Reciprocity and the scattering matrix of waveguide modes

TL;DR

This paper explores how the Lorentz reciprocity theorem constrains the scattering matrix of waveguide modes, showing that a specific matrix product involving the scattering matrix is symmetric, with applications to various waveguide configurations.

Contribution

It generalizes the reciprocity relations for waveguide scatterers to include complex, degenerate, and evanescent modes, providing a unified framework for analyzing waveguide scattering.

Findings

The matrix CS is symmetric for general waveguide modes.

Examples include waveguides surrounded by free space and discontinuities.

The framework applies to arbitrary mode types, including complex and evanescent modes.

Abstract

The implications of the Lorentz reciprocity theorem for a scatterer connected to waveguides with arbitrary modes, including degenerate, evanescent, and complex modes, are discussed. In general it turns out that a matrix $CS$ is symmetric, where $C$ is the matrix of generalized orthogonality coefficients, and $S$ is the scattering matrix. Examples are given, including a scatterer surrounded by waveguides or free space, and discontinuities of waveguides.