Variable Phase S-Matrix Calculations for Asymmetric Potentials and Dielectrics

TL;DR

This paper introduces a variable phase method for calculating the S-matrix of asymmetric potentials and dielectrics, enabling efficient Casimir energy computations for complex objects.

Contribution

It develops a novel combined inward/outward integration algorithm for scalar and electromagnetic scattering, extending to asymmetric and position-dependent dielectric sources.

Findings

Efficient numerical algorithm for scalar potential scattering.

Extension of the method to electromagnetic scattering with mode disentanglement.

Robust computation of S-matrices for asymmetric and dielectric objects.

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.