2D H-polarized Auxiliary Basis Functions for the Extension of the Photonic Wannier Function Expansion for Photonic Crystal Circuitry

Report on accuracy improvements in the numerical computation of localized defect modes (classical light modes) by expanding the wave equations into Wannier functions. Several sets of auxiliary basis functions are suggested which describe non-continuously differentiable magnetic fields in H-polarization properly. Furthermore, improvements of the numerical Souza-Marzari-Vanderbilt Wannier function generation algorithm based on group theoretical analysis are discussed.