Method comparison for simulating non-Gaussian Beams and Diffraction for Precision Interferometry

TL;DR

This paper compares two wavefront decomposition methods, MEM and GBD, for simulating non-Gaussian beams in precision interferometry, evaluating their accuracy across various optical scenarios relevant to space-based gravitational wave detectors.

Contribution

It provides a systematic comparison of MEM and GBD methods, establishing their relative accuracy and applicability for different beam types and optical configurations in high-precision interferometry.

Findings

MEM more accurately models non-clipped Gaussian beams

GBD performs better with clipped Gaussian beams and surface interactions

Both methods are suitable for decomposing non-Gaussian beams depending on the context

Abstract

In the context of simulating precision laser interferometers, we compare via several examples two wavefront decomposition methods: the Mode Expansion Method (MEM) and the Gaussian beam decomposition (GBD) for their precision and applicability. To judge the performance of these methods, we define different types of errors and study their properties. We specify how the two methods can be fairly compared and based on that, the quality of the MEM and GBD are compared in several examples. We test here cases for which analytic results are available, i.e., non-clipped circular and general astigmatic Gaussian beams, as well as clipped circular Gaussian beams, in the near-, far-, and extreme far-field of millions of kilometers occurring in space-gravitational wave detectors. Additionally, we compare the methods for aberrated wavefronts and the interaction with optical components by testing reflections from differently curved mirrors. We find that both methods can be generally used for decomposing non-Gaussian beams. However, which method is more accurate depends on the optical system and simulation settings. In the given examples, the MEM more accurately describes non-clipped Gaussian beams, while for clipped Gaussian beams and the interaction with surfaces, the GBD is more precise.