Exact paraxial diffraction theory for polygonal apertures under Gaussian illumination

TL;DR

This paper develops an exact analytical model for the diffraction of Gaussian beams through polygonal apertures using boundary diffraction wave theory, revealing links between optics and probability theory.

Contribution

It introduces closed-form solutions for paraxial diffraction by polygonal apertures, bridging classical optics and probability theory.

Findings

Exact diffraction expressions derived for polygonal apertures.

Established connection between diffraction phenomena and probability theory.

Provides analytical tools for precise modeling of Gaussian beam diffraction.

Abstract

Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are obtained, as well as an interesting connection between classical optics and probability theory.