tidy3d.Boundary#

class tidy3d.Boundary#

Boundary conditions at the minus and plus extents along a dimension

Parameters

Example

>>> boundary = Boundary(plus = PML(), minus = PECBoundary())

Show JSON schema
{
   "title": "Boundary",
   "description": "Boundary conditions at the minus and plus extents along a dimension\n\nParameters\n----------\nplus : Union[Periodic, PECBoundary, PMCBoundary, PML, StablePML, Absorber, BlochBoundary] = Periodic(name=None, type='Periodic')\n    Boundary condition on the plus side along a dimension.\nminus : Union[Periodic, PECBoundary, PMCBoundary, PML, StablePML, Absorber, BlochBoundary] = Periodic(name=None, type='Periodic')\n    Boundary condition on the minus side along a dimension.\n\nExample\n-------\n>>> boundary = Boundary(plus = PML(), minus = PECBoundary())",
   "type": "object",
   "properties": {
      "plus": {
         "title": "Plus BC",
         "description": "Boundary condition on the plus side along a dimension.",
         "default": {
            "name": null,
            "type": "Periodic"
         },
         "anyOf": [
            {
               "$ref": "#/definitions/Periodic"
            },
            {
               "$ref": "#/definitions/PECBoundary"
            },
            {
               "$ref": "#/definitions/PMCBoundary"
            },
            {
               "$ref": "#/definitions/PML"
            },
            {
               "$ref": "#/definitions/StablePML"
            },
            {
               "$ref": "#/definitions/Absorber"
            },
            {
               "$ref": "#/definitions/BlochBoundary"
            }
         ]
      },
      "minus": {
         "title": "Minus BC",
         "description": "Boundary condition on the minus side along a dimension.",
         "default": {
            "name": null,
            "type": "Periodic"
         },
         "anyOf": [
            {
               "$ref": "#/definitions/Periodic"
            },
            {
               "$ref": "#/definitions/PECBoundary"
            },
            {
               "$ref": "#/definitions/PMCBoundary"
            },
            {
               "$ref": "#/definitions/PML"
            },
            {
               "$ref": "#/definitions/StablePML"
            },
            {
               "$ref": "#/definitions/Absorber"
            },
            {
               "$ref": "#/definitions/BlochBoundary"
            }
         ]
      },
      "type": {
         "title": "Type",
         "default": "Boundary",
         "enum": [
            "Boundary"
         ],
         "type": "string"
      }
   },
   "additionalProperties": false,
   "definitions": {
      "Periodic": {
         "title": "Periodic",
         "description": "Periodic boundary condition class.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for boundary.",
         "type": "object",
         "properties": {
            "name": {
               "title": "Name",
               "description": "Optional unique name for boundary.",
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "Periodic",
               "enum": [
                  "Periodic"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "PECBoundary": {
         "title": "PECBoundary",
         "description": "Perfect electric conductor boundary condition class.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for boundary.",
         "type": "object",
         "properties": {
            "name": {
               "title": "Name",
               "description": "Optional unique name for boundary.",
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "PECBoundary",
               "enum": [
                  "PECBoundary"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "PMCBoundary": {
         "title": "PMCBoundary",
         "description": "Perfect magnetic conductor boundary condition class.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for boundary.",
         "type": "object",
         "properties": {
            "name": {
               "title": "Name",
               "description": "Optional unique name for boundary.",
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "PMCBoundary",
               "enum": [
                  "PMCBoundary"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "PMLParams": {
         "title": "PMLParams",
         "description": "Specifies full set of parameters needed for complex, frequency-shifted PML.\n\nParameters\n----------\nsigma_order : NonNegativeInt = 3\n    Order of the polynomial describing the absorber profile (~dist^sigma_order).\nsigma_min : NonNegativeFloat = 0.0\n    [units = 2*EPSILON_0/dt].  Minimum value of the absorber conductivity.\nsigma_max : NonNegativeFloat = 1.5\n    [units = 2*EPSILON_0/dt].  Maximum value of the absorber conductivity.\nkappa_order : NonNegativeInt = 3\n    Order of the polynomial describing the PML kappa profile (kappa~dist^kappa_order).\nkappa_min : NonNegativeFloat = 0.0\n    \nkappa_max : NonNegativeFloat = 1.5\n    \nalpha_order : NonNegativeInt = 3\n    Order of the polynomial describing the PML alpha profile (alpha~dist^alpha_order).\nalpha_min : NonNegativeFloat = 0.0\n    [units = 2*EPSILON_0/dt].  Minimum value of the PML alpha.\nalpha_max : NonNegativeFloat = 1.5\n    [units = 2*EPSILON_0/dt].  Maximum value of the PML alpha.\n\nExample\n-------\n>>> params = PMLParams(sigma_order=3, sigma_min=0.0, sigma_max=1.5, kappa_min=0.0)",
         "type": "object",
         "properties": {
            "sigma_order": {
               "title": "Sigma Order",
               "description": "Order of the polynomial describing the absorber profile (~dist^sigma_order).",
               "default": 3,
               "minimum": 0,
               "type": "integer"
            },
