PLaSK User Manual

Fourier3D Class

class optical.slab.Fourier3D(name="")

Optical Solver using Fourier expansion in 3D.

It calculates optical modes and optical field distribution using Fourier slab 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].
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].
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
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.
oversampling Factor by which the number of coefficients is increased for FFT.
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.
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 Always update gain.
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, polarization)
Fourier3D.compute_reflectivity(lam, side, coffs)

Compute reflection coefficient on planar incidence [%].

Parameters:
  • lam (float or array of floats) – Incident light wavelength.
  • 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, polarization)
Fourier3D.compute_transmittivity(lam, side, coffs)

Compute transmission coefficient on planar incidence [%].

Parameters:
  • lam (float or array of floats) – Incident light wavelength.
  • 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.
  • k0 (complex) – Normalized frequency.
  • klong (complex) – Longitudinal wavevector.
  • ktran (complex) – Transverse wavevector.
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.
  • k0 (complex) – Normalized frequency.
  • klong (complex) – Longitudinal wavevector.
  • ktran (complex) – Transverse wavevector.
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(z1, z2)
Fourier3D.integrateEE(num, 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(z1, z2)
Fourier3D.integrateHH(num, 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, idx)
Fourier3D.scattering(side, polarization)
Fourier3D.scattering(side, coeffs)

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.
  • k0 (complex) – Normalized frequency.
  • klong (complex) – Longitudinal wavevector.
  • ktran (complex) – Transverse wavevector.

Receiver Details

Fourier3D.inCarriersConcentration

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 reveiver 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.inGain

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 reveiver 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

Receiver of the temperature required for computations [K].

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

Example

Connect the reveiver 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')

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')

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.outLightE(n=0, mesh, interpolation='default')

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')

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')

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
Fourier3D.outRefractiveIndex(mesh, interpolation='default')

Provider of the computed refractive index [-].

Parameters:
  • mesh (mesh) – Target mesh to get the field at.
  • interpolation (str) – Requested interpolation method.
Returns:

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

Example

Connect the provider to a receiver in some other solver:

>>> other_solver.inRefractiveIndex = solver.outRefractiveIndex

Obtain the provided field:

>>> solver.outRefractiveIndex(mesh)
<plask.Data at 0x1234567>
Fourier3D.outUpwardsLightE(n=0, mesh, interpolation='default')

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')

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)

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

Type of discrete cosine transform for symmetric expansion.

Fourier3D.determinant_type

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

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

Geometry provided to the solver

Fourier3D.group_layers

Layer grouping switch.

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

Fourier3D.id

Id of the solver object. (read only)

Example

>>> mysolver.id
mysolver:category.type
Fourier3D.initialized

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

Matching interface position.

Fourier3D.k0

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

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

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

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

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 wavelenght changes even slightly (this is most accurate, but can be very inefficient.

Fourier3D.layer_centers

Vertical posiotions of centers of each layer.

At these positions materials and temperatures are probed.

Fourier3D.layer_edges

Vertical posiotions of egges of each layer.

Fourier3D.modes

Computed modes.

Fourier3D.oversampling

Factor by which the number of coefficients is increased for FFT.

Fourier3D.pmls

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

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

Fourier3D.root

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.size

Orthogonal expansion sizes in longitudinal and transverse directions.

Fourier3D.smooth

Smoothing parameter for material boundaries (increases convergence).

Fourier3D.stack

Stack of distinct layers.

Fourier3D.symmetry

Longitudinal and transverse mode symmetries.

Fourier3D.temp_diff

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

Temperature probing step.

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

Fourier3D.temp_layer

Temperature probing step.

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

Fourier3D.transfer

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

Always update gain.

If this attribute is set to True, material parameters are always recomputed for layers with gains. This allows to set py:attr:lam0 for better efficiency and still update gain for slight changes of wavelength.

Fourier3D.vpml

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

Alias for lam