{
  "title": "PoleResidue",
  "public_path": "flex_rf.tidy3d.PoleResidue",
  "lookup_path": "tidy3d.PoleResidue",
  "slug": "flex_rf/tidy3d/PoleResidue",
  "public_url": "/rf/latest/autogenerated/flex_rf/tidy3d/poleresidue/",
  "object_kind": "class",
  "introduction": "A dispersive medium described by the pole-residue pair model.",
  "notes": "The frequency-dependence of the complex-valued permittivity is described by:\n\n$$\n\\epsilon(\\omega) = \\epsilon_\\infty - \\sum_i\n\\left[\\frac{c_i}{j \\omega + a_i} +\n\\frac{c_i^*}{j \\omega + a_i^*}\\right]\n$$",
  "examples": "```python\npole_res = PoleResidue(eps_inf=2.0, poles=[((-1+2j), (3+4j)), ((-5+6j), (7+8j))])\neps = pole_res.eps_model(200e12)\n```",
  "references": "",
  "signature": "class PoleResidue(DispersiveMedium)",
  "source": {
    "path": "flex/public/tidy3d/tidy3d/components/medium.py",
    "url": "",
    "lineno": 3003,
    "endlineno": 3561
  },
  "bases": [
    "DispersiveMedium"
  ],
  "parameter_rows": [
    {
      "name": "eps_inf",
      "annotation": "TracedPositiveFloat",
      "default": "1.0",
      "description": "Relative permittivity at infinite frequency ($$\\epsilon_\\infty$$).",
      "origin": "declared"
    },
    {
      "name": "poles",
      "annotation": "TracedPolesAndResidues",
      "default": "()",
      "description": "Tuple of complex-valued ($$a_i, c_i$$) poles for the model.",
      "origin": "declared"
    },
    {
      "name": "attrs",
      "annotation": "dict",
      "default": "factory: dict",
      "description": "Dictionary storing arbitrary metadata for a Tidy3D object. This dictionary can be freely used by the user for storing data without affecting the operation of Tidy3D as it is not used internally. Note that, unlike regular Tidy3D fields, `attrs` are mutable. For example, the following is allowed for setting an `attr` `obj.attrs['foo'] = bar`. Also note that Tidy3D will raise a `TypeError` if `attrs` contain objects that can not be serialized. One can check if `attrs` are serializable by calling `obj.model_dump_json()`.",
      "origin": "inherited"
    },
    {
      "name": "name",
      "annotation": "str | None",
      "default": "None",
      "description": "Optional unique name for medium.",
      "origin": "inherited"
    },
    {
      "name": "frequency_range",
      "annotation": "FreqBound | None",
      "default": "None",
      "description": "Optional range of validity for the medium.",
      "origin": "inherited"
    },
    {
      "name": "allow_gain",
      "annotation": "bool",
      "default": "False",
      "description": "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.",
      "origin": "inherited"
    },
    {
      "name": "nonlinear_spec",
      "annotation": "NonlinearSpec | NonlinearSusceptibility | None",
      "default": "None",
      "description": "Nonlinear spec applied on top of the base medium properties.",
      "origin": "inherited"
    },
    {
      "name": "modulation_spec",
      "annotation": "ModulationSpec | None",
      "default": "None",
      "description": "Modulation spec applied on top of the base medium properties.",
      "origin": "inherited"
    },
    {
      "name": "viz_spec",
      "annotation": "VisualizationSpec | None",
      "default": "None",
      "description": "Plotting specification for visualizing medium.",
      "origin": "inherited"
    },
    {
      "name": "heat_spec",
      "annotation": "ThermalSpecType | None",
      "default": "None",
      "description": "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`.",
      "origin": "inherited"
    }
  ],
  "members": [
    {
      "name": "eps_model",
      "kind": "function",
      "signature": "eps_model(frequency: float)",
      "description": "Complex-valued permittivity as a function of frequency."
    },
    {
      "name": "from_admittance_coeffs",
      "kind": "function",
      "signature": "from_admittance_coeffs(a: ArrayFloat, b: ArrayFloat, eps_inf: PositiveFloat = 1, pole_tol: PositiveFloat = 0.01)",
      "description": "Construct a `PoleResidue` model from an admittance function defining the relationship between the electric field and the polarization current density in the Laplace domain."
    },
    {
      "name": "from_lo_to",
      "kind": "function",
      "signature": "from_lo_to(poles: tuple[tuple[float, float, float, float], ...], eps_inf: PositiveFloat = 1)",
      "description": "Construct a pole residue model from the LO-TO form (longitudinal and transverse optical modes). The LO-TO form is $$\\epsilon_\\infty \\prod_{i=1}^l \\frac{\\omega_{LO, i}^2 - \\omega^2 - i \\omega \\gamma_{LO, i}}{\\omega_{TO, i}^2 - \\omega^2 - i \\omega \\gamma_{TO, i}}$$ as given in the paper:"
    },
    {
      "name": "from_medium",
      "kind": "function",
      "signature": "from_medium(medium: Medium)",
      "description": "Convert a `Medium` to a pole residue model."
    },
    {
      "name": "imag_ep_extrema",
      "kind": "function",
      "signature": "imag_ep_extrema(poles: PolesAndResidues)",
      "description": "Extrema of Im[eps] in the same unit as poles."
    },
    {
      "name": "lo_to_eps_model",
      "kind": "function",
      "signature": "lo_to_eps_model(poles: tuple[tuple[float, float, float, float], ...], eps_inf: PositiveFloat, frequency: float)",
      "description": "Complex permittivity as a function of frequency for a given set of LO-TO coefficients. See `from_lo_to` in `PoleResidue` for the detailed form of the model and a reference paper."
    },
    {
      "name": "loss_upper_bound",
      "kind": "function",
      "signature": "loss_upper_bound()",
      "description": "Upper bound of Im[eps] in `frequency_range`"
    },
    {
      "name": "to_medium",
      "kind": "function",
      "signature": "to_medium()",
      "description": "Convert to a `Medium`. Requires the pole residue model to only have a pole at 0 frequency, corresponding to a constant conductivity term."
    }
  ],
  "group": "flex_rf.tidy3d"
}