tidy3d.FieldProjectionAngleData#

class tidy3d.FieldProjectionAngleData#

Data associated with a FieldProjectionAngleMonitor: components of projected fields.

Parameters

Example

>>> from tidy3d import FieldProjectionAngleDataArray
>>> f = np.linspace(1e14, 2e14, 10)
>>> r = np.atleast_1d(5)
>>> theta = np.linspace(0, np.pi, 10)
>>> phi = np.linspace(0, 2*np.pi, 20)
>>> coords = dict(r=r, theta=theta, phi=phi, f=f)
>>> values = (1+1j) * np.random.random((len(r), len(theta), len(phi), len(f)))
>>> scalar_field = FieldProjectionAngleDataArray(values, coords=coords)
>>> monitor = FieldProjectionAngleMonitor(
...     center=(1,2,3), size=(2,2,2), freqs=f, name='n2f_monitor', phi=phi, theta=theta
...     )
>>> data = FieldProjectionAngleData(
...     monitor=monitor, Er=scalar_field, Etheta=scalar_field, Ephi=scalar_field,
...     Hr=scalar_field, Htheta=scalar_field, Hphi=scalar_field,
...     projection_surfaces=monitor.projection_surfaces,
...     )

Show JSON schema
{
   "title": "FieldProjectionAngleData",
   "description": "Data associated with a :class:`.FieldProjectionAngleMonitor`: components of projected fields.\n\nParameters\n----------\nmonitor : FieldProjectionAngleMonitor\n    Field projection monitor with an angle-based projection grid.\nEr : FieldProjectionAngleDataArray\n    Spatial distribution of r-component of the electric field.\nEtheta : FieldProjectionAngleDataArray\n    Spatial distribution of the theta-component of the electric field.\nEphi : FieldProjectionAngleDataArray\n    Spatial distribution of phi-component of the electric field.\nHr : FieldProjectionAngleDataArray\n    Spatial distribution of r-component of the magnetic field.\nHtheta : FieldProjectionAngleDataArray\n    Spatial distribution of theta-component of the magnetic field.\nHphi : FieldProjectionAngleDataArray\n    Spatial distribution of phi-component of the magnetic field.\nmedium : Union[Medium, AnisotropicMedium, PECMedium, PoleResidue, Sellmeier, Lorentz, Debye, Drude] = Medium(name=None, frequency_range=None, type='Medium', permittivity=1.0, conductivity=0.0)\n    Background medium through which to project fields.\nprojection_surfaces : Tuple[FieldProjectionSurface, ...]\n    Surfaces of the monitor where near fields were recorded for projection\n\nExample\n-------\n>>> from tidy3d import FieldProjectionAngleDataArray\n>>> f = np.linspace(1e14, 2e14, 10)\n>>> r = np.atleast_1d(5)\n>>> theta = np.linspace(0, np.pi, 10)\n>>> phi = np.linspace(0, 2*np.pi, 20)\n>>> coords = dict(r=r, theta=theta, phi=phi, f=f)\n>>> values = (1+1j) * np.random.random((len(r), len(theta), len(phi), len(f)))\n>>> scalar_field = FieldProjectionAngleDataArray(values, coords=coords)\n>>> monitor = FieldProjectionAngleMonitor(\n...     center=(1,2,3), size=(2,2,2), freqs=f, name='n2f_monitor', phi=phi, theta=theta\n...     )\n>>> data = FieldProjectionAngleData(\n...     monitor=monitor, Er=scalar_field, Etheta=scalar_field, Ephi=scalar_field,\n...     Hr=scalar_field, Htheta=scalar_field, Hphi=scalar_field,\n...     projection_surfaces=monitor.projection_surfaces,\n...     )",
   "type": "object",
   "properties": {
      "type": {
         "title": "Type",
         "default": "FieldProjectionAngleData",
         "enum": [
            "FieldProjectionAngleData"
         ],
         "type": "string"
      },
      "monitor": {
         "title": "Projection monitor",
         "description": "Field projection monitor with an angle-based projection grid.",
         "allOf": [
            {
               "$ref": "#/definitions/FieldProjectionAngleMonitor"
            }
         ]
      },
      "Er": {
         "title": "DataArray",
         "description": "Spatial distribution of r-component of the electric field.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      },
      "Etheta": {
         "title": "DataArray",
         "description": "Spatial distribution of the theta-component of the electric field.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      },
      "Ephi": {
         "title": "DataArray",
         "description": "Spatial distribution of phi-component of the electric field.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      },
      "Hr": {
         "title": "DataArray",
         "description": "Spatial distribution of r-component of the magnetic field.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      },
      "Htheta": {
         "title": "DataArray",
         "description": "Spatial distribution of theta-component of the magnetic field.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      },
      "Hphi": {
         "title": "DataArray",
         "description": "Spatial distribution of phi-component of the magnetic field.",
         "type": "xr.DataArray",
         "properties": {
            "_dims": {
               "title": "_dims",
               "type": "Tuple[str, ...]"
            }
         },
         "required": [
            "_dims"
         ]
      },
      "medium": {
         "title": "Background Medium",
         "description": "Background medium through which to project fields.",
         "default": {
            "name": null,
            "frequency_range": null,
            "type": "Medium",
            "permittivity": 1.0,
            "conductivity": 0.0
         },
         "anyOf": [
            {
               "$ref": "#/definitions/Medium"
            },
            {
               "$ref": "#/definitions/AnisotropicMedium"
            },
            {
               "$ref": "#/definitions/PECMedium"
            },
            {
               "$ref": "#/definitions/PoleResidue"
            },
            {
               "$ref": "#/definitions/Sellmeier"
            },
            {
               "$ref": "#/definitions/Lorentz"
            },
            {
               "$ref": "#/definitions/Debye"
            },
            {
               "$ref": "#/definitions/Drude"
            }
         ]
      },
      "projection_surfaces": {
         "title": "Projection surfaces",
         "description": "Surfaces of the monitor where near fields were recorded for projection",
         "type": "array",
         "items": {
            "$ref": "#/definitions/FieldProjectionSurface"
         }
      }
   },
   "required": [
      "monitor",
      "Er",
      "Etheta",
      "Ephi",
      "Hr",
      "Htheta",
      "Hphi",
      "projection_surfaces"
   ],
   "additionalProperties": false,
   "definitions": {
      "ApodizationSpec": {
         "title": "ApodizationSpec",
