zero or more PML objects, with multiple objects allowing you to specify different PML layers on different boundaries. The class represents a single PML layer specification, which sets up one or more PML layers around the boundaries according to the following properties.

def __init__(self,
             thickness: float = None,
             direction: int = -1,
             side: int = -1,
             R_asymptotic: float = 1e-15,
             mean_stretch: float = 1.0,
             pml_profile: Callable[[float], float] = lambda u: u * u,
  • thickness [number] — The spatial thickness of the PML layer which extends from the boundary towards the inside of the cell. The thinner it is, the more numerical reflections become a problem. No default value.

  • direction [direction constant ] — Specify the direction of the boundaries to put the PML layers next to. e.g. if X, then specifies PML on the boundaries (depending on the value of side, below). Default is the special value ALL, which puts PML layers on the boundaries in all directions.

  • side [side constant ] — Specify which side, Low or High of the boundary or boundaries to put PML on. e.g. if side is Low and direction is meep.X, then a PML layer is added to the boundary. Default is the special value meep.ALL, which puts PML layers on both sides.

  • R_asymptotic [number] — The asymptotic reflection in the limit of infinite resolution or infinite PML thickness, for reflections from air (an upper bound for other media with index > 1). For a finite resolution or thickness, the reflection will be much larger, due to the discretization of Maxwell's equation. Default value is 10−15, which should suffice for most purposes. You want to set this to be small enough so that waves propagating within the PML are attenuated sufficiently, but making R_asymptotic too small will increase the numerical reflection due to discretization.

  • pml_profile [function] — By default, Meep turns on the PML conductivity quadratically within the PML layer — one doesn't want to turn it on suddenly, because that exacerbates reflections due to the discretization. More generally, with pml_profile one can specify an arbitrary PML "profile" function that determines the shape of the PML absorption profile up to an overall constant factor. u goes from 0 to 1 at the start and end of the PML, and the default is . In some cases where a very thick PML is required, such as in a periodic medium (where there is technically no such thing as a true PML, only a pseudo-PML), it can be advantageous to turn on the PML absorption more smoothly. See Optics Express, Vol. 16, pp. 11376-92 (2008). For example, one can use a cubic profile by specifying pml_profile=lambda u: u*u*u.


Absorber#

class Absorber(PML):

Instead of a PML layer, there is an alternative class called Absorber which is a drop-in replacement for PML. For example, you can do boundary_layers=[mp.Absorber(thickness=2)] instead of boundary_layers=[mp.PML(thickness=2)]. All the parameters are the same as for PML, above. You can have a mix of PML on some boundaries and Absorber on others.

The Absorber class does not implement a perfectly matched layer (PML), however (except in 1d). Instead, it is simply a scalar electric and magnetic conductivity that turns on gradually within the layer according to the pml_profile (defaulting to quadratic). Such a scalar conductivity gradient is only reflectionless in the limit as the layer becomes sufficiently thick.

The main reason to use Absorber is if you have a case in which PML fails:


Source#

class Source(object):

The Source class is used to specify the current sources via the Simulation.sources attribute. Note that all sources in Meep are separable in time and space, i.e. of the form for some functions and . Non-separable sources can be simulated, however, by modifying the sources after each time step. When real fields are being used (which is the default in many cases; see Simulation.force_complex_fields), only the real part of the current source is used.

Important note: These are current sources (J terms in Maxwell's equations), even though they are labelled by electric/magnetic field components. They do not specify a particular electric/magnetic field which would be what is called a "hard" source in the FDTD literature. There is no fixed relationship between the current source and the resulting field amplitudes; it depends on the surrounding geometry, as described in the FAQ and in Section 4.4 ("Currents and Fields: The Local Density of States") in Chapter 4 ("Electromagnetic Wave Source Conditions") of the book Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology.

def __init__(self,
             src,
             component,
             center=None,
             volume=None,
             size=Vector3<0.0, 0.0, 0.0>,
             amplitude=1.0,
             amp_func=None,
             amp_func_file='',
             amp_data=None):

Construct a Source.

  • src [SourceTime class ] — Specify the time-dependence of the source (see below). No default.

  • component [component constant ] — Specify the direction and type of the current component: e.g. mp.Ex, mp.Ey, etcetera for an electric-charge current, and mp.Hx, mp.Hy, etcetera for a magnetic-charge current. Note that currents pointing in an arbitrary direction are specified simply as multiple current sources with the appropriate amplitudes for each component. No default.

  • center [Vector3] — The location of the center of the current source in the cell. No default.

  • size [Vector3] — The size of the current distribution along each direction of the cell. Default is (0,0,0): a point-dipole source.

  • volume [Volume] — A meep.Volume can be used to specify the source region instead of a center and a size.

  • amplitude [complex] — An overall complex amplitude multiplying the current source. Default is 1.0. Note that specifying a complex amplitude imparts a phase shift to the real part of the overall current and thus does not require using complex fields for the entire simulation (via force_complex_fields=True).

  • amp_func [function] — A Python function of a single argument, that takes a Vector3 giving a position and returns a complex current amplitude for that point. The position argument is relative to the center of the current source, so that you can move your current around without changing your function. Default is None, meaning that a constant amplitude of 1.0 is used. Note that your amplitude function (if any) is multiplied by the amplitude property, so both properties can be used simultaneously.

  • amp_func_file [string] — String of the form path_to_h5_file.h5:dataset. The .h5 extension is optional. Meep will read the HDF5 file and create an amplitude function that interpolates into the grid specified by the file. Meep expects the data to be split into real and imaginary parts, so in the above example it will look for dataset.re and dataset.im in the file path_to_h5_file.h5. Defaults to the empty string.

