nidn.trcwa package

Subpackages

• nidn.trcwa.utils package
  • Submodules
  • nidn.trcwa.utils.fft_funs module
  • nidn.trcwa.utils.kbloch module
  • nidn.trcwa.utils.torch_functions module
  • Module contents

Submodules

nidn.trcwa.compute_spectrum module

nidn.trcwa.compute_target_frequencies module

nidn.trcwa.compute_target_frequencies.compute_target_frequencies(min_physical_wl: float, max_physical_wl: float, N_freq: int, distribution: str)

Computes the target frequencies for a given set of physical frequencies.

Parameters

• min_physical_wl (float) – Minimum physical frequency in the target spectrum.

• max_physical_wl (float) – Maximum physical frequency in the target spectrum.

• N_freq (int) – The number of target frequencies.

• distribution (str) – The distribution of the target frequencies. Either linear or log.

Returns

Corresponding target frequencies

Return type

np.array

nidn.trcwa.constants module

nidn.trcwa.init_trcwa module

nidn.trcwa.load_material_data module

nidn.trcwa.trcwa module

nidn.trcwa.trcwa.GetSMatrix(indi, indj, q_list, phi_list, kp_list, thickness_list)

Gets the S matrices, S_ij: size 4n*4n.

Parameters

• indi (int) – Start layer index.

• indj (int) – End layer index. Must be >= indi.

• () (thickness_list) –

• () –

• () –

• () – List of thicknesses for each layer in the stack.

Returns

S11, S12, S21, S22

Return type

torch.tensor, torch.tensor, torch.tensor, torch.tensor

nidn.trcwa.trcwa.GetZPoyntingFlux(ai, bi, omega, kp, phi, q, byorder=0)

Returns 2S_z/A, following Victor Liu’s notation.

Parameters

• () (q) –

• () –

• omega (float) – The angular frequency.

• () –

• () –

• () –

• byorder (int, optional) – If the Poynting flux is to be given for each order (byorder > 0) or summed (= 0). Defaults to 0.

Returns

The Poynting flux in the forward and backward direction, given as a number or a list of numbers

Return type

torch.tensor, torch.tensor

nidn.trcwa.trcwa.Gmeshgrid(x)

.

Parameters

() (x) –

Returns

qi, qj

Return type

torch.tensor, torch.tensor

nidn.trcwa.trcwa.MakeKPMatrix(omega, layer_type, epinv, kx, ky)

Makes KP matrix.

Parameters

• omega (float) – The angular frequency.

• layer_type (int) – Uniform or patterned layer. Set to 0 for uniform layers and >0 for patterned.

• () (ky) –

• () –

• () –

Return type

torch.tensor

nidn.trcwa.trcwa.Matrix_zintegral(q, thickness, shift=1e-12)

Generate matrix for z-integral.

Parameters

• () (q) –

• thickness (float) – Thickness of the layer of interest.

• shift (float, optional) – . Defaults to 1e-12.

Returns

Matrix for z-integral

Return type

torch.tensor

nidn.trcwa.trcwa.SolveExterior(a0, bN, q_list, phi_list, kp_list, thickness_list)

Given a0, bN, solve for b0, aN.

Parameters

• () (thickness_list) –

• () –

• () –

• () –

• () –

• () – List of thicknesses for each layer in the stack.

Returns

aN, b0

Return type

torch.tensor, torch.tensor

nidn.trcwa.trcwa.SolveInterior(which_layer, a0, bN, q_list, phi_list, kp_list, thickness_list)

Given a0, bN, solve for ai, bi

Parameters

• which_layer (int) – The layer to solve for. Layer numbering starts from 0.

• () (thickness_list) –

• () –

• () –

• () –

• () –

• () – List of thicknesses for each layer in the stack.

Returns

ai, bi

Return type

torch.tensor, torch.tensor

nidn.trcwa.trcwa.SolveLayerEigensystem(omega, kx, ky, kp, ep2)

Solves the eigensystem.