         "description": "Stores specifications for the apodizaton of frequency-domain monitors.\n\nParameters\n----------\nstart : Optional[NonNegativeFloat] = None\n    [units = sec].  Defines the time at which the start apodization ends.\nend : Optional[NonNegativeFloat] = None\n    [units = sec].  Defines the time at which the end apodization begins.\nwidth : Optional[PositiveFloat] = None\n    [units = sec].  Characteristic decay length of the apodization function.\n\nExample\n-------\n>>> apod_spec = ApodizationSpec(start=1, end=2, width=0.5)",
         "type": "object",
         "properties": {
            "start": {
               "title": "Start Interval",
               "description": "Defines the time at which the start apodization ends.",
               "units": "sec",
               "minimum": 0,
               "type": "number"
            },
            "end": {
               "title": "End Interval",
               "description": "Defines the time at which the end apodization begins.",
               "units": "sec",
               "minimum": 0,
               "type": "number"
            },
            "width": {
               "title": "Apodization Width",
               "description": "Characteristic decay length of the apodization function.",
               "units": "sec",
               "exclusiveMinimum": 0,
               "type": "number"
            },
            "type": {
               "title": "Type",
               "default": "ApodizationSpec",
               "enum": [
                  "ApodizationSpec"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "FieldProjectionAngleMonitor": {
         "title": "FieldProjectionAngleMonitor",
         "description": ":class:`Monitor` that samples electromagnetic near fields in the frequency domain\nand projects them at given observation angles.\n\nParameters\n----------\ncenter : Tuple[float, float, float] = (0.0, 0.0, 0.0)\n    [units = um].  Center of object in x, y, and z.\nsize : Tuple[NonNegativeFloat, NonNegativeFloat, NonNegativeFloat]\n    [units = um].  Size in x, y, and z directions.\nname : ConstrainedStrValue\n    Unique name for monitor.\nfreqs : Union[Tuple[float, ...], Array]\n    [units = Hz].  Array or list of frequencies stored by the field monitor.\napodization : ApodizationSpec = ApodizationSpec(start=None, end=None, width=None, type='ApodizationSpec')\n    Sets parameters of (optional) apodization. Apodization applies a windowing function to the Fourier transform of the time-domain fields into frequency-domain ones, and can be used to truncate the beginning and/or end of the time signal, for example to eliminate the source pulse when studying the eigenmodes of a system. Note: apodization affects the normalization of the frequency-domain fields.\nnormal_dir : Optional[Literal['+', '-']] = None\n    Direction of the surface monitor's normal vector w.r.t. the positive x, y or z unit vectors. Must be one of ``'+'`` or ``'-'``. Applies to surface monitors only, and defaults to ``'+'`` if not provided.\nexclude_surfaces : Optional[Tuple[Literal['x-', 'x+', 'y-', 'y+', 'z-', 'z+'], ...]] = None\n    Surfaces to exclude in the integration, if a volume monitor.\ncustom_origin : Optional[Tuple[float, float, float]] = None\n    [units = um].  Local origin used for defining observation points. If ``None``, uses the monitor's center.\nfar_field_approx : bool = True\n    Whether to enable the far field approximation when projecting fields.\nproj_distance : float = 1000000.0\n    [units = um].  Radial distance of the projection points from ``local_origin``.\ntheta : Union[Tuple[float, ...], Array]\n    [units = rad].  Polar angles with respect to the global z axis, relative to the location of ``local_origin``, at which to project fields.\nphi : Union[Tuple[float, ...], Array]\n    [units = rad].  Azimuth angles with respect to the global z axis, relative to the location of ``local_origin``, at which to project fields.\n\nExample\n-------\n>>> monitor = FieldProjectionAngleMonitor(\n...     center=(1,2,3),\n...     size=(2,2,2),\n...     freqs=[250e12, 300e12],\n...     name='n2f_monitor',\n...     custom_origin=(1,2,3),\n...     phi=[0, np.pi/2],\n...     theta=np.linspace(-np.pi/2, np.pi/2, 100)\n...     )",
         "type": "object",
         "properties": {
            "type": {
               "title": "Type",
               "default": "FieldProjectionAngleMonitor",
               "enum": [
                  "FieldProjectionAngleMonitor"
               ],
               "type": "string"
            },
            "center": {
               "title": "Center",
               "description": "Center of object in x, y, and z.",
               "default": [
                  0.0,
                  0.0,
                  0.0
               ],
               "units": "um",
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  }
               ]
            },
            "size": {
               "title": "Size",
               "description": "Size in x, y, and z directions.",
               "units": "um",
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "number",
                     "minimum": 0
                  },
                  {
                     "type": "number",
                     "minimum": 0
                  },
                  {
                     "type": "number",
                     "minimum": 0
                  }
               ]
            },
            "name": {
               "title": "Name",
               "description": "Unique name for monitor.",
               "minLength": 1,
               "type": "string"
            },
            "freqs": {
               "title": "Frequencies",
               "description": "Array or list of frequencies stored by the field monitor.",
               "units": "Hz",
               "anyOf": [
                  {
                     "type": "array",
                     "items": {
                        "type": "number"
                     }
                  },
                  {
                     "title": "Array Like",
                     "description": "Accepts sequence (tuple, list, numpy array) and converts to tuple.",
                     "type": "tuple",
                     "properties": {},
                     "required": []
                  }
               ]
            },
            "apodization": {
               "title": "Apodization Specification",
