# PLaSK User Manual

#### Page Contents

- Fourier3D Class
  - `Fourier3D`
  - Subclasses
  - Methods
  - Attributes
    - Receivers
    - Providers
    - Other
  - Descriptions
    - Method Details
      - `Fourier3D.compute_reflectivity()`
      - `Fourier3D.compute_transmittivity()`
      - `Fourier3D.find_mode()`
      - `Fourier3D.gaussian()`
      - `Fourier3D.get_determinant()`
      - `Fourier3D.get_raw_E()`
      - `Fourier3D.get_raw_H()`
      - `Fourier3D.initialize()`
      - `Fourier3D.integrateEE()`
      - `Fourier3D.integrateHH()`
      - `Fourier3D.invalidate()`
      - `Fourier3D.layer_eigenmodes()`
      - `Fourier3D.scattering()`
      - `Fourier3D.scattering_gaussian()`
      - `Fourier3D.set_interface()`
      - `Fourier3D.set_mode()`
    - Receiver Details
      - `Fourier3D.inCarriersConcentration`
      - `Fourier3D.inEpsilon`
      - `Fourier3D.inGain`
      - `Fourier3D.inTemperature`
    - Provider Details
      - `Fourier3D.outDownwardsLightE`
      - `Fourier3D.outDownwardsLightH`
      - `Fourier3D.outEpsilon`
      - `Fourier3D.outGradients`
      - `Fourier3D.outLightE`
      - `Fourier3D.outLightH`
      - `Fourier3D.outLightMagnitude`
      - `Fourier3D.outRefractiveIndex`
      - `Fourier3D.outUpwardsLightE`
      - `Fourier3D.outUpwardsLightH`
      - `Fourier3D.outWavelength`
    - Attribute Details
      - `Fourier3D.dct`
      - `Fourier3D.determinant_type`
      - `Fourier3D.emission`
      - `Fourier3D.geometry`
      - `Fourier3D.grad_smooth`
      - `Fourier3D.group_layers`
      - `Fourier3D.id`
      - `Fourier3D.initialized`
      - `Fourier3D.interface`
      - `Fourier3D.k0`
      - `Fourier3D.klong`
      - `Fourier3D.ktran`
      - `Fourier3D.lam`
      - `Fourier3D.lam0`
      - `Fourier3D.layer_centers`
      - `Fourier3D.layer_edges`
      - `Fourier3D.modes`
      - `Fourier3D.pmls`
      - `Fourier3D.refine`
      - `Fourier3D.root`
      - `Fourier3D.rule`
      - `Fourier3D.size`
      - `Fourier3D.smooth`
      - `Fourier3D.stack`
      - `Fourier3D.symmetry`
      - `Fourier3D.temp_diff`
      - `Fourier3D.temp_dist`
      - `Fourier3D.temp_layer`
      - `Fourier3D.transfer`
      - `Fourier3D.update_gain`
      - `Fourier3D.vpml`
      - `Fourier3D.wavelength`

# Fourier3D Class

class optical.modal.Fourier3D(name='')

  Optical Solver using Fourier expansion in 3D.

  It calculates optical modes and optical field distribution using Fourier modal method and reflection transfer in three-dimensional Cartesian space.

## Subclasses

`Eigenmodes` | Layer eignemodes
`Mode` | Detailed information about the mode.
`Oversampling` | Access wrapper for parameter along long/tran axis
`PMLs` | Access wrapper for parameter along long/tran axis
`Scattering` | Reflected mode proxy.
`Sizes` | Access wrapper for parameter along long/tran axis
`Symmetries` | Access wrapper for parameter along long/tran axis

## Methods

`compute_reflectivity`(...) | Compute reflection coefficient on planar incidence [%].
`compute_transmittivity`(...) | Compute transmission coefficient on planar incidence [%].
`find_mode`(*args, **kwargs) | Compute the mode near the specified effective index.
`gaussian`(side, polarization, sigma[, center]) | Create coefficients vector with Gaussian profile.
`get_determinant`(*args, **kwargs) | Compute discontinuity matrix determinant.
`get_raw_E`(num, level) | Get Fourier expansion coefficients for the electric field.
`get_raw_H`(num, level) | Get Fourier expansion coefficients for the magnetic field.
`initialize`() | Initialize solver.
`integrateEE`(...) | Get average integral of the squared electric field:
`integrateHH`(...) | Get average integral of the squared magnetic field:
`invalidate`() | Set the solver back to uninitialized state.
`layer_eigenmodes`(level) | Get eignemodes for a layer at specified level.
`scattering`(...) | Access to the reflected field.
`scattering_gaussian`(side, polarization, sigma) | Helper function to Access reflected fields for access incidence.
`set_interface`(...) | Set interface at the bottom of the specified object.
`set_mode`(*args, **kwargs) | Set the mode for specified parameters.

