tidy3d.CustomMedium

class CustomMedium

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 (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.

• heat_spec (Union[FluidSpec, SolidSpec, NoneType] = None) – Specification of the medium heat properties. They are used for solving the heat equation via the HeatSimulation interface. Such simulations can be used 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 and simulation’s subpixel is also True, applies subpixel averaging of the permittivity on the interface of the structure, including exterior boundary and intersection interfaces with other structures.

• 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[SpatialDataArray] = None) – [units = None (relative permittivity)]. Spatial profile of relative permittivity.

• conductivity (Optional[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.

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.
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`.

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 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)

Permittivity array at frequency. ()

Parameters:

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

Returns:

The permittivity evaluated at frequency.

Return type:

Tuple[SpatialDataArray, SpatialDataArray, SpatialDataArray]

eps_diagonal_on_grid(frequency, coords)

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)

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

eps_model(frequency)

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

classmethod from_eps_raw(eps, freq=None, interp_method='nearest', **kwargs)

Construct a CustomMedium from datasets containing raw permittivity values.

Parameters:

• eps (Union[SpatialDataArray, ScalarFieldDataArray]) – Dataset containing complex-valued permittivity as a function of space.

• freq (float, optional) – Frequency at which eps are defined.

• interp_method (InterpMethod, optional) – Interpolation method to obtain permittivity values that are not supplied at the Yee grids.

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)

Construct a CustomMedium from datasets containing n and k values.

Parameters:

• n (Union[SpatialDataArray, ScalarFieldDataArray]) – Real part of refractive index.

• k (Union[SpatialDataArray, ScalarFieldDataArray], optional) – Imaginary part of refrative index for lossy medium.

• freq (float, optional) – Frequency at which n and k are defined.

• interp_method (InterpMethod, optional) – Interpolation method to obtain permittivity values that are not supplied at the Yee grids.

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)

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

__hash__()

Hash method.