               "description": "Sets parameters of (optional) apodization. Apodization applies a windowing function to the Fourier transform of the time-domain fields into frequency-domain ones, and can be used to truncate the beginning and/or end of the time signal, for example to eliminate the source pulse when studying the eigenmodes of a system. Note: apodization affects the normalization of the frequency-domain fields.",
               "default": {
                  "start": null,
                  "end": null,
                  "width": null,
                  "type": "ApodizationSpec"
               },
               "allOf": [
                  {
                     "$ref": "#/definitions/ApodizationSpec"
                  }
               ]
            },
            "normal_dir": {
               "title": "Normal vector orientation",
               "description": "Direction of the surface monitor's normal vector w.r.t. the positive x, y or z unit vectors. Must be one of ``'+'`` or ``'-'``. Applies to surface monitors only, and defaults to ``'+'`` if not provided.",
               "enum": [
                  "+",
                  "-"
               ],
               "type": "string"
            },
            "exclude_surfaces": {
               "title": "Excluded surfaces",
               "description": "Surfaces to exclude in the integration, if a volume monitor.",
               "type": "array",
               "items": {
                  "enum": [
                     "x-",
                     "x+",
                     "y-",
                     "y+",
                     "z-",
                     "z+"
                  ],
                  "type": "string"
               }
            },
            "custom_origin": {
               "title": "Local origin",
               "description": "Local origin used for defining observation points. If ``None``, uses the monitor's center.",
               "units": "um",
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  }
               ]
            },
            "far_field_approx": {
               "title": "Far field approximation",
               "description": "Whether to enable the far field approximation when projecting fields.",
               "default": true,
               "type": "boolean"
            },
            "proj_distance": {
               "title": "Projection distance",
               "description": "Radial distance of the projection points from ``local_origin``.",
               "default": 1000000.0,
               "units": "um",
               "type": "number"
            },
            "theta": {
               "title": "Polar angles",
               "description": "Polar angles with respect to the global z axis, relative to the location of ``local_origin``, at which to project fields.",
               "units": "rad",
               "anyOf": [
                  {
                     "type": "array",
                     "items": {
                        "type": "number"
                     }
                  },
                  {
                     "title": "Array Like",
                     "description": "Accepts sequence (tuple, list, numpy array) and converts to tuple.",
                     "type": "tuple",
                     "properties": {},
                     "required": []
                  }
               ]
            },
            "phi": {
               "title": "Azimuth angles",
               "description": "Azimuth angles with respect to the global z axis, relative to the location of ``local_origin``, at which to project fields.",
               "units": "rad",
               "anyOf": [
                  {
                     "type": "array",
                     "items": {
                        "type": "number"
                     }
                  },
                  {
                     "title": "Array Like",
                     "description": "Accepts sequence (tuple, list, numpy array) and converts to tuple.",
                     "type": "tuple",
                     "properties": {},
                     "required": []
                  }
               ]
            }
         },
         "required": [
            "size",
            "name",
            "freqs",
            "theta",
            "phi"
         ],
         "additionalProperties": false
      },
      "Medium": {
         "title": "Medium",
         "description": "Dispersionless medium.\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.\npermittivity : ConstrainedFloatValue = 1.0\n    [units = None (relative permittivity)].  Relative permittivity.\nconductivity : ConstrainedFloatValue = 0.0\n    [units = S/um].  Electric conductivity.  Defined such that the imaginary part of the complex permittivity at angular frequency omega is given by conductivity/omega.\n\nExample\n-------\n>>> dielectric = Medium(permittivity=4.0, 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": "Medium",
               "enum": [
                  "Medium"
               ],
               "type": "string"
            },
            "permittivity": {
               "title": "Permittivity",
               "description": "Relative permittivity.",
               "default": 1.0,
               "minimum": 1.0,
               "units": "None (relative permittivity)",
               "type": "number"
            },
            "conductivity": {
               "title": "Conductivity",
               "description": "Electric conductivity.  Defined such that the imaginary part of the complex permittivity at angular frequency omega is given by conductivity/omega.",
               "default": 0.0,
               "minimum": 0.0,
               "units": "S/um",
               "type": "number"
            }
         },
         "additionalProperties": false
      },
      "ComplexNumber": {
         "title": "ComplexNumber",
         "description": "Complex number with a well defined schema.",
         "type": "object",
         "properties": {
            "real": {
               "title": "Real",
               "type": "number"
            },
            "imag": {
               "title": "Imag",
               "type": "number"
            }
         },
         "required": [
            "real",
            "imag"
         ]
      },
      "PoleResidue": {
         "title": "PoleResidue",