## Attributes

### Receivers

`inCarriersConcentration` | Receiver of the carriers concentration required for computations [1/cm³].
`inEpsilon` | Receiver of the permittivity tensor required for computations [-].
`inGain` | Receiver of the material gain required for computations [1/cm].
`inTemperature` | Receiver of the temperature required for computations [K].

### Providers

`outDownwardsLightE` | Provider of the computed electric field [V/m].
`outDownwardsLightH` | Provider of the computed magnetic field [A/m].
`outEpsilon` | Provider of the computed permittivity tensor [-].
`outGradients` | Provider of the computed refractive index gradient functions cos² and cos·sin [-].
`outLightE` | Provider of the computed electric field [V/m].
`outLightH` | Provider of the computed magnetic field [A/m].
`outLightMagnitude` | Provider of the computed optical field magnitude [W/m²].
`outRefractiveIndex` | Provider of the computed refractive index [-].
`outUpwardsLightE` | Provider of the computed electric field [V/m].
`outUpwardsLightH` | Provider of the computed magnetic field [A/m].
`outWavelength` | Provider of the computed wavelength [nm].

### Other

`dct` | Type of discrete cosine transform for symmetric expansion.
`determinant_type` | Type of determinant that is computed in root finding.
`emission` | Direction of the useful light emission.
`geometry` | Geometry provided to the solver
`grad_smooth` | Smoothing parameter for material boundaries gradients (needed for the new expansion rule).
`group_layers` | Layer grouping switch.
`id` | Id of the solver object.
`initialized` | True if the solver has been initialized.
`interface` | Matching interface position.
`k0` | Normalized frequency of the light (1/µm).
`klong` | Longitudinal propagation constant of the light (1/µm).
`ktran` | Transverse propagation constant of the light (1/µm).
`lam` | Wavelength of the light (nm).
`lam0` | Reference wavelength.
`layer_centers` | Vertical posiotions of centers of each layer.
`layer_edges` | Vertical posiotions of egges of each layer.
`modes` | Computed modes.
`pmls` | Longitudinal and transverse edge Perfectly Matched Layers boundary conditions.
`refine` | Number of refinement points for refractive index averaging in longitudinal and transverse directions.
`root` | Configuration of the root searching algorithm.
`rule` | Permittivity inversion rule.
`size` | Orthogonal expansion sizes in longitudinal and transverse directions.
`smooth` | Smoothing parameter for material boundaries (increases convergence).
`stack` | Stack of distinct layers.
`symmetry` | Longitudinal and transverse mode symmetries.
`temp_diff` | Maximum temperature difference between the layers in one group.
`temp_dist` | Temperature probing step.
`temp_layer` | Temperature probing step.
`transfer` | Preferred transfer method.
`update_gain` | Recompute dynamic parameters.
`vpml` | Vertical Perfectly Matched Layers boundary conditions.
`wavelength` | Alias for `lam`

## Descriptions

### Method Details

Fourier3D.compute_reflectivity(lam, side, index)
Fourier3D.compute_reflectivity(lam, side, coffs)
Fourier3D.compute_reflectivity(lam, side, polarization)

  Compute reflection coefficient on planar incidence [%].

  Parameters:

    - lam (float or array of floats) – Incident light wavelength (nm).

    - side (top or bottom) – Side of the structure where the incident light is present.

    - polarization – Specification of the incident light polarization. It should be a string of the form ‘E#‘, where # is the axis name of the non-vanishing electric field component.

    - idx – Eigenmode number.

    - coeffs – expansion coefficients of the incident vector.

Fourier3D.compute_transmittivity(lam, side, index)
Fourier3D.compute_transmittivity(lam, side, coffs)
Fourier3D.compute_transmittivity(lam, side, polarization)

  Compute transmission coefficient on planar incidence [%].

