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In the context of simulating precision laser interferometers, we compare viaseveral examples two wavefront decomposition methods: the Mode Expansion Method(MEM) and the Gaussian beam decomposition (GBD) for their precision andapplicability. To judge the performance of these methods, we define differenttypes of errors and study their properties. We specify how the two methods canbe fairly compared and based on that, the quality of the MEM and GBD arecompared in several examples. We test here cases for which analytic results areavailable, i.e., non-clipped circular and general astigmatic Gaussian beams, aswell as clipped circular Gaussian beams, in the near-, far-, and extremefar-field of millions of kilometers occurring in space-gravitational wavedetectors. Additionally, we compare the methods for aberrated wavefronts andthe interaction with optical components by testing reflections from differentlycurved mirrors. We find that both methods can be generally used for decomposingnon-Gaussian beams. However, which method is more accurate depends on theoptical system and simulation settings. In the given examples, the MEM moreaccurately describes non-clipped Gaussian beams, while for clipped Gaussianbeams and the interaction with surfaces, the GBD is more precise.

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