  • amp_data [numpy.ndarray with dtype=numpy.complex128] — Like amp_func_file above, but instead of interpolating into an HDF5 file, interpolates into a complex NumPy array. The array should be three dimensions. For a 2d simulation, just pass 1 for the third dimension, e.g., arr = np.zeros((N, M, 1), dtype=np.complex128). Defaults to None.

As described in Section 4.2 ("Incident Fields and Equivalent Currents") in Chapter 4 ("Electromagnetic Wave Source Conditions") of the book Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, it is also possible to supply a source that is designed to couple exclusively into a single waveguide mode (or other mode of some cross section or periodic region) at a single frequency, and which couples primarily into that mode as long as the bandwidth is not too broad. This is possible if you have MPB installed: Meep will call MPB to compute the field profile of the desired mode, and use the field profile to produce an equivalent current source. The mode-launcher feature does not work in cylindrical coordinates. To use the mode launcher, instead of a source you should use an EigenModeSource.


SourceTime#

class SourceTime(object):

This is the parent for classes describing the time dependence of sources; it should not be instantiated directly.


EigenModeSource#

class EigenModeSource(Source):

This is a subclass of Source and has all of the properties of Source above. However, you normally do not specify a component. Instead of component, the current source components and amplitude profile are computed by calling MPB to compute the modes, , of the dielectric profile in the region given by the size and center of the source, with the modes computed as if the source region were repeated periodically in all directions. If an amplitude and/or amp_func are supplied, they are multiplied by this current profile. The desired eigenmode and other features are specified by the properties shown in __init__.

Eigenmode sources are normalized so that in the case of a time-harmonic simulation with all sources and fields having monochromatic time dependence where is the frequency of the eigenmode, the total time-average power of the fields — the integral of the normal Poynting vector over the entire cross-sectional line or plane — is equal to 1. This convention has two use cases:

  • For frequency-domain calculations involving a ContinuousSource time dependence, the time-average power of the fields is 1.

  • For time-domain calculations involving a time dependence which is typically a Gaussian, the amplitude of the fields at frequency will be multiplied by , the Fourier transform of , while field-bilinear quantities like the Poynting flux and energy density are multiplied by . For the particular case of a Gaussian time dependence, the Fourier transform at can be obtained via the fourier_transform class method.

In either case, the eig_power method returns the total power at frequency f. However, for a user-defined CustomSource, eig_power will not include the factor since Meep does not know the Fourier transform of your source function . You will have to multiply by this yourself if you need it.

Note: Due to discretization effects, the normalization of eigenmode sources to yield unit power transmission is only approximate: at any finite resolution, the power of the fields as measured using DFT flux monitors will not precisely match that of calling eig_power but will rather include discretization errors that decrease with resolution. Generally, the most reliable procedure is to normalize your calculations by the power computed in a separate normalization run at the same resolution, as shown in several of the tutorial examples.

Note that Meep's MPB interface only supports dispersionless non-magnetic materials but it does support anisotropic . Any nonlinearities, magnetic responses , conductivities , or dispersive polarizations in your materials will be ignored when computing the eigenmode source. PML will also be ignored.

The SourceTime object (Source.src), which specifies the time dependence of the source, can be one of ContinuousSource, GaussianSource or CustomSource.

def __init__(self,
             src,
             center=None,
             volume=None,
             eig_lattice_size=None,
             eig_lattice_center=None,
             component=mp.ALL_COMPONENTS,
             direction=mp.AUTOMATIC,
             eig_band=1,
             eig_kpoint=Vector3<0.0, 0.0, 0.0>,
             eig_match_freq=True,
             eig_parity=mp.NO_PARITY,
             eig_resolution=0,
             eig_tolerance=1e-12,
             **kwargs):

Construct an EigenModeSource.

  • eig_band [integer or DiffractedPlanewave class] — Either the index (1,2,3,...) of the desired band to compute in MPB where 1 denotes the lowest-frequency band at a given point, and so on, or alternatively a diffracted planewave in homogeneous media.

  • direction [mp.X, mp.Y, or mp.Z; default mp.AUTOMATIC], eig_match_freq [boolean; default True], eig_kpoint [Vector3] — By default (if eig_match_freq is True), Meep tries to find a mode with the same frequency as the src property (above), by scanning vectors in the given direction using MPB's find_k functionality. Alternatively, if eig_kpoint is supplied, it is used as an initial guess for . By default, direction is the direction normal to the source region, assuming size is –1 dimensional in a -dimensional simulation (e.g. a plane in 3d). If direction is set to mp.NO_DIRECTION, then eig_kpoint is not only the initial guess and the search direction of the vectors, but is also taken to be the direction of the waveguide, allowing you to launch modes in oblique ridge waveguides (not perpendicular to the source plane). If eig_match_freq is False, then the vector of the desired mode is specified with eig_kpoint (in Meep units of 2π/(unit length)). Also, the eigenmode frequency computed by MPB overwrites the frequency parameter of the src property for a GaussianSource and ContinuousSource but not CustomSource (the width or any other parameter of src is unchanged). By default, the components in the plane of the source region are zero. However, if the source region spans the entire cell in some directions, and the cell has Bloch-periodic boundary conditions via the k_point parameter, then the mode's components in those directions will match k_point so that the mode satisfies the Meep boundary conditions, regardless of eig_kpoint. Note that once is either found by MPB, or specified by eig_kpoint, the field profile used to create the current sources corresponds to the Bloch mode, , multiplied by the appropriate exponential factor, .