  Parameters:

    - lam (float or array of floats) – Incident light wavelength (nm).

    - side (top or bottom) – Side of the structure where the incident light is present.

    - polarization – Specification of the incident light polarization. It should be a string of the form ‘E#‘, where # is the axis name of the non-vanishing electric field component.

    - idx – Eigenmode number.

    - coeffs – expansion coefficients of the incident vector.

Fourier3D.find_mode(*args, **kwargs)

  Compute the mode near the specified effective index.

  Only one of the following arguments can be given through a keyword. It is the starting point for search of the specified parameter.

  Parameters:

    - lam (complex) – Wavelength (nm).

    - k0 (complex) – Normalized frequency (1/µm).

    - klong (complex) – Longitudinal wavevector (1/µm).

    - ktran (complex) – Transverse wavevector (1/µm).

Fourier3D.gaussian(side, polarization, sigma, center=(0.0, 0.0))

  Create coefficients vector with Gaussian profile.

  This method is intended to use for `scattering()` method.

  Parameters:

    - side (top or bottom) – Side of the structure where the incident light is present.

    - polarization – Specification of the incident light polarization. It should be a string of the form ‘E#‘, where # is the axis name of the non-vanishing electric field component.

    - sigma (float or tuple) – Gaussian standard deviation in longitudinal and transverse directions [µm, µm].

    - center (tuple) – Position of the beam center [µm, µm].

  Example

      >>> scattered = fourier.scattering('top',
      ...     fourier.gaussian('top', 'Ex', 0.2))

Fourier3D.get_determinant(*args, **kwargs)

  Compute discontinuity matrix determinant.

  Arguments can be given through keywords only.

  Parameters:

    - lam (complex) – Wavelength (nm).

    - k0 (complex) – Normalized frequency (1/µm).

    - klong (complex) – Longitudinal wavevector (1/µm).

    - ktran (complex) – Transverse wavevector (1/µm).

Fourier3D.get_raw_E(num, level)

  Get Fourier expansion coefficients for the electric field.

  This is a low-level function returning $E_l$ and/or $E_t$ Fourier expansion coefficients. Please refer to the detailed solver description for their interpretation.

  Parameters:

    - num (int) – Computed mode number.

    - level (float) – Vertical level at which the coefficients are computed.

  Return type:

    numpy.ndarray

Fourier3D.get_raw_H(num, level)

  Get Fourier expansion coefficients for the magnetic field.

  This is a low-level function returning $H_l$ and/or $H_t$ Fourier expansion coefficients. Please refer to the detailed solver description for their interpretation.

  Parameters:

    - num (int) – Computed mode number.

    - level (float) – Vertical level at which the coefficients are computed.

  Return type:

    numpy.ndarray

Fourier3D.initialize()

  Initialize solver.

  This method manually initialized the solver and sets `initialized` to True. Normally calling it is not necessary, as each solver automatically initializes itself when needed.

  Returns:

    solver `initialized` state prior to this method call.

  Return type:

    bool

Fourier3D.integrateEE(num, z1, z2)
Fourier3D.integrateEE(z1, z2)

  Get average integral of the squared electric field:

  \[\frac 1 2 \int_{z_1}^{z_2} |E|^2.\]

  In the lateral direction integration is performed over the whole domain.

  Parameters:

    - num (int) – Computed mode number.

    - z1 (float) – Lower vertical bound of the integral.

    - z2 (float) – Upper vertical bound of the integral.

  Returns:

    Computed integral [V2 / m2].

  Return type:

    float

  Warning

  This method may return incorrect results for layers with gain, due to the strong non-Hemiticity!

Fourier3D.integrateHH(num, z1, z2)
Fourier3D.integrateHH(z1, z2)

  Get average integral of the squared magnetic field:

  \[\frac 1 2 \int_{z_1}^{z_2} |H|^2.\]

  In the lateral direction integration is performed over the whole domain.

  Parameters:

    - num (int) – Computed mode number.

    - z1 (float) – Lower vertical bound of the integral.

    - z2 (float) – Upper vertical bound of the integral.

  Returns:

    Computed integral [A2 / m2].

  Return type:

    float

  Warning

  This method may return incorrect results for layers with gain, due to the strong non-Hemiticity!

Fourier3D.invalidate()

  Set the solver back to uninitialized state.

  This method frees the memory allocated by the solver and sets `initialized` to False.

