Computation of Scattering Matrices and their Derivatives for Waveguides

TL;DR

This paper presents a method for computing the stationary scattering matrix and its derivatives for Euclidean waveguides, including handling its complex continuation and high-order derivatives, supported by numerical results.

Contribution

It extends existing procedures to compute the scattering matrix and its derivatives for Euclidean waveguides, including complex continuation and high-order derivatives.

Findings

Successfully computed scattering matrices for waveguides.

Extended method to calculate high-order derivatives.

Numerical results demonstrating the algorithm's effectiveness.

Abstract

This paper describes the calculation of the stationary scattering matrix and its derivatives for Euclidean waveguides. This is an adaptation and extension to a procedure developed by Levitin and Strohmaier which was used to compute the stationary scattering matrix \cite{alexnew}. On Euclidean waveguides, the scattering matrix can be meromorphically continued from the complex plane to a Riemann surface with a countably infinite number of sheets. We describe in detail how we have dealt with this. In addition, our algorithm is also able to calculate arbitrarily high derivatives. In the final section, we will present the results of some numerical calculations obtained using this method.