  • eig_parity [mp.NO_PARITY (default), mp.EVEN_Z, mp.ODD_Z, mp.EVEN_Y, mp.ODD_Y] — The parity (= polarization in 2d) of the mode to calculate, assuming the structure has and/or mirror symmetry in the source region, with respect to the center of the source region. (In particular, it does not matter if your simulation as a whole has that symmetry, only the cross section where you are introducing the source.) If the structure has both and mirror symmetry, you can combine more than one of these, e.g. EVEN_Z + ODD_Y. Default is NO_PARITY, in which case MPB computes all of the bands which will still be even or odd if the structure has mirror symmetry, of course. This is especially useful in 2d simulations to restrict yourself to a desired polarization.

  • eig_resolution [integer, defaults to 2*resolution ] — The spatial resolution to use in MPB for the eigenmode calculations. This defaults to twice the Meep resolution in which case the structure is linearly interpolated from the Meep pixels.

  • eig_tolerance [number, defaults to 10–12 ] — The tolerance to use in the MPB eigensolver. MPB terminates when the eigenvalues stop changing to less than this fractional tolerance.

  • component [as above, but defaults to ALL_COMPONENTS] — Once the MPB modes are computed, equivalent electric and magnetic sources are created within Meep. By default, these sources include magnetic and electric currents in all transverse directions within the source region, corresponding to the mode fields as described in Section 4.2 ("Incident Fields and Equivalent Currents") in Chapter 4 ("Electromagnetic Wave Source Conditions") of the book Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology. If you specify a component property, however, you can include only one component of these currents if you wish. Most users won't need this feature.

  • eig_lattice_size [Vector3], eig_lattice_center [Vector3] — Normally, the MPB computational unit cell is the same as the source volume given by the size and center parameters. However, occasionally you want the unit cell to be larger than the source volume. For example, to create an eigenmode source in a periodic medium, you need to pass MPB the entire unit cell of the periodic medium, but once the mode is computed then the actual current sources need only lie on a cross section of that medium. To accomplish this, you can specify the optional eig_lattice_size and eig_lattice_center, which define a volume (which must enclose size and center) that is used for the unit cell in MPB with the dielectric function ε taken from the corresponding region in the Meep simulation.

def eig_power(self, freq):

Returns the total power of the fields from the eigenmode source at frequency freq.


GaussianBeam3DSource#

class GaussianBeam3DSource(Source):

This is a subclass of Source and has all of the properties of Source above. However, the component parameter of the Source object is ignored. The Gaussian beam is a transverse electromagnetic mode for which the source region must be a line (in 2d) or plane (in 3d). For a beam polarized in the direction with propagation along , the electric field is defined by where is the radial distance from the center axis of the beam, is the axial distance from the beam's focus (or "waist"), is the wavenumber (for a free-space wavelength and refractive index of the homogeneous, lossless medium in which the beam propagates), is the electric-field amplitude at the origin, is the radius at which the field amplitude decays by of its axial values, is the beam waist radius, and is the radius of curvature of the beam's wavefront at . The only independent parameters that need to be specified are , , , and the location of the beam focus (i.e., the origin: ).

In 3d, we use a "complex point-source" method to define a source that generates an exact Gaussian-beam solution. In 2d, we currently use the simple approximation of taking a cross-section of the 3d beam. In both cases, the beam is most accurate near the source's center frequency.) To use the true solution for a 2d Gaussian beam, use the GaussianBeam2DSource class instead.

The SourceTime object (Source.src), which specifies the time dependence of the source, should normally be a narrow-band ContinuousSource or GaussianSource. (For a CustomSource, the beam frequency is determined by the source's center_frequency parameter.

def __init__(self,
             src,
             center=None,
             volume=None,
             component=mp.ALL_COMPONENTS,
             beam_x0=Vector3<0.0, 0.0, 0.0>,
             beam_kdir=Vector3<0.0, 0.0, 0.0>,
             beam_w0=None,
             beam_E0=Vector3<0.0, 0.0, 0.0>,
             **kwargs):

Construct a GaussianBeamSource.

  • beam_x0 [Vector3] — The location of the beam focus relative to the center of the source. The beam focus does not need to lie within the source region (i.e., the beam focus can be anywhere, inside or outside the cell, independent of the position of the source).

  • beam_kdir [Vector3] — The propagation direction of the beam. The length is ignored. The wavelength of the beam is determined by the center frequency of the Source.src object and the refractive index (real part only) at the center of the source region.

  • beam_w0 [number] — The beam waist radius.

  • beam_E0 [Vector3] — The polarization vector of the beam. Elements can be complex valued (i.e., for circular polarization). The polarization vector must be parallel to the source region in order to generate a transverse mode.


GaussianBeam2DSource#

class GaussianBeam2DSource(GaussianBeam3DSource):

Identical to GaussianBeam3DSource except that the beam is defined in 2d. This is useful for 2d simulations where the 3d beam is not exact.


ContinuousSource#

class ContinuousSource(SourceTime):

A continuous-wave (CW) source is proportional to , possibly with a smooth (exponential/tanh) turn-on/turn-off. In practice, the CW source never produces an exact single-frequency response.

def __init__(self,
             frequency=None,
             start_time=0,
             end_time=1e+20,
             width=0,
             fwidth=inf,
             cutoff=None,
             slowness=3.0,
             wavelength=None,
             is_integrated=False,
             **kwargs):

Construct a ContinuousSource.

  • frequency [number] — The frequency f in units of /distance or ω in units of 2π/distance. See Units. No default value. You can instead specify wavelength=x or period=x, which are both a synonym for frequency=1/x; i.e. 1/ω in these units is the vacuum wavelength or the temporal period.

  • start_time [number] — The starting time for the source. Default is 0 (turn on at ).

  • end_time [number] — The end time for the source. Default is 1020 (never turn off).