         "description": "A dispersive medium described by the pole-residue pair model.\nThe frequency-dependence of the complex-valued permittivity is described by:\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_inf : float = 1.0\n    [units = None (relative permittivity)].  Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).\npoles : Tuple[Tuple[Union[tidy3d.components.types.tidycomplex, tidy3d.components.types.ComplexNumber], Union[tidy3d.components.types.tidycomplex, tidy3d.components.types.ComplexNumber]], ...] = ()\n    [units = (rad/sec, rad/sec)].  Tuple of complex-valued (:math:`a_i, c_i`) poles for the model.\n\nNote\n----\n.. math::\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\nExample\n-------\n>>> pole_res = PoleResidue(eps_inf=2.0, poles=[((1+2j), (3+4j)), ((5+6j), (7+8j))])\n>>> eps = pole_res.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": "PoleResidue",
               "enum": [
                  "PoleResidue"
               ],
               "type": "string"
            },
            "eps_inf": {
               "title": "Epsilon at Infinity",
               "description": "Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).",
               "default": 1.0,
               "units": "None (relative permittivity)",
               "type": "number"
            },
            "poles": {
               "title": "Poles",
               "description": "Tuple of complex-valued (:math:`a_i, c_i`) poles for the model.",
               "default": [],
               "units": [
                  "rad/sec",
                  "rad/sec"
               ],
               "type": "array",
               "items": {
                  "type": "array",
                  "minItems": 2,
                  "maxItems": 2,
                  "items": [
                     {
                        "anyOf": [
                           {
                              "title": "ComplexNumber",
                              "description": "Complex number with a well defined schema.",
                              "type": "object",
                              "properties": {
                                 "real": {
                                    "title": "Real",
                                    "type": "number"
                                 },
                                 "imag": {
                                    "title": "Imag",
                                    "type": "number"
                                 }
                              },
                              "required": [
                                 "real",
                                 "imag"
                              ]
                           },
                           {
                              "$ref": "#/definitions/ComplexNumber"
                           }
                        ]
                     },
                     {
                        "anyOf": [
                           {
                              "title": "ComplexNumber",
                              "description": "Complex number with a well defined schema.",
                              "type": "object",
                              "properties": {
                                 "real": {
                                    "title": "Real",
                                    "type": "number"
                                 },
                                 "imag": {
                                    "title": "Imag",
                                    "type": "number"
                                 }
                              },
                              "required": [
                                 "real",
                                 "imag"
                              ]
                           },
                           {
                              "$ref": "#/definitions/ComplexNumber"
                           }
                        ]
                     }
                  ]
               }
            }
         },
         "additionalProperties": false
      },
      "Sellmeier": {
         "title": "Sellmeier",
         "description": "A dispersive medium described by the Sellmeier model.\nThe frequency-dependence of the refractive index is described by:\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.\ncoeffs : Tuple[Tuple[float, pydantic.types.PositiveFloat], ...]\n    [units = (None, um^2)].  List of Sellmeier (:math:`B_i, C_i`) coefficients.\n\nNote\n----\n.. math::\n\n    n(\\lambda)^2 = 1 + \\sum_i \\frac{B_i \\lambda^2}{\\lambda^2 - C_i}\n\nExample\n-------\n>>> sellmeier_medium = Sellmeier(coeffs=[(1,2), (3,4)])\n>>> eps = sellmeier_medium.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": "Sellmeier",
               "enum": [
                  "Sellmeier"
               ],
               "type": "string"
            },
            "coeffs": {
               "title": "Coefficients",
               "description": "List of Sellmeier (:math:`B_i, C_i`) coefficients.",
               "units": [
                  null,
                  "um^2"
               ],
               "type": "array",
               "items": {
                  "type": "array",
                  "minItems": 2,
                  "maxItems": 2,
                  "items": [
                     {
                        "type": "number"
                     },
                     {
                        "type": "number",
                        "exclusiveMinimum": 0
                     }
                  ]
               }
            }
         },
         "required": [
            "coeffs"
         ],
         "additionalProperties": false
      },
      "Lorentz": {
         "title": "Lorentz",
         "description": "A dispersive medium described by the Lorentz model.\nThe frequency-dependence of the complex-valued permittivity is described by:\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_inf : float = 1.0\n    [units = None (relative permittivity)].  Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).\ncoeffs : Tuple[Tuple[float, float, float], ...]\n    [units = (None (relative permittivity), Hz, Hz)].  List of (:math:`\\Delta\\epsilon_i, f_i, \\delta_i`) values for model.\n\nNote\n----\n.. math::\n\n    \\epsilon(f) = \\epsilon_\\infty + \\sum_i\n    \\frac{\\Delta\\epsilon_i f_i^2}{f_i^2 - 2jf\\delta_i - f^2}\n\nExample\n-------\n>>> lorentz_medium = Lorentz(eps_inf=2.0, coeffs=[(1,2,3), (4,5,6)])\n>>> eps = lorentz_medium.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": "Lorentz",
               "enum": [
                  "Lorentz"
               ],
               "type": "string"
            },
            "eps_inf": {
