TM_Polar_FDFD#

class TM_Polar_FDFD(omega, geometry)[source]#

Bases: Maxwell_Polar_FDFD

TM polarization FDFD solver in polar coordinates.

Solves the scalar Helmholtz equation for Ez field.

Parameters:
All attributes from Maxwell_Polar_FDFD, plus
M0#

Vacuum Maxwell operator (Laplacian - omega^2).

Type:

sp.csr_array

Methods Summary

get_GaaInv(A_mask[, chigrid])

Compute the inverse Green's function on region A, G_{AA}^{-1}.

get_TM_Gba(design_mask, observe_mask)

Compute vacuum Green's function from design to observation region.

get_TM_dipole_field(ir, iphi[, chigrid])

Get the field from a point dipole source at grid location (ir, iphi).

get_TM_field(sourcegrid[, chigrid])

Solve for the TM field given a source distribution.

get_symmetric_grids()

Get coordinate grid arrays.

Methods Documentation

get_GaaInv(A_mask, chigrid=None)[source]#

Compute the inverse Green’s function on region A, G_{AA}^{-1}.

Uses the Woodbury identity for block inversion.

Convention: J_A = GaaInv @ E_A

Parameters:

  • A_mask (BoolGrid) – Boolean mask for design region A.

  • chigrid (ComplexGrid, optional) – Material susceptibility. Default is vacuum.

Returns:

  • GaaInv (sp.csc_array) – Inverse Green’s function on region A.

  • M (sp.csc_array) – Full Maxwell operator used.

Return type:

tuple[csc_array, csc_array]

get_TM_Gba(design_mask, observe_mask)[source]#

Compute vacuum Green’s function from design to observation region.

Convention: E_obs = (i/ω) * G_ba @ J This means it is a propagator (i.e., it already contains its integral). Thus, G is scaled so we do not need to modify the field by areas before applying it.

Parameters:

  • design_mask (BoolGrid) – Boolean mask for source/design region (shape Nr x Nphi).

  • observe_mask (BoolGrid) – Boolean mask for observation region (shape Nr x Nphi).

Returns:

G_ba – Green’s function matrix (N_obs x N_design).

Return type:

ComplexArray

get_TM_dipole_field(ir, iphi, chigrid=None)[source]#

Get the field from a point dipole source at grid location (ir, iphi).

Parameters:

  • ir (int) – Radial grid index.

  • iphi (int) – Azimuthal grid index.

  • chigrid (ComplexGrid, optional) – Material susceptibility. Default is vacuum.

Returns:

Ez – Electric field solution.

Return type:

ComplexArray

get_TM_field(sourcegrid, chigrid=None)[source]#

Solve for the TM field given a source distribution.

Parameters:

  • sourcegrid (ComplexGrid) – Current source distribution (shape: Nphi * Nr or (Nphi, Nr)).

  • chigrid (ComplexGrid, optional) – Material susceptibility distribution. Default is vacuum.

Returns:

Ez – Electric field solution (flattened).

Return type:

ComplexArray

get_symmetric_grids()[source]#

Get coordinate grid arrays.

Returns:

  • phi_grid (FloatNDArray) – Azimuthal coordinates for the sector.

  • r_grid (FloatNDArray) – Radial coordinates.

  • phi_grid_full (FloatNDArray) – Azimuthal coordinates for full circle (for plotting).

Return type:

tuple[ndarray[tuple[int, …], dtype[float64]], ndarray[tuple[int, …], dtype[float64]], ndarray[tuple[int, …], dtype[float64]]]