  • width [number] — Roughly, the temporal width of the smoothing (technically, the inverse of the exponential rate at which the current turns off and on). Default is 0 (no smoothing). You can instead specify fwidth=x, which is a synonym for width=1/x (i.e. the frequency width is proportional to the inverse of the temporal width).

  • slowness [number] — Controls how far into the exponential tail of the tanh function the source turns on. Default is 3.0. A larger value means that the source turns on more gradually at the beginning. For a detailed explanation of the effects of width and slowness on the time profile of the source, see here.

  • is_integrated [boolean] — If True, the source is the integral of the current (the dipole moment) which oscillates but does not increase for a sinusoidal current. In practice, there is little difference between integrated and non-integrated sources except for planewaves extending into PML. Default is False.


GaussianSource#

class GaussianSource(SourceTime):

A Gaussian-pulse source roughly proportional to . Technically, the "Gaussian" sources in Meep are the (discrete-time) derivative of a Gaussian, i.e. they are , but the difference between this and a true Gaussian is usually irrelevant.

def __init__(self,
             frequency=None,
             width=0,
             fwidth=inf,
             start_time=0,
             cutoff=5.0,
             is_integrated=False,
             wavelength=None,
             **kwargs):

Construct a GaussianSource.

  • frequency [number] — The center frequency in units of /distance (or in units of /distance). See Units. No default value. You can instead specify wavelength=x or period=x, which are both a synonym for frequency=1/x; i.e. in these units is the vacuum wavelength or the temporal period.

  • width [number] — The width used in the Gaussian. No default value. You can instead specify fwidth=x, which is a synonym for width=1/x (i.e. the frequency width is proportional to the inverse of the temporal width).

  • start_time [number] — The starting time for the source; default is 0 (turn on at ). This is not the time of the peak. See below.

  • cutoff [number] — How many widths the current decays for before it is cut off and set to zero — this applies for both turn-on and turn-off of the pulse. Default is 5.0. A larger value of cutoff will reduce the amount of high-frequency components that are introduced by the start/stop of the source, but will of course lead to longer simulation times. The peak of the Gaussian is reached at the time =start_time + cutoff*width.

  • is_integrated [boolean] — If True, the source is the integral of the current (the dipole moment) which is guaranteed to be zero after the current turns off. In practice, there is little difference between integrated and non-integrated sources except for planewaves extending into PML. Default is False.

  • fourier_transform(f) — Returns the Fourier transform of the current evaluated at frequency () given by: where is the current (not the dipole moment). In this formula, is the fwidth of the source, is times its frequency, and is the peak time discussed above. Note that this does not include any amplitude or amp_func factor that you specified for the source.


CustomSource#

class CustomSource(SourceTime):

A user-specified source function . You can also specify start/end times at which point your current is set to zero whether or not your function is actually zero. These are optional, but you must specify an end_time explicitly if you want run functions like until_after_sources to work, since they need to know when your source turns off. To use a custom source within an EigenModeSource, you must specify the center_frequency parameter, since Meep does not know the frequency content of the CustomSource. The resultant eigenmode is calculated at this frequency only. For a demonstration of a linear-chirped pulse, see examples/chirped_pulse.py.

def __init__(self,
             src_func,
             start_time=-1e+20,
             end_time=1e+20,
             is_integrated=False,
             center_frequency=0,
             fwidth=0,
             **kwargs):

Construct a CustomSource.

  • src_func [function] — The function specifying the time-dependence of the source. It should take one argument (the time in Meep units) and return a complex number.

  • start_time [number] — The starting time for the source. Default is -1020: turn on at . Note, however, that the simulation normally starts at with zero fields as the initial condition, so there is implicitly a sharp turn-on at whether you specify it or not.

  • end_time [number] — The end time for the source. Default is 1020 (never turn off).

  • is_integrated [boolean] — If True, the source is the integral of the current (the dipole moment) which is guaranteed to be zero after the current turns off. In practice, there is little difference between integrated and non-integrated sources except for planewaves extending into PML. Default is False.

  • center_frequency [number] — Optional center frequency so that the CustomSource can be used within an EigenModeSource. Defaults to 0.

  • fwidth [number] — Optional bandwidth in frequency units. Default is 0. For bandwidth-limited sources, this parameter is used to automatically determine the decimation factor of the time-series updates of the DFT fields monitors (if any).


FluxRegion#

class FluxRegion(object):

A FluxRegion object is used with add_flux to specify a region in which Meep should accumulate the appropriate Fourier-transformed fields in order to compute a flux spectrum. It represents a region (volume, plane, line, or point) in which to compute the integral of the Poynting vector of the Fourier-transformed fields. ModeRegion is an alias for FluxRegion for use with add_mode_monitor.

Note that the flux is always computed in the positive coordinate direction, although this can effectively be flipped by using a weight of -1.0. This is useful, for example, if you want to compute the outward flux through a box, so that the sides of the box add instead of subtract.

def __init__(self,
             center: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
             size: Union[meep.geom.Vector3, Tuple[float, ...]] = Vector3<0.0, 0.0, 0.0>,
             direction: int = -1,
             weight: float = 1.0,
             volume: Optional[meep.simulation.Volume] = None):

Construct a FluxRegion object.

  • center [Vector3] — The center of the flux region (no default).

  • size [Vector3] — The size of the flux region along each of the coordinate axes. Default is (0,0,0); a single point.

  • direction [direction constant ] — The direction in which to compute the flux (e.g. mp.X, mp.Y, etcetera). Default is AUTOMATIC, in which the direction is determined by taking the normal direction if the flux region is a plane (or a line, in 2d). If the normal direction is ambiguous (e.g. for a point or volume), then you must specify the direction explicitly (not doing so will lead to an error).