               "title": "Epsilon at Infinity",
               "description": "Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).",
               "default": 1.0,
               "units": "None (relative permittivity)",
               "type": "number"
            },
            "coeffs": {
               "title": "Coefficients",
               "description": "List of (:math:`\\Delta\\epsilon_i, f_i, \\delta_i`) values for model.",
               "units": [
                  "None (relative permittivity)",
                  "Hz",
                  "Hz"
               ],
               "type": "array",
               "items": {
                  "type": "array",
                  "minItems": 3,
                  "maxItems": 3,
                  "items": [
                     {
                        "type": "number"
                     },
                     {
                        "type": "number"
                     },
                     {
                        "type": "number"
                     }
                  ]
               }
            }
         },
         "required": [
            "coeffs"
         ],
         "additionalProperties": false
      },
      "Debye": {
         "title": "Debye",
         "description": "A dispersive medium described by the Debye model.\nThe frequency-dependence of the complex-valued permittivity is described by:\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_inf : float = 1.0\n    [units = None (relative permittivity)].  Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).\ncoeffs : Tuple[Tuple[float, pydantic.types.PositiveFloat], ...]\n    [units = (None (relative permittivity), sec)].  List of (:math:`\\Delta\\epsilon_i, \\tau_i`) values for model.\n\nNote\n----\n.. math::\n\n    \\epsilon(f) = \\epsilon_\\infty + \\sum_i\n    \\frac{\\Delta\\epsilon_i}{1 - jf\\tau_i}\n\nExample\n-------\n>>> debye_medium = Debye(eps_inf=2.0, coeffs=[(1,2),(3,4)])\n>>> eps = debye_medium.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": "Debye",
               "enum": [
                  "Debye"
               ],
               "type": "string"
            },
            "eps_inf": {
               "title": "Epsilon at Infinity",
               "description": "Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).",
               "default": 1.0,
               "units": "None (relative permittivity)",
               "type": "number"
            },
            "coeffs": {
               "title": "Coefficients",
               "description": "List of (:math:`\\Delta\\epsilon_i, \\tau_i`) values for model.",
               "units": [
                  "None (relative permittivity)",
                  "sec"
               ],
               "type": "array",
               "items": {
                  "type": "array",
                  "minItems": 2,
                  "maxItems": 2,
                  "items": [
                     {
                        "type": "number"
                     },
                     {
                        "type": "number",
                        "exclusiveMinimum": 0
                     }
                  ]
               }
            }
         },
         "required": [
            "coeffs"
         ],
         "additionalProperties": false
      },
      "Drude": {
         "title": "Drude",
         "description": "A dispersive medium described by the Drude model.\nThe frequency-dependence of the complex-valued permittivity is described by:\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_inf : float = 1.0\n    [units = None (relative permittivity)].  Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).\ncoeffs : Tuple[Tuple[float, pydantic.types.PositiveFloat], ...]\n    [units = (Hz, Hz)].  List of (:math:`f_i, \\delta_i`) values for model.\n\nNote\n----\n.. math::\n\n    \\epsilon(f) = \\epsilon_\\infty - \\sum_i\n    \\frac{ f_i^2}{f^2 + jf\\delta_i}\n\nExample\n-------\n>>> drude_medium = Drude(eps_inf=2.0, coeffs=[(1,2), (3,4)])\n>>> eps = drude_medium.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": "Drude",
               "enum": [
                  "Drude"
               ],
               "type": "string"
            },
            "eps_inf": {
               "title": "Epsilon at Infinity",
               "description": "Relative permittivity at infinite frequency (:math:`\\epsilon_\\infty`).",
               "default": 1.0,
               "units": "None (relative permittivity)",
               "type": "number"
            },
            "coeffs": {
               "title": "Coefficients",
               "description": "List of (:math:`f_i, \\delta_i`) values for model.",
               "units": [
                  "Hz",
                  "Hz"
               ],
               "type": "array",
               "items": {
                  "type": "array",
                  "minItems": 2,
                  "maxItems": 2,
                  "items": [
                     {
                        "type": "number"
                     },
                     {
                        "type": "number",
                        "exclusiveMinimum": 0
                     }
                  ]
               }
            }
         },
         "required": [
            "coeffs"
         ],
         "additionalProperties": false
      },
      "AnisotropicMedium": {
         "title": "AnisotropicMedium",
         "description": "Diagonally anisotropic medium.\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.\nxx : Union[Medium, PoleResidue, Sellmeier, Lorentz, Debye, Drude]\n    Medium describing the xx-component of the diagonal permittivity tensor.\nyy : Union[Medium, PoleResidue, Sellmeier, Lorentz, Debye, Drude]\n    Medium describing the yy-component of the diagonal permittivity tensor.\nzz : Union[Medium, PoleResidue, Sellmeier, Lorentz, Debye, Drude]\n    Medium describing the zz-component of the diagonal permittivity tensor.\n\nNote\n----\nOnly diagonal anisotropy is currently supported.\n\nExample\n-------\n>>> medium_xx = Medium(permittivity=4.0)\n>>> medium_yy = Medium(permittivity=4.1)\n>>> medium_zz = Medium(permittivity=3.9)\n>>> anisotropic_dielectric = AnisotropicMedium(xx=medium_xx, yy=medium_yy, zz=medium_zz)",
         "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": "AnisotropicMedium",
               "enum": [
                  "AnisotropicMedium"
               ],
               "type": "string"
            },
            "xx": {