            "sigma_min": {
               "title": "Sigma Minimum",
               "description": "Minimum value of the absorber conductivity.",
               "default": 0.0,
               "units": "2*EPSILON_0/dt",
               "minimum": 0,
               "type": "number"
            },
            "sigma_max": {
               "title": "Sigma Maximum",
               "description": "Maximum value of the absorber conductivity.",
               "default": 1.5,
               "units": "2*EPSILON_0/dt",
               "minimum": 0,
               "type": "number"
            },
            "type": {
               "title": "Type",
               "default": "PMLParams",
               "enum": [
                  "PMLParams"
               ],
               "type": "string"
            },
            "kappa_order": {
               "title": "Kappa Order",
               "description": "Order of the polynomial describing the PML kappa profile (kappa~dist^kappa_order).",
               "default": 3,
               "minimum": 0,
               "type": "integer"
            },
            "kappa_min": {
               "title": "Kappa Minimum",
               "default": 0.0,
               "minimum": 0,
               "type": "number"
            },
            "kappa_max": {
               "title": "Kappa Maximum",
               "default": 1.5,
               "minimum": 0,
               "type": "number"
            },
            "alpha_order": {
               "title": "Alpha Order",
               "description": "Order of the polynomial describing the PML alpha profile (alpha~dist^alpha_order).",
               "default": 3,
               "minimum": 0,
               "type": "integer"
            },
            "alpha_min": {
               "title": "Alpha Minimum",
               "description": "Minimum value of the PML alpha.",
               "default": 0.0,
               "units": "2*EPSILON_0/dt",
               "minimum": 0,
               "type": "number"
            },
            "alpha_max": {
               "title": "Alpha Maximum",
               "description": "Maximum value of the PML alpha.",
               "default": 1.5,
               "units": "2*EPSILON_0/dt",
               "minimum": 0,
               "type": "number"
            }
         },
         "additionalProperties": false
      },
      "PML": {
         "title": "PML",
         "description": "Specifies a standard PML along a single dimension.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for boundary.\nnum_layers : NonNegativeInt = 12\n    Number of layers of standard PML.\nparameters : PMLParams = PMLParams(sigma_order=3, sigma_min=0.0, sigma_max=1.5, type='PMLParams', kappa_order=3, kappa_min=1.0, kappa_max=3.0, alpha_order=1, alpha_min=0.0, alpha_max=0.0)\n    Parameters of the complex frequency-shifted absorption poles.\n\nExample\n-------\n>>> pml = PML(num_layers=10)",
         "type": "object",
         "properties": {
            "name": {
               "title": "Name",
               "description": "Optional unique name for boundary.",
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "PML",
               "enum": [
                  "PML"
               ],
               "type": "string"
            },
            "num_layers": {
               "title": "Number of Layers",
               "description": "Number of layers of standard PML.",
               "default": 12,
               "minimum": 0,
               "type": "integer"
            },
            "parameters": {
               "title": "PML Parameters",
               "description": "Parameters of the complex frequency-shifted absorption poles.",
               "default": {
                  "sigma_order": 3,
                  "sigma_min": 0.0,
                  "sigma_max": 1.5,
                  "type": "PMLParams",
                  "kappa_order": 3,
                  "kappa_min": 1.0,
                  "kappa_max": 3.0,
                  "alpha_order": 1,
                  "alpha_min": 0.0,
                  "alpha_max": 0.0
               },
               "allOf": [
                  {
                     "$ref": "#/definitions/PMLParams"
                  }
               ]
            }
         },
         "additionalProperties": false
      },
      "StablePML": {
         "title": "StablePML",
         "description": "Specifies a 'stable' PML along a single dimension.\nThis PML deals handles possbly divergent simulations better, but at the expense of more layers.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for boundary.\nnum_layers : NonNegativeInt = 40\n    Number of layers of 'stable' PML.\nparameters : PMLParams = PMLParams(sigma_order=3, sigma_min=0.0, sigma_max=1.0, type='PMLParams', kappa_order=3, kappa_min=1.0, kappa_max=5.0, alpha_order=1, alpha_min=0.0, alpha_max=0.9)\n    'Stable' parameters of the complex frequency-shifted absorption poles.\n\nExample\n-------\n>>> pml = StablePML(num_layers=40)",
         "type": "object",
         "properties": {
            "name": {
               "title": "Name",
               "description": "Optional unique name for boundary.",
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "StablePML",
               "enum": [
                  "StablePML"
               ],
               "type": "string"
            },
            "num_layers": {
               "title": "Number of Layers",
               "description": "Number of layers of 'stable' PML.",
               "default": 40,
               "minimum": 0,
               "type": "integer"
            },
            "parameters": {
               "title": "Stable PML Parameters",
               "description": "'Stable' parameters of the complex frequency-shifted absorption poles.",
