fmm.fourier_matrices_patterned_anisotropic_media

Return Fourier convolution matrices for patterned anisotropic media.

The transverse permittivity matrix E is defined as,

[-Dy, Dx]^T = E [-Ey, Ex]^T

while the transverse permeability matrix M is defined as,

[Bx, By]^T = M [Hx, Hy]^T

The Fourier factorization is done as for E1 given in equation 47 of [2012 Liu].

primitive_lattice_vectors: The primitive vectors for the real-space lattice.
permittivities: The elements of the permittivity tensor: (eps_xx, eps_xy, eps_yx, eps_yy, eps_zz), each having shape (..., nx, ny).
permeabilities: The elements of the permeability tensor: (mu_xx, mu_xy, mu_yx, mu_yy, mu_zz), each having shape (..., nx, ny).
expansion: The field expansion to be used.
formulation: Specifies the formulation to be used.
vector_field_source: Array used to calculate the vector field, with shape matching the permittivities and permeabilities.

inverse_z_permittivity_matrix: The Fourier convolution matrix for the inverse of the z-component of the permittivity. z_permittivity_matrix: The Fourier convolution matrix for the z-component of the permittivity. transverse_permittivity_matrix: The transverse permittivity matrix from equation 15 of [2012 Liu], computed in the manner prescribed by fmm_formulation. inverse_z_permeability_matrix: The Fourier convolution matrix for the inverse of the z-component of the permeability. z_permeability_matrix: The Fourier convolution matrix for the z-component of the permeability. transverse_permeability_matrix: The transverse permittivity matrix. tangent_vector_field: The tangent vector field (tx, ty) used to compute the transverse permittivity matrix, if a vector FMM formulation is used. If the FFT formulation is used, the vector field is None.