               "title": "XX Component",
               "description": "Medium describing the xx-component of the diagonal permittivity tensor.",
               "discriminator": {
                  "propertyName": "type",
                  "mapping": {
                     "Medium": "#/definitions/Medium",
                     "PoleResidue": "#/definitions/PoleResidue",
                     "Sellmeier": "#/definitions/Sellmeier",
                     "Lorentz": "#/definitions/Lorentz",
                     "Debye": "#/definitions/Debye",
                     "Drude": "#/definitions/Drude"
                  }
               },
               "oneOf": [
                  {
                     "$ref": "#/definitions/Medium"
                  },
                  {
                     "$ref": "#/definitions/PoleResidue"
                  },
                  {
                     "$ref": "#/definitions/Sellmeier"
                  },
                  {
                     "$ref": "#/definitions/Lorentz"
                  },
                  {
                     "$ref": "#/definitions/Debye"
                  },
                  {
                     "$ref": "#/definitions/Drude"
                  }
               ]
            },
            "yy": {
               "title": "YY Component",
               "description": "Medium describing the yy-component of the diagonal permittivity tensor.",
               "discriminator": {
                  "propertyName": "type",
                  "mapping": {
                     "Medium": "#/definitions/Medium",
                     "PoleResidue": "#/definitions/PoleResidue",
                     "Sellmeier": "#/definitions/Sellmeier",
                     "Lorentz": "#/definitions/Lorentz",
                     "Debye": "#/definitions/Debye",
                     "Drude": "#/definitions/Drude"
                  }
               },
               "oneOf": [
                  {
                     "$ref": "#/definitions/Medium"
                  },
                  {
                     "$ref": "#/definitions/PoleResidue"
                  },
                  {
                     "$ref": "#/definitions/Sellmeier"
                  },
                  {
                     "$ref": "#/definitions/Lorentz"
                  },
                  {
                     "$ref": "#/definitions/Debye"
                  },
                  {
                     "$ref": "#/definitions/Drude"
                  }
               ]
            },
            "zz": {
               "title": "ZZ Component",
               "description": "Medium describing the zz-component of the diagonal permittivity tensor.",
               "discriminator": {
                  "propertyName": "type",
                  "mapping": {
                     "Medium": "#/definitions/Medium",
                     "PoleResidue": "#/definitions/PoleResidue",
                     "Sellmeier": "#/definitions/Sellmeier",
                     "Lorentz": "#/definitions/Lorentz",
                     "Debye": "#/definitions/Debye",
                     "Drude": "#/definitions/Drude"
                  }
               },
               "oneOf": [
                  {
                     "$ref": "#/definitions/Medium"
                  },
                  {
                     "$ref": "#/definitions/PoleResidue"
                  },
                  {
                     "$ref": "#/definitions/Sellmeier"
                  },
                  {
                     "$ref": "#/definitions/Lorentz"
                  },
                  {
                     "$ref": "#/definitions/Debye"
                  },
                  {
                     "$ref": "#/definitions/Drude"
                  }
               ]
            }
         },
         "required": [
            "xx",
            "yy",
            "zz"
         ],
         "additionalProperties": false
      },
      "PECMedium": {
         "title": "PECMedium",
         "description": "Perfect electrical conductor class.\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.\n\nNote\n----\nTo avoid confusion from duplicate PECs, should import ``tidy3d.PEC`` instance directly.",
         "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": "PECMedium",
               "enum": [
                  "PECMedium"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "FieldMonitor": {
         "title": "FieldMonitor",
         "description": ":class:`Monitor` that records electromagnetic fields in the frequency domain.\n\nParameters\n----------\ncenter : Tuple[float, float, float] = (0.0, 0.0, 0.0)\n    [units = um].  Center of object in x, y, and z.\nsize : Tuple[NonNegativeFloat, NonNegativeFloat, NonNegativeFloat]\n    [units = um].  Size in x, y, and z directions.\nname : ConstrainedStrValue\n    Unique name for monitor.\nfreqs : Union[Tuple[float, ...], Array]\n    [units = Hz].  Array or list of frequencies stored by the field monitor.\napodization : ApodizationSpec = ApodizationSpec(start=None, end=None, width=None, type='ApodizationSpec')\n    Sets parameters of (optional) apodization. Apodization applies a windowing function to the Fourier transform of the time-domain fields into frequency-domain ones, and can be used to truncate the beginning and/or end of the time signal, for example to eliminate the source pulse when studying the eigenmodes of a system. Note: apodization affects the normalization of the frequency-domain fields.\nfields : Tuple[Literal['Ex', 'Ey', 'Ez', 'Hx', 'Hy', 'Hz'], ...] = ['Ex', 'Ey', 'Ez', 'Hx', 'Hy', 'Hz']\n    Collection of field components to store in the monitor.\ninterval_space : Tuple[PositiveInt, PositiveInt, PositiveInt] = (1, 1, 1)\n    Number of grid step intervals between monitor recordings. If equal to 1, there will be no downsampling. If greater than 1, fields will be downsampled and automatically colocated.\ncolocate : Optional[bool] = None\n    Toggle whether fields should be colocated to grid cell centers. Default: ``False`` if ``interval_space`` is 1 in each direction, ``True`` if ``interval_space`` is greater than one in any direction.\n\nExample\n-------\n>>> monitor = FieldMonitor(\n...     center=(1,2,3),\n...     size=(2,2,2),\n...     fields=['Hx'],\n...     freqs=[250e12, 300e12],\n...     name='steady_state_monitor')",
         "type": "object",
         "properties": {
            "type": {
               "title": "Type",
               "default": "FieldMonitor",
