Analysis of numerical diffraction calculation methods: from the perspective of phase space optics and the sampling...

Area of Science:

• Optics and Photonics
• Computational Physics
• Wave Propagation

Background:

• Numerical simulations of optical wave propagation are crucial for various applications.
• Existing diffraction calculation methods possess distinct transform and sampling properties.

Purpose of the Study:

• To provide a unified analysis of five popular fast diffraction calculation methods.
• To evaluate these methods from the perspective of phase space optics and sampling theorem.
• To illustrate the evolution of the space-bandwidth product (SBP) during wave propagation.

Main Methods:

• Analysis using phase space optics and sampling theorem.
• Utilizing phase space diagrams (PSD) and ABCD matrices.
• Comparison of single fast Fourier transform-based Fresnel transform, Fresnel transfer function, Fresnel impulse response, angular spectrum method, and Rayleigh-Sommerfeld convolution.

Main Results:

• All analyzed methods do not fully exploit the SBP of the input signal post-diffraction.
• Each method exhibits specific limitations and applicable ranges.
• Physical models explain the varying applicability of different diffraction calculation techniques.

Conclusions:

• Suggestions are provided for selecting appropriate diffraction calculation methods based on SBP and sampling properties.
• Guidance is offered on overcoming the inherent restrictions of existing methods.
• The study highlights the utility of PSD and ABCD matrices for intuitive understanding and discusses avenues for developing novel diffraction calculation methods.