               "default": {
                  "sigma_order": 3,
                  "sigma_min": 0.0,
                  "sigma_max": 1.0,
                  "type": "PMLParams",
                  "kappa_order": 3,
                  "kappa_min": 1.0,
                  "kappa_max": 5.0,
                  "alpha_order": 1,
                  "alpha_min": 0.0,
                  "alpha_max": 0.9
               },
               "allOf": [
                  {
                     "$ref": "#/definitions/PMLParams"
                  }
               ]
            }
         },
         "additionalProperties": false
      },
      "AbsorberParams": {
         "title": "AbsorberParams",
         "description": "Specifies parameters common to Absorbers and PMLs.\n\nParameters\n----------\nsigma_order : NonNegativeInt = 3\n    Order of the polynomial describing the absorber profile (~dist^sigma_order).\nsigma_min : NonNegativeFloat = 0.0\n    [units = 2*EPSILON_0/dt].  Minimum value of the absorber conductivity.\nsigma_max : NonNegativeFloat = 1.5\n    [units = 2*EPSILON_0/dt].  Maximum value of the absorber conductivity.\n\nExample\n-------\n>>> params = AbsorberParams(sigma_order=3, sigma_min=0.0, sigma_max=1.5)",
         "type": "object",
         "properties": {
            "sigma_order": {
               "title": "Sigma Order",
               "description": "Order of the polynomial describing the absorber profile (~dist^sigma_order).",
               "default": 3,
               "minimum": 0,
               "type": "integer"
            },
            "sigma_min": {
               "title": "Sigma Minimum",
               "description": "Minimum value of the absorber conductivity.",
               "default": 0.0,
               "units": "2*EPSILON_0/dt",
               "minimum": 0,
               "type": "number"
            },
            "sigma_max": {
               "title": "Sigma Maximum",
               "description": "Maximum value of the absorber conductivity.",
               "default": 1.5,
               "units": "2*EPSILON_0/dt",
               "minimum": 0,
               "type": "number"
            },
            "type": {
               "title": "Type",
               "default": "AbsorberParams",
               "enum": [
                  "AbsorberParams"
               ],
               "type": "string"
            }
         },
         "additionalProperties": false
      },
      "Absorber": {
         "title": "Absorber",
         "description": "Specifies an adiabatic absorber along a single dimension.\nThis absorber is well-suited for dispersive materials\nintersecting with absorbing edges of the simulation at the expense of more layers.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for boundary.\nnum_layers : NonNegativeInt = 40\n    Number of layers of absorber to add to + and - boundaries.\nparameters : AbsorberParams = AbsorberParams(sigma_order=3, sigma_min=0.0, sigma_max=6.4, type='AbsorberParams')\n    Adiabatic absorber parameters.\n\nExample\n-------\n>>> pml = Absorber(num_layers=40)",
         "type": "object",
         "properties": {
            "name": {
               "title": "Name",
               "description": "Optional unique name for boundary.",
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "Absorber",
               "enum": [
                  "Absorber"
               ],
               "type": "string"
            },
            "num_layers": {
               "title": "Number of Layers",
               "description": "Number of layers of absorber to add to + and - boundaries.",
               "default": 40,
               "minimum": 0,
               "type": "integer"
            },
            "parameters": {
               "title": "Absorber Parameters",
               "description": "Adiabatic absorber parameters.",
               "default": {
                  "sigma_order": 3,
                  "sigma_min": 0.0,
                  "sigma_max": 6.4,
                  "type": "AbsorberParams"
               },
               "allOf": [
                  {
                     "$ref": "#/definitions/AbsorberParams"
                  }
               ]
            }
         },
         "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"
         ]
      },
      "BlochBoundary": {
         "title": "BlochBoundary",
         "description": "Specifies a Bloch boundary condition along a single dimension.\n\nParameters\n----------\nname : Optional[str] = None\n    Optional unique name for boundary.\nbloch_vec : Union[tidycomplex, ComplexNumber] = None\n    Normalized component of the Bloch vector in units of 2 * pi / (size along dimension) in the background medium, along the dimension in which the boundary is specified.\n\nExample\n-------\n>>> bloch = BlochBoundary(bloch_vec=1)",
         "type": "object",
         "properties": {
            "name": {
               "title": "Name",
               "description": "Optional unique name for boundary.",
               "type": "string"
            },
            "type": {
               "title": "Type",
               "default": "BlochBoundary",
               "enum": [
                  "BlochBoundary"
               ],
               "type": "string"
            },
            "bloch_vec": {
               "title": "Normalized Bloch vector component",
               "description": "Normalized component of the Bloch vector in units of 2 * pi / (size along dimension) in the background medium, along the dimension in which the boundary is specified.",
               "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"
                  }
               ]
            }
         },
         "required": [
            "bloch_vec"
         ],
         "additionalProperties": false
      }
   }
}