Parameters

• omega (float) – The angular frequency. Unused (from GRCWA).

• () (ep2) –

• () –

• () –

• () –

Returns

q, phi

Return type

torch.tensor, torch.tensor

nidn.trcwa.trcwa.SolveLayerEigensystem_uniform(omega, kx, ky, epsilon)

Solves the eigensystem for uniform layers.

Parameters

• omega (float) – The angular frequency.

• () (epsilon) –

• () –

• () –

Returns

q, phi

Return type

torch.tensor, torch.tensor

class nidn.trcwa.trcwa.TRCWA(nG, L1, L2, freq, theta, phi, verbose=1)

Bases: object

Add_LayerFourier(thickness, params)

Add_LayerGrid(thickness, Nx, Ny)

Add_LayerUniform(thickness, epsilon)

GetAmplitudes(which_layer, z_offset)

To get the Fourier amplitude of the eigenvectors at some layer and at some zoffset. Returns the raw mode amplitudes within a particular layer. For uniform (unpatterned) layers, the modes are simply the diffracted orders The first value is guaranteed to be the straight transmitted or specularly reflected diffraction order. For patterned layers, there is typically no meaningful information in these amplitudes.

Parameters

• which_layer (int) – Which layer to return the Fourier amplitude from.

• z_offset (float) – The z-offset at which to obtain the mode amplitudes. Must be 0 < z_offset < layer thickness.

Returns

ai, bi; containing the complex amplitudes of each forward and backward mode

Return type

torch.tensor

GetAmplitudes_noTranslate(which_layer)

To get the amplitude of the eigenvectors at some layer.

Parameters

which_layer (int) – Which layer to return the Fourier amplitude from.

Returns

ai, bi; each containing the complex amplitudes of each forward and backward mode

Return type

torch.tensor

GridLayer_geteps(ep_all)

Fourier transform + eigenvalue for grid layer.

Parameters

ep_all (torch.tensor) – A tensor containing all epsilon values.

Init_Setup(Pscale=1.0, Gmethod=0)

Set up the reciprocal lattice, compute eigenvalues for uniform layers, and initialize vectors for patterned layers.

Parameters

• Pscale (float, optional) – To scale the periodicity in both lateral directions simultaneously (as an autogradable parameter). Period will be Pscale*Lx and Pscale*Ly.

• Gmethod (int, optional) – Fourier space truncation scheme; 0 for circular, 1 for rectangular.

MakeExcitationPlanewave(p_amp, p_phase, s_amp, s_phase, order=0, direction='forward')

Sets the excitation to be a planewave incident upon the front (first layer specified) or back of the structure. If both tilt angles are specified to be zero, then the planewave is normally incident with the electric field polarized along the x-axis for the p-polarization. The phase of each polarization is defined at the origin (z = 0).

Parameters

• p_amp (complex float) – The electric field amplitude of the p-polarizations of the planewave. Is a complex number with absolute value between 0 and 1.

• p_phase (float) – Phase of the p-polarized part of the light.

• s_amp (complex float) – The electric field amplitude of the s-polarizations of the planewave. Is a complex number with absolute value between 0 and 1.

• s_phase (float) – Phase of the s-polarized part of the light.

• order (int, optional) – A positive integer specifying which order (mode index) to excite. Defaults to 0.

• direction (string, optional) – The direction of the planewave (forward is incident upon the front). Defaults to “forward”.

RT_Solve(normalize=0, byorder=0)

Reflection and transmission power computation. Returns 2R and 2T, following Victor Liu’s notation (https://web.stanford.edu/group/fan/S4/python_api.html?highlight=power#S4.Simulation.GetPowerFlux).

Parameters

• normalize (int, optional) – To normalize the output when the 0-th media is not vacuum, or for oblique incidence. If normalize = 1, the output will be divided by n[0]*cos(theta). Defaults to 0.

• byorder (int, optional) – To get Poynting flux by order. If 0, the total power is computed. Defaults to 0.