  • weight [complex] — A weight factor to multiply the flux by when it is computed. Default is 1.0.

  • volume [Volume] — A meep.Volume can be used to specify the flux region instead of a center and a size.


EnergyRegion#

class EnergyRegion(FluxRegion):

A region (volume, plane, line, or point) in which to compute the integral of the energy density of the Fourier-transformed fields. Its properties are:

  • center [Vector3] — The center of the energy region (no default).

  • size [Vector3] — The size of the energy region along each of the coordinate axes. Default is (0,0,0): a single point.

  • weight [complex] — A weight factor to multiply the energy density by when it is computed. Default is 1.0.


ForceRegion#

class ForceRegion(FluxRegion):

A region (volume, plane, line, or point) in which to compute the integral of the stress tensor of the Fourier-transformed fields. Its properties are:

  • center [ Vector3 ] — The center of the force region (no default).

  • size [ Vector3 ] — The size of the force region along each of the coordinate axes. Default is (0,0,0) (a single point).

  • direction [ direction constant ] — The direction of the force that you wish to compute (e.g. X, Y, etcetera). Unlike FluxRegion, you must specify this explicitly, because there is not generally any relationship between the direction of the force and the orientation of the force region.

  • weight [ complex ] — A weight factor to multiply the force by when it is computed. Default is 1.0.

  • volume [Volume] — A meep.Volume can be used to specify the force region instead of a center and a size.

In most circumstances, you should define a set of ForceRegions whose union is a closed surface lying in vacuum and enclosing the object that is experiencing the force.


Volume#

class Volume(object):

Many Meep functions require you to specify a volume in space, corresponding to the C++ type meep::volume. This class creates such a volume object, given the center and size properties (just like e.g. a Block object). If the size is not specified, it defaults to (0,0,0), i.e. a single point. Any method that accepts such a volume also accepts center and size keyword arguments. If these are specified instead of the volume, the library will construct a volume for you. Alternatively, you can specify a list of Vector3 vertices using the vertices parameter. The center and size will automatically be computed from this list.

def __init__(self,
             center: Union[meep.geom.Vector3, Tuple[float, ...]] = Vector3<0.0, 0.0, 0.0>,
             size: Union[meep.geom.Vector3, Tuple[float, ...]] = Vector3<0.0, 0.0, 0.0>,
             dims: int = 2,
             is_cylindrical: bool = False,
             vertices: List[Union[meep.geom.Vector3, Tuple[float, ...]]] = []):

Construct a Volume.

** Related function:**

def get_center_and_size(vol):

Utility function that takes a meep::volume vol and returns the center and size of the volume as a tuple of Vector3.


Animate2D#

class Animate2D(object):

A class used to record the fields during timestepping (i.e., a run function). The object is initialized prior to timestepping by specifying the field component. The object can then be passed to any step-function modifier. For example, one can record the fields at every one time unit using:

animate = mp.Animate2D(fields=mp.Ez,
                       realtime=True,
                       field_parameters={'alpha':0.8, 'cmap':'RdBu', 'interpolation':'none'},
                       boundary_parameters={'hatch':'o', 'linewidth':1.5, 'facecolor':'y', 'edgecolor':'b', 'alpha':0.3})

sim.run(mp.at_every(1,animate),until=25)

By default, the object saves each frame as a PNG image into memory (not disk). This is typically more memory efficient than storing the actual fields. If the user sets the normalize argument, then the object will save the actual field information as a NumPy array to be normalized for post processing. The fields of a figure can also be updated in realtime by setting the realtime flag. This does not work for IPython/Jupyter notebooks, however.

Once the simulation is run, the animation can be output as an interactive JSHTML object, an mp4, or a GIF.

Multiple Animate2D objects can be initialized and passed to the run function to track different volume locations (using mp.in_volume) or field components.

def __call__(self,
             sim: meep.simulation.Simulation,
             todo: str):

Call self as a function.

def __init__(self,
             sim: Optional[meep.simulation.Simulation] = None,
             fields: Optional = None,
             f: Optional[matplotlib.figure.Figure] = None,
             realtime: bool = False,
             normalize: bool = False,
             plot_modifiers: Optional[list] = None,
             update_epsilon: bool = False,
             nb: bool = False,
             **customization_args):

Construct an Animate2D object.

  • sim=None — Optional Simulation object (this has no effect, and is included for backwards compatibility).

  • fields=None — Optional Field component to record at each time instant.

  • f=None — Optional matplotlib figure object that the routine will update on each call. If not supplied, then a new one will be created upon initialization.

  • realtime=False — Whether or not to update a figure window in realtime as the simulation progresses. Disabled by default.

  • normalize=False — Records fields at each time step in memory in a NumPy array and then normalizes the result by dividing by the maximum field value at a single point in the cell over all the time snapshots.

  • plot_modifiers=None — A list of functions that can modify the figure's axis object. Each function modifier accepts a single argument, an axis object, and must return that same axis object. The following modifier changes the xlabel:

  def mod1(ax):
      ax.set_xlabel('Testing')
      return ax

  plot_modifiers = [mod1]
  • update_epsilon=False — Redraw epsilon on each call. (Useful for topology optimization)

  • nb=False — For the animation work in a Jupyter notebook, set to True and use the cell magic: %matplotlib ipympl

  • **customization_args — Customization keyword arguments passed to plot2D() (i.e. labels, eps_parameters, boundary_parameters, etc.)

def to_gif(self, fps: int, filename: str) -> None:

Generates and outputs a GIF file of the animation with the filename, filename, and the frame rate, fps. Note that GIFs are significantly larger than mp4 videos since they don't use any compression. Artifacts are also common because the GIF format only supports 256 colors from a predefined color palette. Requires ffmpeg.

def to_jshtml(self,
              fps: int):

Outputs an interactable JSHTML animation object that is embeddable in Jupyter notebooks. The object is packaged with controls to manipulate the video's playback. User must specify a frame rate fps in frames per second.

def to_mp4(self, fps: int, filename: str) -> None:

Generates and outputs an mp4 video file of the animation with the filename, filename, and the frame rate, fps. Default encoding is h264 with yuv420p format. Requires ffmpeg.