Fourier3D.layer_eigenmodes(level)

  Get eignemodes for a layer at specified level.

  This is a low-level function to access diagonalized eigenmodes for a specific layer. Please refer to the detailed solver description for the interpretation of the returned values.

  Parameters:

    level (float) – Vertical level at which the coefficients are computed.

  Return type:

    `Eigenmodes`

Fourier3D.scattering(side, coeffs)
Fourier3D.scattering(side, idx)
Fourier3D.scattering(side, polarization)

  Access to the reflected field.

  Parameters:

    - side (top or bottom) – Side of the structure where the incident light is present.

    - polarization – Specification of the incident light polarization. It should be a string of the form ‘E#‘, where # is the axis name of the non-vanishing electric field component.

    - idx – Eigenmode number.

    - coeffs – expansion coefficients of the incident vector.

  Return type:

    Fourier3D.Scattering

Fourier3D.scattering_gaussian(side, polarization, sigma, center=(0.0, 0.0))

  Helper function to Access reflected fields for access incidence.

  This method is equivalent to calling:

      >>> fourier.scattering(side,
      ...     fourier.gaussian(side, polarization, sigma, center))

  Parameters:

    - side (top or bottom) – Side of the structure where the incident light is present.

    - polarization – Specification of the incident light polarization. It should be a string of the form ‘E#‘, where # is the axis name of the non-vanishing electric field component.

    - sigma (float) – Gaussian standard deviation (µm).

    - center (float) – Position of the beam center (µm).

Fourier3D.set_interface(object, path=None)
Fourier3D.set_interface(pos)

  Set interface at the bottom of the specified object.

  Parameters:

    - object (geometry object) – object to set the interface at.

    - path (path) – Optional path specifying an instance of the object.

  Set interface as close as possible to the specified position.

  Parameters:

    pos (float) – Position, near which the interface will be located.

Fourier3D.set_mode(*args, **kwargs)

  Set the mode for specified parameters.

  This method should be used if you have found a mode manually and want to insert it into the solver in order to determine the fields. Calling this will raise an exception if the determinant for the specified parameters is too large.

  Arguments can be given through keywords only.

  Parameters:

    - lam (complex) – Wavelength (nm).

    - k0 (complex) – Normalized frequency (1/µm).

    - klong (complex) – Longitudinal wavevector (1/µm).

    - ktran (complex) – Transverse wavevector (1/µm).

### Receiver Details

Fourier3D.inCarriersConcentration = <property object>

  Receiver of the carriers concentration required for computations [1/cm³].

  You will find usage details in the documentation of the receiver class `CarriersConcentrationReceiver3D`.

  Example

  Connect the receiver to a provider from some other solver:

      >>> solver.inCarriersConcentration = other_solver.outCarriersConcentration

  See also

  Receciver class: `plask.flow.CarriersConcentrationReceiver3D`

  Provider class: `plask.flow.CarriersConcentrationProvider3D`

  Data filter: `plask.filter.CarriersConcentrationFilter3D`

Fourier3D.inEpsilon = <property object>

  Receiver of the permittivity tensor required for computations [-].

  You will find usage details in the documentation of the receiver class `EpsilonReceiver3D`.

  Example

  Connect the receiver to a provider from some other solver:

      >>> solver.inEpsilon = other_solver.outEpsilon

  See also

  Receciver class: `plask.flow.EpsilonReceiver3D`

  Provider class: `plask.flow.EpsilonProvider3D`

  Data filter: `plask.filter.EpsilonFilter3D`

Fourier3D.inGain = <property object>

  Receiver of the material gain required for computations [1/cm].

  You will find usage details in the documentation of the receiver class `GainReceiver3D`.

  Example

  Connect the receiver to a provider from some other solver:

      >>> solver.inGain = other_solver.outGain

  See also

  Receciver class: `plask.flow.GainReceiver3D`

  Provider class: `plask.flow.GainProvider3D`

  Data filter: `plask.filter.GainFilter3D`

Fourier3D.inTemperature = <property object>

  Receiver of the temperature required for computations [K].

  You will find usage details in the documentation of the receiver class `TemperatureReceiver3D`.

