tidy3d.FieldProjectionAngleData
tidy3d.FieldProjectionAngleData#
- class tidy3d.FieldProjectionAngleData#
Data associated with a
FieldProjectionAngleMonitor: components of projected fields.- Parameters
monitor (FieldProjectionAngleMonitor) – Field projection monitor with an angle-based projection grid.
Er (FieldProjectionAngleDataArray) – Spatial distribution of r-component of the electric field.
Etheta (FieldProjectionAngleDataArray) – Spatial distribution of the theta-component of the electric field.
Ephi (FieldProjectionAngleDataArray) – Spatial distribution of phi-component of the electric field.
Hr (FieldProjectionAngleDataArray) – Spatial distribution of r-component of the magnetic field.
Htheta (FieldProjectionAngleDataArray) – Spatial distribution of theta-component of the magnetic field.
Hphi (FieldProjectionAngleDataArray) – Spatial distribution of phi-component of the magnetic field.
medium (Union[Medium, CustomMedium, AnisotropicMedium, PECMedium, PoleResidue, Sellmeier, Lorentz, Debye, Drude] = Medium(name=None, frequency_range=None, type='Medium', permittivity=1.0, conductivity=0.0)) – Background medium through which to project fields.
projection_surfaces (Tuple[FieldProjectionSurface, ...]) – Surfaces of the monitor where near fields were recorded for projection
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, CustomMedium, 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" }, { "$ref": "#/definitions/CustomMedium" }, { "$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 }, "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 }, "CustomMedium": { "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 }, "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
FieldProjectionAngleDatawith fields re-normalized to a new projection distance, by applying a phase factor based onproj_distance.- Parameters
proj_distance (float = None) – (micron) new radial distance relative to the monitor’s local origin.
- Returns
Copy of this
FieldProjectionAngleDatawith fields re-projected toproj_distance.- Return type
- property phi: numpy.ndarray#
Azimuthal angles.
- property r: numpy.ndarray#
Radial distance.
- property theta: numpy.ndarray#
Polar angles.