tidy3d.CustomMedium#

class tidy3d.CustomMedium#

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.

  • eps_dataset (PermittivityDataset) – 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.

  • 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.

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)
>>> freqs = [2e14]
>>> data = np.ones((Nx, Ny, Nz, 1))
>>> eps_diagonal_data = ScalarFieldDataArray(data, coords=dict(x=X, y=Y, z=Z, f=freqs))
>>> eps_components = {f"eps_{d}{d}": eps_diagonal_data for d in "xyz"}
>>> eps_dataset = PermittivityDataset(**eps_components)
>>> dielectric = CustomMedium(eps_dataset=eps_dataset, name='my_medium')
>>> eps = dielectric.eps_model(200e12)

Show JSON schema
{
   "title": "CustomMedium",
   "description": ":class:`.Medium` with user-supplied permittivity distribution.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for medium.\nfrequency_range : Optional[Tuple[float, float]] = None\n    [units = (Hz, Hz)].  Optional range of validity for the medium.\neps_dataset : PermittivityDataset\n    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``.\ninterp_method : Literal['nearest', 'linear'] = nearest\n    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.\n\nExample\n-------\n>>> Nx, Ny, Nz = 10, 9, 8\n>>> X = np.linspace(-1, 1, Nx)\n>>> Y = np.linspace(-1, 1, Ny)\n>>> Z = np.linspace(-1, 1, Nz)\n>>> freqs = [2e14]\n>>> data = np.ones((Nx, Ny, Nz, 1))\n>>> eps_diagonal_data = ScalarFieldDataArray(data, coords=dict(x=X, y=Y, z=Z, f=freqs))\n>>> eps_components = {f\"eps_{d}{d}\": eps_diagonal_data for d in \"xyz\"}\n>>> eps_dataset = PermittivityDataset(**eps_components)\n>>> dielectric = CustomMedium(eps_dataset=eps_dataset, name='my_medium')\n>>> eps = dielectric.eps_model(200e12)",
   "type": "object",
   "properties": {
      "name": {
         "title": "Name",
         "description": "Optional unique name for medium.",
         "type": "string"
      },
      "frequency_range": {
         "title": "Frequency Range",
         "description": "Optional range of validity for the medium.",
         "units": [
            "Hz",
            "Hz"
         ],
         "type": "array",
         "minItems": 2,
         "maxItems": 2,
         "items": [
            {
               "type": "number"
            },
            {
               "type": "number"
            }
         ]
      },
      "type": {
         "title": "Type",
         "default": "CustomMedium",
         "enum": [
            "CustomMedium"
         ],
         "type": "string"
      },
      "eps_dataset": {
         "title": "Permittivity Dataset",
         "description": "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``.",
         "allOf": [
            {
               "$ref": "#/definitions/PermittivityDataset"
            }
         ]
      },
      "interp_method": {
         "title": "Interpolation method",
         "description": "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.",
         "default": "nearest",
         "enum": [
            "nearest",
            "linear"
         ],
         "type": "string"
      }
   },
   "required": [
      "eps_dataset"
   ],
   "additionalProperties": false,
   "definitions": {
      "PermittivityDataset": {
         "title": "PermittivityDataset",
         "description": "Dataset storing the diagonal components of the permittivity tensor.\n\nParameters\n----------\neps_xx : ScalarFieldDataArray\n    Spatial distribution of the xx-component of the relative permittivity.\neps_yy : ScalarFieldDataArray\n    Spatial distribution of the yy-component of the relative permittivity.\neps_zz : ScalarFieldDataArray\n    Spatial distribution of the zz-component of the relative permittivity.\n\nExample\n-------\n>>> x = [-1,1]\n>>> y = [-2,0,2]\n>>> z = [-3,-1,1,3]\n>>> f = [2e14, 3e14]\n>>> coords = dict(x=x, y=y, z=z, f=f)\n>>> sclr_fld = ScalarFieldDataArray((1+1j) * np.random.random((2,3,4,2)), coords=coords)\n>>> data = PermittivityDataset(eps_xx=sclr_fld, eps_yy=sclr_fld, eps_zz=sclr_fld)",
         "type": "object",
         "properties": {
            "type": {
               "title": "Type",
               "default": "PermittivityDataset",
               "enum": [
                  "PermittivityDataset"
               ],
               "type": "string"
            },
            "eps_xx": {
               "title": "DataArray",
               "description": "Spatial distribution of the xx-component of the relative permittivity.",
               "type": "xr.DataArray",
               "properties": {
                  "_dims": {
                     "title": "_dims",
                     "type": "Tuple[str, ...]"
                  }
               },
               "required": [
                  "_dims"
               ]
            },
            "eps_yy": {
               "title": "DataArray",
               "description": "Spatial distribution of the yy-component of the relative permittivity.",
               "type": "xr.DataArray",
               "properties": {
                  "_dims": {
                     "title": "_dims",
                     "type": "Tuple[str, ...]"
                  }
               },
               "required": [
                  "_dims"
               ]
            },
            "eps_zz": {
               "title": "DataArray",
               "description": "Spatial distribution of the zz-component of the relative permittivity.",
               "type": "xr.DataArray",
               "properties": {
                  "_dims": {
                     "title": "_dims",
                     "type": "Tuple[str, ...]"
                  }
               },
               "required": [
                  "_dims"
               ]
            }
         },
         "required": [
            "eps_xx",
            "eps_yy",
            "eps_zz"
         ],
         "additionalProperties": false
      }
   }
}

attribute eps_dataset: tidy3d.components.data.dataset.PermittivityDataset [Required]#

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.

Validated by

  • _eps_inf_greater_no_less_than_one_sigma_positive

  • _single_frequency

attribute 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.

eps_dataset_freq(frequency: float) → tidy3d.components.data.dataset.PermittivityDataset#

Permittivity dataset at frequency. The dispersion comes from DC conductivity that results in nonzero Im[eps].

Parameters

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

Returns

The permittivity evaluated at frequency.

Return type

PermittivityDataset

eps_diagonal(frequency: float) → Tuple[complex, complex, complex]#

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

eps_diagonal_on_grid(frequency: float, coords: tidy3d.components.grid.grid.Coords) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]#

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[Numpy, Numpy, Numpy]

eps_model(frequency: float) → complex#

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

classmethod from_eps_raw(eps: tidy3d.components.data.data_array.ScalarFieldDataArray, interp_method: Literal['nearest', 'linear'] = 'nearest') → tidy3d.components.medium.CustomMedium#

Construct a CustomMedium from datasets containing raw permittivity values.

Parameters

  • eps (ScalarFieldDataArray) – Dataset containing complex-valued permittivity as a function of space.

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

Returns

Medium containing the spatially varying permittivity data.

Return type

CustomMedium

classmethod from_nk(n: tidy3d.components.data.data_array.ScalarFieldDataArray, k: Optional[tidy3d.components.data.data_array.ScalarFieldDataArray] = None, interp_method: Literal['nearest', 'linear'] = 'nearest') → tidy3d.components.medium.CustomMedium#

Construct a CustomMedium from datasets containing n and k values.

Parameters

  • n (ScalarFieldDataArray) – Real part of refractive index.

  • k (ScalarFieldDataArray = None) – Imaginary part of refrative index.

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

Returns

Medium containing the spatially varying permittivity data.

Return type

CustomMedium