Variable-phaseS-matrix calculations for asymmetric potentials and dielectrics

Abstract

Motivated by recently developed techniques making it possible to compute Casimir energies for any object whose scattering $S$ matrix (or, equivalently, $T$ matrix) is available, we develop a variable phase method to compute the $S$ matrix for localized but asymmetric sources. Starting from the case of scalar potential scattering, we develop a combined inward-outward integration algorithm that is numerically efficient and extends robustly to imaginary wave number. We then extend these results to electromagnetic scattering from a position-dependent dielectric. This case requires additional modifications to disentangle the transverse and longitudinal modes.