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Abstract：
In the context of simulating precision laser interferometers, we use several examples to compare two wavefront decomposition methods-the Mode Expansion Method (MEM) and the Gaussian Beam Decomposition (GBD) method-for their precision and applicability. To assess 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, compare the quality of the MEM and GBD through several examples. Here, we test 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 extremely far fields of millions of kilometers occurring in space-gravitational wave detectors. Additionally, we compare the methods for aberrated wavefronts and their interaction with optical components by testing reflections from differently curved mirrors. We find that both methods can generally be 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, whereas for clipped Gaussian beams and the interaction with surfaces, the GBD is more precise.
摘要：
在模拟精密激光干涉仪的背景下，我们使用几个例子来比较两种波前分解方法-模式扩展方法（MEM）和高斯光束分解（GBD）方法-它们的精度和适用性。为了评估这些方法的性能，我们定义不同类型的错误并研究它们的性质。我们指定如何公平地比较这两种方法，并以此为基础，通过几个例子比较MEM和GBD的质量。这里,我们测试分析结果可用的案例，即，非限幅圆形和一般像散高斯光束，以及削波的圆形高斯光束，在附近，远,空间引力波探测器中出现了数百万公里的极远场。此外,通过测试不同曲面反射镜的反射，我们比较了畸变波前及其与光学元件相互作用的方法。我们发现这两种方法通常都可以用于分解非高斯光束。然而,哪种方法更准确取决于光学系统和模拟设置。在给定的例子中，MEM更准确地描述非限幅高斯光束，而对于限幅高斯光束和与表面的相互作用，GBD更精确。
