Paraxial Sharp-Edge Diffraction: A General Computational Approach

TL;DR

This paper introduces a versatile computational method for sharp-edge diffraction within the paraxial approximation, transforming the problem into a single boundary integral applicable to various wavefields and aperture shapes.

Contribution

It presents a novel reformulation using Poincaré vector potential within Fresnel integrals, enabling efficient analysis of arbitrary wavefields and aperture geometries.

Findings

Method reduces diffraction calculation to a single boundary integral.

Applicable to arbitrary wavefield distributions and aperture shapes.

Demonstrated with practical examples.

Abstract

A general reformulation of classical sharp-edge diffraction theory is proposed within paraxial approximation. The, not so much known, Poincar\'e vector potential construction is employed directly inside Fresnel's 2D integral in order for it to be converted into a single 1D contour integral over the aperture boundary. Differently from the recently developed paraxial revisitation of BDW's theory, such approach can be applied to arbitrary wavefield distributions impinging onto arbitrarily shaped sharp-edge planar apertures. A couple of interesting examples of application of the proposed method is presented.