  Example

  Connect the receiver to a provider from some other solver:

      >>> solver.inTemperature = other_solver.outTemperature

  See also

  Receciver class: `plask.flow.TemperatureReceiver3D`

  Provider class: `plask.flow.TemperatureProvider3D`

  Data filter: `plask.filter.TemperatureFilter3D`

### Provider Details

Fourier3D.outDownwardsLightE(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed electric field [V/m].

  Parameters:

    - n (int) – Number of the mode found with `find_mode()`.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the electric field on the specified mesh [V/m].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeLightE = solver.outDownwardsLightE

  Obtain the provided field:

      >>> solver.outDownwardsLightE(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outDownwardsLightE)
      3

  See also

  Provider class: `plask.flow.ModeLightEProvider3D`

  Receciver class: `plask.flow.ModeLightEReceiver3D`

Fourier3D.outDownwardsLightH(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed magnetic field [A/m].

  Parameters:

    - n (int) – Number of the mode found with `find_mode()`.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the magnetic field on the specified mesh [A/m].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeLightH = solver.outDownwardsLightH

  Obtain the provided field:

      >>> solver.outDownwardsLightH(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outDownwardsLightH)
      3

  See also

  Provider class: `plask.flow.ModeLightHProvider3D`

  Receciver class: `plask.flow.ModeLightHReceiver3D`

Fourier3D.outEpsilon(mesh, lam=DEFAULT, interpolation='default') = <property object>

  Provider of the computed permittivity tensor [-].

  Parameters:

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

    - lam (float) – Complex wavelength at which the epsilon tensor is computed (nm).

  Returns:

    Data with the permittivity tensor on the specified mesh [-].

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inEpsilon = solver.outEpsilon

  Obtain the provided field:

      >>> solver.outEpsilon(mesh, lam=DEFAULT)
      <plask.Data at 0x1234567>

  See also

  Provider class: `plask.flow.EpsilonProvider3D`

  Receciver class: `plask.flow.EpsilonReceiver3D`

Fourier3D.outGradients(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed refractive index gradient functions cos² and cos·sin [-]. Gradients are important if the new factorization rule is used.

  Parameters:

    - n (int) – Value number.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the refractive index gradient functions cos² and cos·sin on the specified mesh [-].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inGradientFunctions = solver.outGradients

  Obtain the provided field:

      >>> solver.outGradients(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outGradients)
      3

  See also

  Provider class: `plask.flow.GradientFunctionsProvider3D`

  Receciver class: `plask.flow.GradientFunctionsReceiver3D`

Fourier3D.outLightE(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed electric field [V/m].

  Parameters:

    - n (int) – Number of the mode found with `find_mode()`.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the electric field on the specified mesh [V/m].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeLightE = solver.outLightE

  Obtain the provided field:

      >>> solver.outLightE(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outLightE)
      3

  See also

  Provider class: `plask.flow.ModeLightEProvider3D`

  Receciver class: `plask.flow.ModeLightEReceiver3D`

Fourier3D.outLightH(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed magnetic field [A/m].

  Parameters:

    - n (int) – Number of the mode found with `find_mode()`.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the magnetic field on the specified mesh [A/m].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeLightH = solver.outLightH

  Obtain the provided field:

      >>> solver.outLightH(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outLightH)
      3

  See also

  Provider class: `plask.flow.ModeLightHProvider3D`

  Receciver class: `plask.flow.ModeLightHReceiver3D`

Fourier3D.outLightMagnitude(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed optical field magnitude [W/m²].

  Parameters:

    - n (int) – Number of the mode found with `find_mode()`.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the optical field magnitude on the specified mesh [W/m²].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeLightMagnitude = solver.outLightMagnitude

  Obtain the provided field:

      >>> solver.outLightMagnitude(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outLightMagnitude)
      3

  See also

  Provider class: `plask.flow.ModeLightMagnitudeProvider3D`

  Receciver class: `plask.flow.ModeLightMagnitudeReceiver3D`

Fourier3D.outRefractiveIndex(n=0, mesh, lam=DEFAULT, interpolation='default') = <property object>

  Provider of the computed refractive index [-].

  Parameters:

    - comp (str) – Component of a diagonal refractive index derivative to return. Can be ‘ll’, ‘tt’, ‘vv’, or equivalent using current axes names. For scalar solvers this argument is ignored and can be skipped.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

    - lam (float) – Complex wavelength at which the refractive index is computed (nm).

