tidy3d.CustomMedium

tidy3d.CustomMedium#

class CustomMedium[source]#

Bases: AbstractCustomMedium

Medium with user-supplied permittivity distribution.

Parameters:

  • name (Optional[str] = None) – Optional unique name for medium.

  • frequency_range (Optional[tuple[float, float]] = None) – [units = (Hz, Hz)]. Optional range of validity for the medium.

  • allow_gain (bool = False) – Allow the medium to be active. Caution: simulations with a gain medium are unstable, and are likely to diverge.Simulations where allow_gain is set to True will still be charged even if diverged. Monitor data up to the divergence point will still be returned and can be useful in some cases.

  • nonlinear_spec (Optional[Union[NonlinearSpec, NonlinearSusceptibility]] = None) – Nonlinear spec applied on top of the base medium properties.

  • modulation_spec (Optional[ModulationSpec] = None) – Modulation spec applied on top of the base medium properties.

  • viz_spec (Optional[VisualizationSpec] = None) – Plotting specification for visualizing medium.

  • heat_spec (Optional[Union[FluidSpec, SolidSpec, SolidMedium, FluidMedium]] = None) – DEPRECATED: Use MultiPhysicsMedium. Specification of the medium heat properties. They are used for solving the heat equation via the HeatSimulation interface. Such simulations can beused for investigating the influence of heat propagation on the properties of optical systems. Once the temperature distribution in the system is found using HeatSimulation object, Simulation.perturbed_mediums_copy() can be used to convert mediums with perturbation models defined into spatially dependent custom mediums. Otherwise, the heat_spec does not directly affect the running of an optical Simulation.

  • interp_method (Literal['nearest', 'linear'] = nearest) – Interpolation method to obtain permittivity values that are not supplied at the Yee grids; For grids outside the range of the supplied data, extrapolation will be applied. When the extrapolated value is smaller (greater) than the minimal (maximal) of the supplied data, the extrapolated value will take the minimal (maximal) of the supplied data.

  • subpixel (bool = False) – If True, apply the subpixel averaging method specified by Simulation’s field subpixel for this type of material on the interface of the structure, including exterior boundary and intersection interfaces with other structures.

  • derived_from (Optional[Union[PerturbationMedium, PerturbationPoleResidue]] = None) – If not None, it records the parent medium from which this medium was derived.

  • eps_dataset (Optional[PermittivityDataset] = None) – [To be deprecated] User-supplied dataset containing complex-valued permittivity as a function of space. Permittivity distribution over the Yee-grid will be interpolated based on interp_method.

  • permittivity (Optional[Union[Union[TriangularGridDataset, TetrahedralGridDataset], SpatialDataArray]] = None) – [units = None (relative permittivity)]. Spatial profile of relative permittivity.

  • conductivity (Optional[Union[Union[TriangularGridDataset, TetrahedralGridDataset], SpatialDataArray]] = None) – [units = S/um]. Spatial profile Electric conductivity. Defined such that the imaginary part of the complex permittivity at angular frequency omega is given by conductivity/omega.

Notes

Practical Advice

Use CustomMedium when permittivity varies spatially — for example, graded-index (GRIN) lenses or topology-optimized design regions. Define the permittivity on a rectangular grid using SpatialDataArray:

from tidy3d import SpatialDataArray
import numpy as np

x = np.linspace(-5, 5, 100)
y = np.linspace(-5, 5, 100)
z = [0]  # 2D variation
X, Y = np.meshgrid(x, y, indexing="ij")
eps_data = 1 + 3 * np.exp(-(X**2 + Y**2) / 4)
eps_data = eps_data[:, :, np.newaxis]

permittivity = SpatialDataArray(eps_data, coords=dict(x=x, y=y, z=z))
custom_medium = CustomMedium(permittivity=permittivity)

For uniform pixelated grids (e.g. topology optimization), consider the convenience method Structure.from_permittivity_array(), which creates a Structure with a CustomMedium directly from a 3D numpy array and a geometry.

For wavelength-independent homogeneous materials, use Medium instead. For dispersive materials, use FastDispersionFitter or an analytical model.

