Analytical Solutions for Beams Passing Apertures with Sharp Boundaries

TL;DR

This paper develops an analytical approximation for the diffraction of beams passing through apertures with sharp boundaries, applicable to complex obstacle geometries, and validated by numerical and experimental comparisons.

Contribution

It introduces a new approximation method for paraxial beam diffraction through sharp-edged apertures, enabling exact solutions for certain initial conditions.

Findings

High accuracy demonstrated through numerical and experimental validation.

Exact solutions obtained for uniform fields with sharp boundaries.

Method applicable to complex obstacle structures and multiple sharp features.

Abstract

An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.