               "enum": [
                  "FieldMonitor"
               ],
               "type": "string"
            },
            "center": {
               "title": "Center",
               "description": "Center of object in x, y, and z.",
               "default": [
                  0.0,
                  0.0,
                  0.0
               ],
               "units": "um",
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  },
                  {
                     "type": "number"
                  }
               ]
            },
            "size": {
               "title": "Size",
               "description": "Size in x, y, and z directions.",
               "units": "um",
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "number",
                     "minimum": 0
                  },
                  {
                     "type": "number",
                     "minimum": 0
                  },
                  {
                     "type": "number",
                     "minimum": 0
                  }
               ]
            },
            "name": {
               "title": "Name",
               "description": "Unique name for monitor.",
               "minLength": 1,
               "type": "string"
            },
            "freqs": {
               "title": "Frequencies",
               "description": "Array or list of frequencies stored by the field monitor.",
               "units": "Hz",
               "anyOf": [
                  {
                     "type": "array",
                     "items": {
                        "type": "number"
                     }
                  },
                  {
                     "title": "Array Like",
                     "description": "Accepts sequence (tuple, list, numpy array) and converts to tuple.",
                     "type": "tuple",
                     "properties": {},
                     "required": []
                  }
               ]
            },
            "apodization": {
               "title": "Apodization Specification",
               "description": "Sets parameters of (optional) apodization. Apodization applies a windowing function to the Fourier transform of the time-domain fields into frequency-domain ones, and can be used to truncate the beginning and/or end of the time signal, for example to eliminate the source pulse when studying the eigenmodes of a system. Note: apodization affects the normalization of the frequency-domain fields.",
               "default": {
                  "start": null,
                  "end": null,
                  "width": null,
                  "type": "ApodizationSpec"
               },
               "allOf": [
                  {
                     "$ref": "#/definitions/ApodizationSpec"
                  }
               ]
            },
            "fields": {
               "title": "Field Components",
               "description": "Collection of field components to store in the monitor.",
               "default": [
                  "Ex",
                  "Ey",
                  "Ez",
                  "Hx",
                  "Hy",
                  "Hz"
               ],
               "type": "array",
               "items": {
                  "enum": [
                     "Ex",
                     "Ey",
                     "Ez",
                     "Hx",
                     "Hy",
                     "Hz"
                  ],
                  "type": "string"
               }
            },
            "interval_space": {
               "title": "Spatial interval",
               "description": "Number of grid step intervals between monitor recordings. If equal to 1, there will be no downsampling. If greater than 1, fields will be downsampled and automatically colocated.",
               "default": [
                  1,
                  1,
                  1
               ],
               "type": "array",
               "minItems": 3,
               "maxItems": 3,
               "items": [
                  {
                     "type": "integer",
                     "exclusiveMinimum": 0
                  },
                  {
                     "type": "integer",
                     "exclusiveMinimum": 0
                  },
                  {
                     "type": "integer",
                     "exclusiveMinimum": 0
                  }
               ]
            },
            "colocate": {
               "title": "Colocate fields",
               "description": "Toggle whether fields should be colocated to grid cell centers. Default: ``False`` if ``interval_space`` is 1 in each direction, ``True`` if ``interval_space`` is greater than one in any direction.",
               "type": "boolean"
            }
         },
         "required": [
            "size",
            "name",
            "freqs"
         ],
         "additionalProperties": false
      },
      "FieldProjectionSurface": {
         "title": "FieldProjectionSurface",
         "description": "Data structure to store surface monitors where near fields are recorded for\nfield projections.\n\nParameters\n----------\nmonitor : FieldMonitor\n    :class:`.FieldMonitor` on which near fields will be sampled and integrated.\nnormal_dir : Literal['+', '-']\n    :class:`.Direction` of the surface monitor's normal vector w.r.t. the positive x, y or z unit vectors. Must be one of '+' or '-'.",
         "type": "object",
         "properties": {
            "monitor": {
               "title": "Field monitor",
               "description": ":class:`.FieldMonitor` on which near fields will be sampled and integrated.",
               "allOf": [
                  {
                     "$ref": "#/definitions/FieldMonitor"
                  }
               ]
            },
            "normal_dir": {
               "title": "Normal vector orientation",
               "description": ":class:`.Direction` of the surface monitor's normal vector w.r.t. the positive x, y or z unit vectors. Must be one of '+' or '-'.",
               "enum": [
                  "+",
                  "-"
               ],
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "FieldProjectionSurface",
               "enum": [
                  "FieldProjectionSurface"
               ],
               "type": "string"
            }
         },
         "required": [
            "monitor",
            "normal_dir"
         ],
         "additionalProperties": false
      }
   }
}

