Asymmetric Cauchy-Riemann Beams

TL;DR

This paper explores the propagation dynamics of asymmetric Cauchy-Riemann beams, combining theoretical analysis and experiments to understand how Gaussian modulation and entire functions affect beam evolution in free space.

Contribution

It introduces a novel approach using quantum optics operators to analyze asymmetric Gaussian-modulated beams with Bessel and Airy functions, providing a new method for computing their propagation.

Findings

Parameter variations significantly affect beam propagation.

Asymmetry influences the beam's evolution in free space.

The study offers a comprehensive computational method for these beams.

Abstract

We investigate, theoretically and experimentally, the evolution of a paraxial beam propagating in free space when its initial transverse structure is characterized by an asymmetric Gaussian modulation combined with an entire function. Utilizing a quantum optics operator approach, our study specifically examines the effects of parameter variations within the Gaussian modulation on two entire functions: the Bessel function and the Airy function. Through this investigation, we aim to elucidate how these parameter variations influence the beam's propagation dynamics and the role played by the asymmetry of the Gaussian modulation in the propagation of such paraxial beams. Additionally, we provide a comprehensive method for computing the propagated field under these conditions.