Fields
  • minus (Union[tidy3d.components.boundary.Periodic, tidy3d.components.boundary.PECBoundary, tidy3d.components.boundary.PMCBoundary, tidy3d.components.boundary.PML, tidy3d.components.boundary.StablePML, tidy3d.components.boundary.Absorber, tidy3d.components.boundary.BlochBoundary])

  • plus (Union[tidy3d.components.boundary.Periodic, tidy3d.components.boundary.PECBoundary, tidy3d.components.boundary.PMCBoundary, tidy3d.components.boundary.PML, tidy3d.components.boundary.StablePML, tidy3d.components.boundary.Absorber, tidy3d.components.boundary.BlochBoundary])

attribute minus: Union[tidy3d.components.boundary.Periodic, tidy3d.components.boundary.PECBoundary, tidy3d.components.boundary.PMCBoundary, tidy3d.components.boundary.PML, tidy3d.components.boundary.StablePML, tidy3d.components.boundary.Absorber, tidy3d.components.boundary.BlochBoundary] = Periodic(name=None, type='Periodic')#

Boundary condition on the minus side along a dimension.

Validated by
  • bloch_on_both_sides

  • periodic_with_pec_pmc

  • periodic_with_pml

attribute plus: Union[tidy3d.components.boundary.Periodic, tidy3d.components.boundary.PECBoundary, tidy3d.components.boundary.PMCBoundary, tidy3d.components.boundary.PML, tidy3d.components.boundary.StablePML, tidy3d.components.boundary.Absorber, tidy3d.components.boundary.BlochBoundary] = Periodic(name=None, type='Periodic')#

Boundary condition on the plus side along a dimension.

