TM_FDFD#

class TM_FDFD(omega, geometry)[source]#

Bases: Maxwell_FDFD

Finite-difference frequency-domain solver for TM fields in 2D, with PMLs.

Parameters:
All of the attributes of the parent class Maxwell_FDFD, plus
M0#

Maxwell operator in sparse matrix format, representing the operator ∇x∇x - omega^2 I in 2D for TM fields.

Type:

sp.csc_array

Methods Summary

get_GaaInv(A_mask[, chigrid])

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

get_TM_Gba(A_mask, B_mask)

Compute the vacuum Green's function G_{BA}.

get_TM_dipole_field(cx, cy[, chigrid])

Get the field of a TM dipole source at position (cx, cy).

get_TM_field(sourcegrid[, chigrid])

Get the field of a TM source at positions in sourcegrid.

Methods Documentation

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

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

Utilizes the Woodbury identity to perform inversion. We partition the full Maxwell operator M into blocks corresponding to region A (design) and its complement B (background):

M = [[A, B],

[C, D]]

Then G_{AA}^{-1} = D - C A^{-1} B, up to a multiplicative constant MU_0 / k^2.

Parameters:

  • A_mask (np.ndarray of bool, shape (Nx, Ny)) – Mask for the design region A.

  • chigrid (np.ndarray of complex, optional) – Material susceptibility distribution. If provided, M = M0 + diag(ω² χ).

Returns:

  • GaaInv (sp.csc_array of shape (n_A, n_A)) – The inverse Green’s function on region A.

  • M (sp.csc_array) – The full Maxwell operator used in the computation.

Return type:

tuple[csc_array, csc_array]

get_TM_Gba(A_mask, B_mask)[source]#

Compute the vacuum Green’s function G_{BA}.

This function maps sources in region A to fields in region B.

This routine exploits translational symmetry by embedding two copies of the non-PML domain into a larger “big” grid. A single dipole solve at the center of the big grid produces a field map Ezfield. For each source location in the design (A_mask), we extract the corresponding window of size (nonpmlNx × nonpmlNy) and sample at the observation mask B_mask.

Parameters:

  • A_mask (np.ndarray of bool, shape (Nx, Ny)) – Mask specifying the source/design region in the full grid.

  • B_mask (np.ndarray of bool, shape (Nx, Ny)) – Mask specifying the observation region in the full grid.

Returns:

Gba – Green’s function matrix where each column is the field at B_mask due to a unit dipole at a location in A_mask.

Return type:

np.ndarray of complex, shape (n_B, n_A)

get_TM_dipole_field(cx, cy, chigrid=None)[source]#

Get the field of a TM dipole source at position (cx, cy).

Parameters:

  • cx (int) – x-coordinate of the dipole source.

  • cy (int) – y-coordinate of the dipole source.

  • chigrid (np.ndarray (dtype complex), optional) – spatial distribution of material susceptibility. The default is None, corresponding to vacuum.

Returns:

Ez – Field of the dipole source at position (cx, cy).

Return type:

np.ndarray (dtype complex)

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

Get the field of a TM source at positions in sourcegrid.

Parameters:

  • sourcegrid (np.ndarray (dtype complex)) – spatial distribution of the source.

  • chigrid (np.ndarray (dtype complex), optional) – spatial distribution of material susceptibility. The default is None, corresponding to vacuum.

Returns:

Ez – Field of the dipole source.

Return type:

np.ndarray (dtype complex)