Modeling of Thermally Aberrated Optical Cavities for Gravitational Wave Detectors

As current and next-generation gravitational wave detectors strive for greater sensitivity, higher beam powers result in more thermal absorption within the interferometer cavities and test masses. This causes mirror deformation and scattering of the incident beam into higher order modes (HOMs), effects that are not fully understood. While attempts have been made to model these phenomena using the FINESSE software package, its modal basis for constructing optical fields requires and exponentially increasing number of HOMs for high accuracy results, leading to computational inefficiencies. Therefore, we model these effects using a linear canonical transform (LCT) framework. This grid-based numerical approach yields high spatial-frequency results and scales more effectively than FINESSE with increasingly complex optical fields. We present a discussion and analysis of this modeling in a LIGO detector arm cavity.