On optical Weber waves and Weber-Gauss beams

TL;DR

This paper investigates the normalization, mathematical relations, and decomposition of Weber waves and Weber-Gauss beams, providing methods to approximate these beams using Bessel-Gauss beams for practical applications.

Contribution

It introduces normalization techniques, integral relations, and decomposition methods for Weber waves and Weber-Gauss beams, enhancing understanding and computational approaches.

Findings

Normalized energy divergent Weber waves and Weber-Gauss beams are characterized.

Integral relations between Weber, Bessel, Mathieu, and elliptic waves are derived.

Efficient approximation of Weber-Gauss beams by Bessel-Gauss beams is demonstrated.

Abstract

The normalization of energy divergent Weber waves and finite energy Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used to derive the integral relations between circular, elliptic, and parabolic waves and to present the Bessel and Mathieu wave decomposition of the Weber waves. The efficiency to approximate a Weber-Gauss beam as a finite superposition of Bessel-Gauss beams is also given.