attribute Ephi: tidy3d.components.data.data_array.FieldProjectionAngleDataArray [Required]#

Spatial distribution of phi-component of the electric field.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

attribute Er: tidy3d.components.data.data_array.FieldProjectionAngleDataArray [Required]#

Spatial distribution of r-component of the electric field.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

attribute Etheta: tidy3d.components.data.data_array.FieldProjectionAngleDataArray [Required]#

Spatial distribution of the theta-component of the electric field.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

attribute Hphi: tidy3d.components.data.data_array.FieldProjectionAngleDataArray [Required]#

Spatial distribution of phi-component of the magnetic field.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

attribute Hr: tidy3d.components.data.data_array.FieldProjectionAngleDataArray [Required]#

Spatial distribution of r-component of the magnetic field.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

attribute Htheta: tidy3d.components.data.data_array.FieldProjectionAngleDataArray [Required]#

Spatial distribution of theta-component of the magnetic field.

Constraints
  • title = DataArray

  • type = xr.DataArray

  • properties = {‘_dims’: {‘title’: ‘_dims’, ‘type’: ‘Tuple[str, …]’}}

  • required = [‘_dims’]

attribute monitor: tidy3d.components.monitor.FieldProjectionAngleMonitor [Required]#

Field projection monitor with an angle-based projection grid.

attribute projection_surfaces: Tuple[tidy3d.components.monitor.FieldProjectionSurface, ...] [Required]#

Surfaces of the monitor where near fields were recorded for projection

renormalize_fields(proj_distance: float) tidy3d.components.data.monitor_data.FieldProjectionAngleData#

Return a FieldProjectionAngleData with fields re-normalized to a new projection distance, by applying a phase factor based on proj_distance.

Parameters

proj_distance (float = None) – (micron) new radial distance relative to the monitor’s local origin.

Returns

Copy of this FieldProjectionAngleData with fields re-projected to proj_distance.

Return type

FieldProjectionAngleData

property phi: numpy.ndarray#

Azimuthal angles.

property r: numpy.ndarray#

Radial distance.

property theta: numpy.ndarray#

Polar angles.