# Gaussian sharp-edge diffraction: a paraxial revisitation of Miyamoto-Wolf's theory

## TL;DR

This paper develops a paraxial extension of Miyamoto-Wolf's diffraction theory for Gaussian beams, introducing complex angles to model sharp-edge diffraction, and shows it aligns well with previous results.

## Contribution

It presents a novel paraxial formulation of Miyamoto-Wolf's theory for Gaussian beams using complex angles, enabling straightforward extension of boundary diffraction wave concepts.

## Key findings

- The extended theory agrees with existing diffraction results.
- Introduction of complex angles simplifies Gaussian beam diffraction analysis.
- Open questions remain on evaluating Gaussian geometrical shadows for complex apertures.

## Abstract

A "genuinely" paraxial version of Miyamoto-Wolf's theory aimed at dealing with sharp-edge diffraction under Gaussian beam illumination is presented. The theoretical analysis is carried out in such a way the well known Young-Maggi-Rubinowicz boundary diffraction wave theory can be extended to deal with Gaussian beams in an apparently straightforward way. The key for achieving such an extension is the introduction of suitable "complex angles" within the integral representations of the geometrical and BDW components of the total diffracted wavefield. Surprisingly enough, such a simple (although not rigorously justified) mathematical generalization seems to work well within the complex Gaussian realm. The resulting integrals provide meaningful quantities that, once suitably combined, give rise to predictions which are in perfect agreement with results already obtained in the past. An interesting and still open theoretical question about how to evaluate "Gaussian geometrical shadows" for arbitrarily shaped apertures is also discussed.