Matrix operators for complex interferometer analysis

TL;DR

This paper introduces a matrix formalism and operator approach for analyzing complex interferometric waveguide systems, effectively handling polarization, backreflection, and device dependencies for improved modeling accuracy.

Contribution

It presents a novel non-commutative operator and embedding matrices that simplify the analysis of complex interferometric systems, separating topology from device characteristics.

Findings

Enhanced modeling accuracy for complex interferometers

Simplified calculation of transfer functions

Effective handling of polarization and backreflection effects

Abstract

A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of the dependencies on connection topology from the dependencies on the devices and their specifications. A non-commutative operator and embedding matrices are introduced allowing a compact depiction of the salient optical equations, and straightforward calculation of the amplitude and intensity transfer functions.