Harminv#

class Harminv(object):

Harminv is implemented as a class with a __call__ method, which allows it to be used as a step function that collects field data from a given point and runs Harminv on that data to extract the frequencies, decay rates, and other information.

See __init__ for details about constructing a Harminv.

Important: normally, you should only use Harminv to analyze data after the sources are off. Wrapping it in after_sources(mp.Harminv(...)) is sufficient.

In particular, Harminv takes the time series corresponding to the given field component as a function of time and decomposes it (within the specified bandwidth) as:

The results are stored in the list Harminv.modes, which is a list of tuples holding the frequency, amplitude, and error of the modes. Given one of these tuples (e.g., first_mode = harminv_instance.modes[0]), you can extract its various components:

  • freq — The real part of frequency ω (in the usual Meep 2πc units).

  • decay — The imaginary part of the frequency ω.

  • Q — The dimensionless lifetime, or quality factor defined as .

  • amp — The complex amplitude .

  • err — A crude measure of the error in the frequency (both real and imaginary). If the error is much larger than the imaginary part, for example, then you can't trust the to be accurate. Note: this error is only the uncertainty in the signal processing, and tells you nothing about the errors from finite resolution, finite cell size, and so on.

For example, [m.freq for m in harminv_instance.modes] gives a list of the real parts of the frequencies. Be sure to save a reference to the Harminv instance if you wish to use the results after the simulation:

sim = mp.Simulation(...)
h = mp.Harminv(...)
sim.run(mp.after_sources(h))
# do something with h.modes

def __call__(self, sim, todo):

Allows a Haminv instance to be used as a step function.

def __init__(self,
             c: int = None,
             pt: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
             fcen: float = None,
             df: float = None,
             mxbands: Optional[int] = None):

Construct a Harminv object.

A Harminv is a step function that collects data from the field component c (e.g. , etc.) at the given point pt (a Vector3). Then, at the end of the run, it uses Harminv to look for modes in the given frequency range (center fcen and width df), printing the results to standard output (prefixed by harminv:) as comma-delimited text, and also storing them to the variable Harminv.modes. The optional argument mxbands is the maximum number of modes to search for. Defaults to 100.


PadeDFT#

class PadeDFT(object):

Padé approximant based spectral extrapolation is implemented as a class with a __call__ method, which allows it to be used as a step function that collects field data from a given point and runs Padé on that data to extract an analytic rational function which approximates the frequency response. For more information about the Padé approximant, see the Wikipedia article.

See __init__ for details about constructing a PadeDFT.

In particular, PadeDFT stores the discrete time series corresponding to the given field component as a function of time and expresses it as:

The above is a "Taylor-like" polynomial in with a Fourier basis and coefficients which are the sampled field data. We then compute the Padé approximant to be the analytic form of this function as:

Where and are polynomials of degree and , and is the degree of agreement of the Padé approximant to the analytic function . This function is stored in the callable method pade_instance.dft. Note that the computed polynomials and for each spatial point are stored as well in the instance variable pade_instance.polys, as a spatial array of dicts: [{"P": P(t), "Q": Q(t)}] with no spectral extrapolation performed. Be sure to save a reference to the Pade instance if you wish to use the results after the simulation:

sim = mp.Simulation(...)
p = mp.PadeDFT(...)
sim.run(p, until=time)
# do something with p.dft

def __call__(self, sim, todo):

Allows a PadeDFT instance to be used as a step function.

def __init__(self,
             c: int = None,
             vol: meep.simulation.Volume = None,
             center: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
             size: Union[meep.geom.Vector3, Tuple[float, ...]] = None,
             m: Optional[int] = None,
             n: Optional[int] = None,
             m_frac: float = 0.5,
             n_frac: Optional[float] = None,
             sampling_interval: int = 1,
             start_time: int = 0,
             stop_time: Optional[int] = None):

Construct a Padé DFT object.

A PadeDFT is a step function that collects data from the field component c (e.g. meep.Ex, etc.) at the given point pt (a Vector3). Then, at the end of the run, it uses the scipy Padé algorithm to approximate the analytic frequency response at the specified point.

  • c [ component constant ] — The field component to use for extrapolation. No default.
  • vol [ Volume class ] — The volume over which to accumulate the fields (may be 0d, 1d, 2d, or 3d). No default.
  • center [ Vector3 class ] — Alternative method for specifying volume, using a center point
  • size [ Vector3 class ] — Alternative method for specifying volume, using a size vector
  • m [ int ] — The order of the numerator . If not specified, defaults to the length of aggregated field data times m_frac.
  • n [ int ] — The order of the denominator . Defaults to length of field data - m - 1.
  • m_frac [ float ] — Method for specifying m as a fraction of field samples to use as the order for numerator. Default is 0.5.
  • n_frac [ float ] — Fraction of field samples to use as order for denominator. No default.
  • sampling_interval [ int ] — The interval at which to sample the field data. Defaults to 1.
  • start_time [ int ] — The time (in increments of ) at which to start sampling the field data. Default is 0 (beginning of simulation).
  • stop_time [ int ] — The time (in increments of ) at which to stop sampling the field data. Default is None (end of simulation).