Returns

Reflection power, Transmission power

Return type

torch.tensor

Return_eps(which_layer, Nx, Ny, component='xx')

Used to get real-space epsilon profile reconstructured from the truncated Fourier orders.

Parameters

• which_layer (int) – Which layer to return the epsilon values from.

• Nx (int) – Grid points within the unit cell in the x direction.

• Ny (int) – Grid points within the unit cell in the y direction.

• component (string, optional) – For patterned layer, component = ‘xx’,’xy’,’yx’,’yy’,’zz’. For uniform layer, currently it’s assumed to be isotropic. Defaults to “xx”.

Returns

Real-space epsilon profile

Return type

torch.tensor

Solve_FieldFourier(which_layer, z_offset)

Returns the field amplitude in Fourier space: [Ex,Ey,Ez], [Hx,Hy,Hz] :param which_layer: Which layer to return the field amplitude from. :type which_layer: int :param z_offset: The z-offset at which to obtain the field amplitude. Must be 0 < z_offset < layer thickness. Can be a single number or a list of numbers. :type z_offset: torch.tensor

Returns

Tensors containing the field amplitudes [Ex,Ey,Ez], [Hx,Hy,Hz] in Fourier space

Return type

torch.tensor

Solve_FieldOnGrid(which_layer, z_offset, Nxy=None)

To get fields in real space on grid points. If single z_offset, the output is [[Ex,Ey,Ez], [Hx,Hy,Hz]]. If z_offset is a list, the output os [[[Ex1,Ey1,Ez1],[Hx1,Hy1,Hz1]], [[Ex2,Ey2,Ez2],[Hx2,Hy2,Hz2]], …].

Parameters

• which_layer (int) – Which layer to return the field amplitude from.

• z_offset (torch.tensor) – The z-offset at which to obtain the field amplitude. Must be 0 < z_offset < layer thickness. Can be a single number or a list of numbers.

• Nxy (torch.tensor, optional) – Nxy = [Nx,Ny], if not supplied, will use the number in patterned layer.

Returns

Tensor containing the field amplitudes [[Ex,Ey,Ez], [Hx,Hy,Hz]] in Fourier space for each z-offset

Return type

torch.tensor

Solve_ZStressTensorIntegral(which_layer)

To compute the Maxwell stress tensor, integrated over the z-plane. Returns the integral of the electromagnetic stress tensor over a unit cell surface normal to the z-direction. Returns 2F_x,2F_y,2F_z, integrated over the z-plane.

Parameters

which_layer (int) – The layer in which the integration surface lies.

Returns

The real and imaginary parts of the x-, y-, and z-components of the stress tensor integrated over the specified surface, assuming a unit normal vector in the +z direction.

Return type

torch.tensor

Volume_integral(which_layer, Mx, My, Mz, normalize=0)

To get volume integration with respect to some convolution matrix M defined for 3 directions, respectively. Returns the volume integral of a particular density over a unit cell throughout the entire thickness of a layer. Mxyz is the convolution matrix. This function computes 1/Aint_V Mx|Ex|^2+My|Ey|^2+Mz|Ez|^2. To be consistent with Poynting vector defintion here, the absorbed power will be just omega*output.

Parameters

• which_layer (int) – Which layer to get the volume integral from.

• () (Mz) – Some convolution matrix M defined for the x-direction.

• () – Some convolution matrix M defined for the y-direction.

• () – Some convolution matrix M defined for the z-direction.

• normalize (int, optional) – If 1, the return value is normalized according to self.normalization. Defaults to 0.

Returns

Integration value.

Return type

float

nidn.trcwa.trcwa.TranslateAmplitudes(q, thickness, dz, ai, bi)

Parameters

• () (bi) – q for the layer of interest.

• thickness (float) – The thickness of the layer of interest.

• dz (float) – The z-offset at which to translate the amplitudes.

• () –

• () –

Returns

aim, bim

Return type

torch.tensor, torch.tensor

Module contents