Example

>>> Nx, Ny, Nz = 10, 9, 8
>>> X = np.linspace(-1, 1, Nx)
>>> Y = np.linspace(-1, 1, Ny)
>>> Z = np.linspace(-1, 1, Nz)
>>> coords = dict(x=X, y=Y, z=Z)
>>> permittivity= SpatialDataArray(np.ones((Nx, Ny, Nz)), coords=coords)
>>> conductivity= SpatialDataArray(np.ones((Nx, Ny, Nz)), coords=coords)
>>> dielectric = CustomMedium(permittivity=permittivity, conductivity=conductivity)
>>> eps = dielectric.eps_model(200e12)

Attributes

freqs

float array of frequencies.

is_isotropic

Check if the medium is isotropic or anisotropic.

is_spatially_uniform

Whether the medium is spatially uniform.

n_cfl

This property computes the index of refraction related to CFL condition, so that the FDTD with this medium is stable when the time step size that doesn't take material factor into account is multiplied by n_cfl`.

eps_dataset

permittivity

conductivity

interp_method

subpixel

derived_from

name

frequency_range

allow_gain

nonlinear_spec

modulation_spec

viz_spec

heat_spec

Methods

eps_dataarray_freq(frequency)

Permittivity array at frequency.

eps_diagonal(frequency)

Main diagonal of the complex-valued permittivity tensor at frequency.

eps_diagonal_on_grid(frequency, coords)

Spatial profile of main diagonal of the complex-valued permittivity at frequency interpolated at the supplied coordinates.

eps_model(frequency)

Spatial and polarizaiton average of complex-valued permittivity as a function of frequency.

from_eps_raw(eps[, freq, interp_method])

Construct a CustomMedium from datasets containing raw permittivity values.

from_nk(n[, k, freq, interp_method])

Construct a CustomMedium from datasets containing n and k values.

grids(bounds)

Make a Grid corresponding to the data in each eps_ii component.
eps_dataset#
permittivity#
conductivity#
property is_isotropic#

Check if the medium is isotropic or anisotropic.

property is_spatially_uniform#

Whether the medium is spatially uniform.

property freqs#

float array of frequencies. This field is to be deprecated in v3.0.

property n_cfl#

This property computes the index of refraction related to CFL condition, so that the FDTD with this medium is stable when the time step size that doesn’t take material factor into account is multiplied by n_cfl`.

For dispersiveless custom medium, it equals min[sqrt(eps_inf)], where min is performed over all components and spatial points.

eps_dataarray_freq(frequency)[source]#

Permittivity array at frequency. ()

Parameters:

frequency (float) – Frequency to evaluate permittivity at (Hz).

Returns:

eps_diagonal_on_grid(frequency, coords)[source]#

Spatial profile of main diagonal of the complex-valued permittivity at frequency interpolated at the supplied coordinates.

Parameters:

  • frequency (float) – Frequency to evaluate permittivity at (Hz).

  • coords (Coords) – The grid point coordinates over which interpolation is performed.

Returns:

The complex-valued permittivity tensor at frequency interpolated at the supplied coordinate.

Return type:

tuple[ArrayComplex3D, ArrayComplex3D, ArrayComplex3D]

eps_diagonal(frequency)[source]#

Main diagonal of the complex-valued permittivity tensor at frequency. Spatially, we take max{|eps|}, so that autoMesh generation works appropriately.

eps_model(frequency)[source]#

Spatial and polarizaiton average of complex-valued permittivity as a function of frequency.

classmethod from_eps_raw(eps, freq=None, interp_method='nearest', **kwargs)[source]#

Construct a CustomMedium from datasets containing raw permittivity values.

Parameters:

Notes

For lossy medium that has a complex-valued eps, if eps is supplied through SpatialDataArray, which doesn’t contain frequency information, the freq kwarg will be used to evaluate the permittivity and conductivity. Alternatively, eps can be supplied through ScalarFieldDataArray, which contains a frequency coordinate. In this case, leave freq kwarg as the default of None.

Returns:

Medium containing the spatially varying permittivity data.

Return type:

CustomMedium

classmethod from_nk(n, k=None, freq=None, interp_method='nearest', **kwargs)[source]#

Construct a CustomMedium from datasets containing n and k values.

Parameters:

Note

For lossy medium, if both n and k are supplied through SpatialDataArray, which doesn’t contain frequency information, the freq kwarg will be used to evaluate the permittivity and conductivity. Alternatively, n and k can be supplied through ScalarFieldDataArray, which contains a frequency coordinate. In this case, leave freq kwarg as the default of None.

Returns:

Medium containing the spatially varying permittivity data.

Return type:

CustomMedium

grids(bounds)[source]#

Make a Grid corresponding to the data in each eps_ii component. The min and max coordinates along each dimension are bounded by bounds.