Verbosity#

class Verbosity(object):

A class to help make accessing and setting the global verbosity level a bit more pythonic. It manages one or more verbosity flags that are located in the C/C++ libraries used by Meep.

The verbosity levels are:

  • 0: minimal output
  • 1: a little
  • 2: a lot
  • 3: debugging

An instance of Verbosity is created when meep is imported, and is accessible as meep.verbosity. The meep.mpb package also has a verbosity flag in its C library, and it can also be managed via the Verbosity class after meep.mpb is imported.

Note that this class is a Singleton, meaning that each call to create a new Verbosity actually gives you the same instance. The new C verbosity flag will be added to a list of verbosity flags managed by this class.

The Verbosity instance can be used as a global verbosity controller, and assignments to any instance of Verbosity will set the global verbosity level for all library components. For example, this:

meep.verbosity(2)
# or meep.verbosity.set(2) if you prefer being more explicit

will set all of the managed verbosity flags to level 2.

Each managed verbosity flag can also be accessed individually if desired. Each time a new C/C++ library verbosity flag is added to this Python class a new property is added which can be used to access that individual flag. Currently the properties that are available are named simply meep and mpb. This means that you can set two different verbosity levels like this:

verbosity = meep.verbosity # not required, it's just to save some typing
verbosity.meep = 2
verbosity.mpb = 1

def __init__(self, cvar=None, name=None, initial_level=1):

See add_verbosity_var()

def __call__(self, level):

Convenience for setting the verbosity level. This lets you set the global level by calling the instance like a function. For example, if verbosity is an instance of this class, then its value can be changed like this:

verbosity(0)

def add_verbosity_var(self, cvar=None, name=None, initial_level=1):

Add a new verbosity flag to be managed. cvar should be some object that has a verbosity attribute, such as meep.cvar or mpb.cvar.

def get(self):

Returns the current global verbosity level.

def set(self, level):

Validates the range, and sets the global verbosity level. Returns the former value.


BinaryPartition#

class BinaryPartition(object):

Binary tree class used for specifying a cell partition of arbitrary sized chunks for use as the chunk_layout parameter of the Simulation class object.

def __init__(self,
             data=None,
             split_dir=None,
             split_pos=None,
             left=None,
             right=None,
             proc_id=None):

The constructor accepts three separate groups of arguments: (1) data: a list of lists where each list entry is either (a) a node defined as [ (split_dir,split_pos), left, right ] for which split_dir and split_pos define the splitting direction (i.e., mp.X, mp.Y, mp.Z) and position (e.g., 3.5, -4.2, etc.) and left and right are the two branches (themselves BinaryPartition objects) or (b) a leaf with integer value for the process ID proc_id in the range between 0 and number of processes - 1 (inclusive), (2) a node defined using split_dir, split_pos, left, and right, or (3) a leaf with proc_id. Note that the same process ID can be assigned to as many chunks as you want, which means that one process timesteps multiple chunks. If you use fewer MPI processes, then the process ID is taken modulo the number of processes.

def print(self):

Pretty-prints the tree structure of the BinaryPartition object.

Miscellaneous Functions Reference#

def interpolate(n, nums):

Given a list of numbers or Vector3s as nums, linearly interpolates between them to add n new evenly-spaced values between each pair of consecutive values in the original list.

Flux functions#

def get_flux_freqs(f):

Given a flux object, returns a list of the frequencies that it is computing the spectrum for.

def get_fluxes(f):

Given a flux object, returns a list of the current flux spectrum that it has accumulated.

def scale_flux_fields(s, flux):

Scale the Fourier-transformed fields in flux by the complex number s. e.g. load_minus_flux is equivalent to load_flux followed by scale_flux_fields with s=-1.

def get_eigenmode_freqs(f):

Given a flux object, returns a list of the frequencies that it is computing the spectrum for.

Energy Functions#

def get_energy_freqs(f):

Given an energy object, returns a list of the frequencies that it is computing the spectrum for.

def get_electric_energy(f):

Given an energy object, returns a list of the current energy density spectrum for the electric fields that it has accumulated.

def get_magnetic_energy(f):

Given an energy object, returns a list of the current energy density spectrum for the magnetic fields that it has accumulated.

def get_total_energy(f):

Given an energy object, returns a list of the current energy density spectrum for the total fields that it has accumulated.

Force Functions#

def get_force_freqs(f):

Given a force object, returns a list of the frequencies that it is computing the spectrum for.

def get_forces(f):

Given a force object, returns a list of the current force spectrum that it has accumulated.

LDOS Functions#

def Ldos(*args):
def Ldos(fcen, df, nfreq, freq):

Create an LDOS object with either frequency bandwidth df centered at fcen and nfreq equally spaced frequency points or an array/list freq for arbitrarily spaced frequencies. This can be passed to the dft_ldos step function below as a keyword argument.

def get_ldos_freqs(l):

Given an LDOS object, returns a list of the frequencies that it is computing the spectrum for.

def dft_ldos(*args, **kwargs):
def dft_ldos(fcen=None, df=None, nfreq=None, freq=None, ldos=None):

Compute the power spectrum of the sources (usually a single point dipole source), normalized to correspond to the LDOS, in either a frequency bandwidth df centered at fcen and nfreq equally spaced frequency points or an array/list freq for arbitrarily spaced frequencies. One can also pass in an Ldos object as dft_ldos(ldos=my_Ldos).

The resulting spectrum is outputted as comma-delimited text, prefixed by ldos:,, and is also stored in the ldos_data variable of the Simulation object after the run is complete. The Fourier-transformed electric field and current source are stored in the ldos_Fdata and ldos_Jdata of the Simulation object, respectively.

