Method Comparison for Simulating Non-Gaussian Beams and Diffraction for Precision Interferometry

Area of Science:

• Optical physics
• Computational optics
• Interferometry

Background:

• Precision laser interferometers are crucial for applications like gravitational wave detection.
• Accurate wavefront decomposition is essential for simulating these complex optical systems.
• Existing methods like MEM and GBD have different strengths and weaknesses.

Purpose of the Study:

• To compare the precision and applicability of the Mode Expansion Method (MEM) and Gaussian Beam Decomposition (GBD).
• To define and analyze errors associated with wavefront decomposition methods.
• To evaluate method performance across various optical scenarios, including extreme distances and aberrations.

Main Methods:

• Defined specific error types to quantitatively assess MEM and GBD performance.
• Developed a fair comparison framework for the two wavefront decomposition techniques.
• Tested methods on analytic cases: non-clipped and clipped Gaussian beams, astigmatic beams.
• Simulated performance in near, far, and extremely far fields (millions of kilometers).
• Evaluated method accuracy with aberrated wavefronts and reflections from curved mirrors.

Main Results:

• Both MEM and GBD are generally applicable for non-Gaussian beam decomposition.
• MEM demonstrated higher accuracy for non-clipped Gaussian beams.
• GBD showed greater precision for clipped Gaussian beams and simulations involving surface interactions.
• Method accuracy is contingent on the specific optical system and simulation parameters.

Conclusions:

• The choice between MEM and GBD depends on the specific requirements of the optical simulation.
• MEM is preferred for simulations prioritizing accuracy of non-clipped beam propagation.
• GBD is more suitable for scenarios involving beam clipping or complex optical surface interactions.
• This comparative analysis provides guidance for selecting the optimal wavefront decomposition method in optical simulations.