flex_rf.tidy3d.CustomPoleResidue

Type: class │ Base(s): CustomDispersiveMedium, PoleResidue

Description

A spatially varying dispersive medium described by the pole-residue pair model.

Notes

In this method, the frequency-dependent permittivity $\epsilon(\omega)$ is expressed as a sum of resonant material poles [1].

\epsilon(\omega) = \epsilon_\infty - \sum_i \left[\frac{c_i}{j \omega + a_i} + \frac{c_i^*}{j \omega + a_i^*}\right]

For each of these resonant poles identified by the index $i$ , an auxiliary differential equation is used to relate the auxiliary current $J_i(t)$ to the applied electric field $E(t)$ . The sum of all these auxiliary current contributions describes the total dielectric response of the material.

\frac{d}{dt} J_i (t) - a_i J_i (t) = \epsilon_0 c_i \frac{d}{dt} E (t)

Hence, the computational cost increases with the number of poles.

Example(s)

x = np.linspace(-1, 1, 5)
y = np.linspace(-1, 1, 6)
z = np.linspace(-1, 1, 7)
coords = dict(x=x, y=y, z=z)
eps_inf = SpatialDataArray(np.ones((5, 6, 7)), coords=coords)
a1 = SpatialDataArray(-np.random.random((5, 6, 7)), coords=coords)
c1 = SpatialDataArray(np.random.random((5, 6, 7)), coords=coords)
a2 = SpatialDataArray(-np.random.random((5, 6, 7)), coords=coords)
c2 = SpatialDataArray(np.random.random((5, 6, 7)), coords=coords)
pole_res = CustomPoleResidue(eps_inf=eps_inf, poles=[(a1, c1), (a2, c2)])
eps = pole_res.eps_model(200e12)

References

[1] M. Han, R.W. Dutton and S. Fan, IEEE Microwave and Wireless Component Letters, 16, 119 (2006).

.. TODO add links to notebooks using this.

Parameters

eps_inf [CustomSpatialDataTypeAnnotated]

Relative permittivity at infinite frequency ( $\epsilon_\infty$ ).

name [str | None] = None

Optional unique name for medium.

frequency_range [FreqBound | None] = None

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 [NonlinearSpec | NonlinearSusceptibility | None] = None

Nonlinear spec applied on top of the base medium properties.

modulation_spec [ModulationSpec | None] = None

Modulation spec applied on top of the base medium properties.

viz_spec [VisualizationSpec | None] = None

Plotting specification for visualizing medium.

heat_spec [ThermalSpecType | None] = 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 [InterpMethod] = '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 [PerturbationMediumType | None] = None

If not None, it records the parent medium from which this medium was derived.

poles [tuple[tuple[CustomSpatialDataTypeAnnotated, CustomSpatialDataTypeAnnotated], ...]] = ()

Tuple of complex-valued ( $a_i, c_i$ ) poles for the model.

Methods

eps_dataarray_freq(frequency: float)

Permittivity array at frequency.

from_medium(medium: CustomMedium)

Convert a CustomMedium to a pole residue model.

is_spatially_uniform()

Whether the medium is spatially uniform.

loss_upper_bound()

Not implemented yet.

poles_on_grid(coords: Coords)

Spatial profile of poles interpolated at the supplied coordinates.

to_medium()

Convert to a CustomMedium. Requires the pole residue model to only have a pole at 0 frequency, corresponding to a constant conductivity term.