  Returns:

    Data with the refractive index on the specified mesh [-].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inRefractiveIndex = solver.outRefractiveIndex

  Obtain the provided field:

      >>> solver.outRefractiveIndex(0, mesh, lam=DEFAULT)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outRefractiveIndex)
      3

  See also

  Provider class: `plask.flow.RefractiveIndexProvider3D`

  Receciver class: `plask.flow.RefractiveIndexReceiver3D`

Fourier3D.outUpwardsLightE(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed electric field [V/m].

  Parameters:

    - n (int) – Number of the mode found with `find_mode()`.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the electric field on the specified mesh [V/m].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeLightE = solver.outUpwardsLightE

  Obtain the provided field:

      >>> solver.outUpwardsLightE(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outUpwardsLightE)
      3

  See also

  Provider class: `plask.flow.ModeLightEProvider3D`

  Receciver class: `plask.flow.ModeLightEReceiver3D`

Fourier3D.outUpwardsLightH(n=0, mesh, interpolation='default') = <property object>

  Provider of the computed magnetic field [A/m].

  Parameters:

    - n (int) – Number of the mode found with `find_mode()`.

    - mesh (mesh) – Target mesh to get the field at.

    - interpolation (str) – Requested interpolation method.

  Returns:

    Data with the magnetic field on the specified mesh [A/m].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeLightH = solver.outUpwardsLightH

  Obtain the provided field:

      >>> solver.outUpwardsLightH(0, mesh)
      <plask.Data at 0x1234567>

  Test the number of provided values:

      >>> len(solver.outUpwardsLightH)
      3

  See also

  Provider class: `plask.flow.ModeLightHProvider3D`

  Receciver class: `plask.flow.ModeLightHReceiver3D`

Fourier3D.outWavelength(n=0) = <property object>

  Provider of the computed wavelength [nm].

  Parameters:

    n (int) – Value number.

  Returns:

    Value of the wavelength [nm].

  You may obtain the number of different values this provider can return by testing its length.

  Example

  Connect the provider to a receiver in some other solver:

      >>> other_solver.inModeWavelength = solver.outWavelength

  Obtain the provided value:

      >>> solver.outWavelength(n=0)
      1000

  Test the number of provided values:

      >>> len(solver.outWavelength)
      3

  See also

  Provider class: `plask.flow.ModeWavelengthProvider`

  Receciver class: `plask.flow.ModeWavelengthReceiver`

### Attribute Details

Fourier3D.dct = <property object>

  Type of discrete cosine transform for symmetric expansion.

Fourier3D.determinant_type = <property object>

  Type of determinant that is computed in root finding.

  This attribute specifies what is returned by the `get_determinant()` method. Regardless of the determinant type, its value must be zero for any mode.

  Can take on of the following values that specified what quantity is computed for the characteristic matrix:

  eigenvalue | Eigenvalue with the smallest magnitude
  full | Determinant of the matrix

Fourier3D.emission = <property object>

  Direction of the useful light emission.

  Necessary for the over-threshold model to correctly compute the output power. Currently the fields are normalized only if this parameter is set to `top` or `bottom`. Otherwise, it is `undefined` (default) and the fields are not normalized.

Fourier3D.geometry = <property object>

  Geometry provided to the solver

Fourier3D.grad_smooth = <property object>

  Smoothing parameter for material boundaries gradients (needed for the new expansion rule).

Fourier3D.group_layers = <property object>

  Layer grouping switch.

  If this property is `True`, similar layers are grouped for efficiency.

Fourier3D.id = <property object>

  Id of the solver object. (read only)

  Example

      >>> mysolver.id
      mysolver:category.type

Fourier3D.initialized = <property object>

  True if the solver has been initialized. (read only)

  Solvers usually get initialized at the beginning of the computations. You can clean the initialization state and free the memory by calling the `invalidate()` method.

Fourier3D.interface = <property object>

  Matching interface position.

Fourier3D.k0 = <property object>

  Normalized frequency of the light (1/µm).

  Use this property only if you are looking for anything else than the wavelength,e.g. the effective index of lateral wavevector.

Fourier3D.klong = <property object>

  Longitudinal propagation constant of the light (1/µm).

  Use this property only if you are looking for anything else than the longitudinal component of the propagation vector and the effective index.

Fourier3D.ktran = <property object>

  Transverse propagation constant of the light (1/µm).

  Use this property only if you are looking for anything else than the transverse component of the propagation vector.

