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

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.