Validated by
  • bloch_on_both_sides

  • periodic_with_pec_pmc

  • periodic_with_pml

classmethod absorber(num_layers: pydantic.types.NonNegativeInt = 40, parameters: tidy3d.components.boundary.PMLParams = AbsorberParams(sigma_order=3, sigma_min=0.0, sigma_max=6.4, type='AbsorberParams'))#

Adiabatic absorber boundary specification on both sides along a dimension.

Parameters
  • num_layers (int = 40) – Number of layers of absorber to add to + and - boundaries.

  • parameters (PMLParams) – Adiabatic absorber parameters.

Example

>>> absorber = Boundary.absorber(num_layers=40)
classmethod bloch(bloch_vec: complex)#

Bloch boundary specification on both sides along a dimension.

Parameters

bloch_vec (complex) – Normalized component of the Bloch vector in units of 2 * pi / (size along dimension) in the background medium, along the dimension in which the boundary is specified.

Example

>>> bloch = Boundary.bloch(bloch_vec=1)
classmethod bloch_from_source(source: Union[tidy3d.components.source.GaussianBeam, tidy3d.components.source.ModeSource, tidy3d.components.source.PlaneWave], domain_size: float, axis: Literal[0, 1, 2], medium: Optional[tidy3d.components.medium.Medium] = None)#

Bloch boundary specification on both sides along a dimension based on a given source.

Parameters
  • source (Union[GaussianBeam, ModeSource, PlaneWave]) – Angled source.

  • domain_size (float) – Size of the domain in the direction normal to the Bloch boundary

  • axis (int) – Axis normal to the Bloch boundary

  • medium (Medium) – Background medium associated with the Bloch vector. Default: free space.

Example

>>> from tidy3d import GaussianPulse, PlaneWave, inf
>>> pulse = GaussianPulse(freq0=200e12, fwidth=20e12)
>>> pw_source = PlaneWave(
...     size=(inf,inf,0), source_time=pulse, direction='+', angle_theta=1.5, angle_phi=0.3)
>>> bloch = Boundary.bloch_from_source(source=pw_source, domain_size=5, axis=0)
classmethod pec()#

PEC boundary specification on both sides along a dimension.

Example

>>> pec = Boundary.pec()
classmethod periodic()#

Periodic boundary specification on both sides along a dimension.

Example

>>> pbc = Boundary.periodic()
classmethod pmc()#

PMC boundary specification on both sides along a dimension.

Example

>>> pmc = Boundary.pmc()
classmethod pml(num_layers: pydantic.types.NonNegativeInt = 12, parameters: tidy3d.components.boundary.PMLParams = PMLParams(sigma_order=3, sigma_min=0.0, sigma_max=1.5, type='PMLParams', kappa_order=3, kappa_min=1.0, kappa_max=3.0, alpha_order=1, alpha_min=0.0, alpha_max=0.0))#

PML boundary specification on both sides along a dimension.

Parameters
  • num_layers (int = 12) – Number of layers of standard PML to add to + and - boundaries.

  • parameters (PMLParams) – Parameters of the complex frequency-shifted absorption poles.

Example

>>> pml = Boundary.pml(num_layers=20)
classmethod stable_pml(num_layers: pydantic.types.NonNegativeInt = 40, parameters: tidy3d.components.boundary.PMLParams = PMLParams(sigma_order=3, sigma_min=0.0, sigma_max=1.0, type='PMLParams', kappa_order=3, kappa_min=1.0, kappa_max=5.0, alpha_order=1, alpha_min=0.0, alpha_max=0.9))#

Stable PML boundary specification on both sides along a dimension.

Parameters
  • num_layers (int = 40) – Number of layers of ‘stable’ PML to add to + and - boundaries.

  • parameters (PMLParams) – ‘Stable’ parameters of the complex frequency-shifted absorption poles.

Example

>>> stable_pml = Boundary.stable_pml(num_layers=40)