Paraxial wave propagation: Operator techniques

TL;DR

This paper explores the use of operator techniques to analyze paraxial wave propagation, drawing analogies with quantum mechanics, and demonstrates their application with Airy and Bessel function initial conditions.

Contribution

It introduces a novel application of operator methods to the paraxial wave equation, leveraging quantum analogies for practical electromagnetic field analysis.

Findings

Operator techniques effectively model paraxial wave propagation.

Analogies between Schrödinger and paraxial equations facilitate new analytical approaches.

Application with Airy and Bessel functions demonstrates practical utility.

Abstract

The similarity between the Schr\"odinger equation and the paraxial wave equation permits numerous analogies linking these fields, which is pivotal in advancing both quantum mechanics and wave optics. In this study, we demonstrate the application of operator techniques to an electromagnetic field characterized by the function $f(x + ay)$, leveraging the structural analogies between these equations. Specifically, we employ initial conditions defined by Airy and Bessel functions to illustrate the practical implementation of these techniques.