Near2Far Functions#

def get_near2far_freqs(f):

Given a near2far object, returns a list of the frequencies that it is computing the spectrum for.

def scale_near2far_fields(s, near2far):

Scale the Fourier-transformed fields in near2far by the complex number s. e.g. load_minus_near2far is equivalent to load_near2far followed by scale_near2far_fields with s=-1.

GDSII Functions#

def GDSII_layers(fname):

Returns a list of integer-valued layer indices for the layers present in the specified GDSII file.

mp.GDSII_layers('python/examples/coupler.gds')
Out[2]: [0, 1, 2, 3, 4, 5, 31, 32]

def GDSII_prisms(material, fname, layer=-1, zmin=0.0, zmax=0.0):

Returns a list of GeometricObjects with material (mp.Medium) on layer number layer of a GDSII file fname with zmin and zmax (default 0).

def GDSII_vol(fname, layer, zmin, zmax):

Returns a mp.Volume read from a GDSII file fname on layer number layer with zmin and zmax (default 0). This function is useful for creating a FluxRegion from a GDSII file as follows:

fr = mp.FluxRegion(volume=mp.GDSII_vol(fname, layer, zmin, zmax))

Run and Step Functions#

def stop_when_fields_decayed(dt=None, c=None, pt=None, decay_by=None):

Return a condition function, suitable for passing to Simulation.run as the until or until_after_sources parameter, that examines the component c (e.g. meep.Ex, etc.) at the point pt (a Vector3) and keeps running until its absolute value squared has decayed by at least decay_by from its maximum previous value. In particular, it keeps incrementing the run time by dt (in Meep units) and checks the maximum value over that time period — in this way, it won't be fooled just because the field happens to go through zero at some instant.

Note that, if you make decay_by very small, you may need to increase the cutoff property of your source(s), to decrease the amplitude of the small high-frequency components that are excited when the source turns off. High frequencies near the Nyquist frequency of the grid have slow group velocities and are absorbed poorly by PML.

def stop_after_walltime(t):

Return a condition function, suitable for passing to Simulation.run as the until parameter. Stops the simulation after t seconds of wall time have passed.

def stop_on_interrupt():

Return a condition function, suitable for passing to Simulation.run as the until parameter. Instead of terminating when receiving a SIGINT or SIGTERM signal from the system, the simulation will abort time stepping and continue executing any code that follows the run function (e.g., outputting fields).

Output Functions#

def output_epsilon(sim=None, *step_func_args, **kwargs):

Given a frequency frequency, (provided as a keyword argument) output (relative permittivity); for an anisotropic tensor the output is the harmonic mean of the eigenvalues. If frequency is non-zero, the output is complex; otherwise it is the real, frequency-independent part of (the limit). When called as part of a step function, the sim argument specifying the Simulation object can be omitted, e.g., sim.run(mp.at_beginning(mp.output_epsilon(frequency=1/0.7)),until=10).

def output_mu(sim=None, *step_func_args, **kwargs):

Given a frequency frequency, (provided as a keyword argument) output (relative permeability); for an anisotropic tensor the output is the harmonic mean of the eigenvalues. If frequency is non-zero, the output is complex; otherwise it is the real, frequency-independent part of (the limit). When called as part of a step function, the sim argument specifying the Simulation object can be omitted, e.g., sim.run(mp.at_beginning(mp.output_mu(frequency=1/0.7)),until=10).

def output_poynting(sim):

Output the Poynting flux . Note that you might want to wrap this step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_hpwr(sim):

Output the magnetic-field energy density

def output_dpwr(sim):

Output the electric-field energy density

def output_tot_pwr(sim):

Output the total electric and magnetic energy density. Note that you might want to wrap this step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_png(compnt, options, rm_h5=True):

Output the given field component (e.g. Ex, etc.) as a PNG image, by first outputting the HDF5 file, then converting to PNG via h5topng, then deleting the HDF5 file. The second argument is a string giving options to pass to h5topng (e.g. "-Zc bluered"). See also Tutorial/Basics/Output Tips and Tricks.

It is often useful to use the h5topng -C or -A options to overlay the dielectric function when outputting fields. To do this, you need to know the name of the dielectric-function .h5 file which must have been previously output by output_epsilon. To make this easier, a built-in shell variable $EPS is provided which refers to the last-output dielectric-function .h5 file. So, for example output_png(mp.Ez,"-C $EPS") will output the field and overlay the dielectric contours.

By default, output_png deletes the .h5 file when it is done. To preserve the .h5 file requires output_png(component, h5topng_options, rm_h5=False).

def output_hfield(sim):

Outputs all the components of the field h, (magnetic) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_hfield_x(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_y(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_z(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_r(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_hfield_p(sim):

Output the component of the field h (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield(sim):

Outputs all the components of the field b, (magnetic) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_bfield_x(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_y(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_z(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_r(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_bfield_p(sim):

Output the component of the field b (magnetic). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_efield(sim):

Outputs all the components of the field e, (electric) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_efield_x(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_y(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_z(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_r(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_efield_p(sim):

Output the component of the field e (electric). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_dfield(sim):

Outputs all the components of the field d, (displacement) to an HDF5 file. That is, the different components are stored as different datasets within the same file.

def output_dfield_x(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_y(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_z(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_r(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_dfield_p(sim):

Output the component of the field d (displacement). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_sfield(sim):

Outputs all the components of the field s, (poynting flux) to an HDF5 file. That is, the different components are stored as different datasets within the same file. Note that you might want to wrap this step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.

def output_sfield_x(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_y(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_z(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_r(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively.

def output_sfield_p(sim):

Output the component of the field s (poynting flux). If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting flux, you might want to wrap the step function in synchronized_magnetic to compute it more accurately. See Synchronizing the Magnetic and Electric Fields.