Modeling circulating cavity fields using the discrete linear canonical transform

TL;DR

This paper introduces a novel application of discrete linear canonical transforms (LCTs) to model circulating optical fields in complex Fabry-Perot cavities, enhancing accuracy in high-precision optical systems like aLIGO.

Contribution

It is the first to demonstrate that discrete LCTs can accurately model circulating fields in cavities with arbitrary optical properties, including imperfections.

Findings

LCT models match well with alternative methods.

LCT effectively models cavities with arbitrary apertures and profiles.

Application to aLIGO mirrors shows practical utility.

Abstract

Fabry-Perot cavities are central to many optical measurement systems. In high precision experiments, such as aLIGO and AdV, coupled cavities are often required leading to complex optical dynamics, particularly when optical imperfections are considered. We show, for the first time, that discrete LCTs can be used to compute circulating optical fields for cavities in which the optics have arbitrary apertures, reflectance and transmittance profiles, and shape. We compare the predictions of LCT models with those of alternative methods. To further highlight the utility of the LCT, we present a case study of point absorbers on the aLIGO mirrors and compare with recently published results.