Fourier3D.lam = <property object>

  Wavelength of the light (nm).

  Use this property only if you are looking for anything else than the wavelength, e.g. the effective index of lateral wavevector.

Fourier3D.lam0 = <property object>

  Reference wavelength.

  This is a wavelength at which refractive index is retrieved from the structure. If this parameter is None, material parameters are computed each time, the wavelength changes even slightly (this is most accurate, but can be very inefficient.

Fourier3D.layer_centers = <property object>

  Vertical posiotions of centers of each layer.

  At these positions materials and temperatures are probed.

Fourier3D.layer_edges = <property object>

  Vertical posiotions of egges of each layer.

Fourier3D.modes = <property object>

  Computed modes.

Fourier3D.pmls = <property object>

  Longitudinal and transverse edge Perfectly Matched Layers boundary conditions.

  Attributes:

  `factor` | PML scaling factor.
  `shape` | PML shape order (0 → flat, 1 → linearly increasing, 2 → quadratic, etc.).
  `dist` | PML distance from the structure.
  `size` | PML size.

  Return type:

    PML

Fourier3D.refine = <property object>

  Number of refinement points for refractive index averaging in longitudinal and transverse directions.

Fourier3D.root = <property object>

  Configuration of the root searching algorithm.

  Attributes:

  `alpha` | Parameter ensuring sufficient decrease of determinant in each step (Broyden method only).
  `lambd` | Minimum decrease ratio of one step (Broyden method only).
  `initial_range` | Initial range size (Muller and Brent methods only).
  `maxiter` | Maximum number of iterations.
  `maxstep` | Maximum step in one iteration (Broyden method only).
  `method` | Root finding method ('muller', 'broyden', or 'brent')
  `tolf_max` | Required tolerance on the function value.
  `tolf_min` | Sufficient tolerance on the function value.
  `tolx` | Absolute tolerance on the argument.

  Return type:

    RootParams

Fourier3D.rule = <property object>

  Permittivity inversion rule.

  Can be ‘direct’, ‘inverse’, ‘combined’, or ‘old’. The new ‘combined’ rule is supposed to provide the best convergence. ‘old’ is available for consistency with old results.

Fourier3D.size = <property object>

  Orthogonal expansion sizes in longitudinal and transverse directions.

Fourier3D.smooth = <property object>

  Smoothing parameter for material boundaries (increases convergence).

Fourier3D.stack = <property object>

  Stack of distinct layers.

Fourier3D.symmetry = <property object>

  Longitudinal and transverse mode symmetries.

Fourier3D.temp_diff = <property object>

  Maximum temperature difference between the layers in one group.

  If a temperature in a single layer varies vertically more than this value, the layer is split into two and put into separate groups. If this is empty, temperature gradient is ignored in layers grouping.

Fourier3D.temp_dist = <property object>

  Temperature probing step.

  If `temp_diff` is not `None`, the temperature is laterally probed in points approximately separated by this distance.

Fourier3D.temp_layer = <property object>

  Temperature probing step.

  If `temp_diff` is not `None`, this is the minimum thickness of sublayers resulting from temperature-gradient division.

Fourier3D.transfer = <property object>

  Preferred transfer method.

  Can take on of the following values:

  auto | Automatically choose the best method
  reflection | Reflection Transfer Method
  admittance | Admittance Transfer Method
  impedance | Impedance Transfer Method

  Reflection transfer can have optional suffix `-admittance` (default) or `-impedance`, in which case the admittance/impedance matching is done at interface (for eigenmode search). You should prefer admittance if electric field is expected to have significant horizontal components (particularly at the interface) i.e. for TE-like modes and impedance for TM-like modes.

Fourier3D.update_gain = <property object>

  Recompute dynamic parameters.

  If this attribute is set to True, material parameters are always recomputed for layers with gain or permittivity provided by py:`inEpsilon`. This allows to set ‘lam0’ for better efficiency and still consider slight changes of wavelength, where it matters the most.

Fourier3D.vpml = <property object>

  Vertical Perfectly Matched Layers boundary conditions.

  Attributes

  `factor` | PML scaling factor.
  `dist` | PML distance from the structure.
  `size` | PML size.

  Attribute `shape` is ignored for vertical PML (it is always 0).

Fourier3D.wavelength = <property object>

  Alias for `lam`