Operator based propagation of Whittaker and Helmholtz Gauss beams

TL;DR

This paper presents an operator-based method for solving the paraxial wave equation, enabling efficient propagation of structured light fields like Gaussian apodized Whittaker and Helmholtz beams, with experimental validation.

Contribution

The authors develop a compact operator technique that unifies and extends Gaussian beam families and simplifies the propagation of complex structured light fields.

Findings

Derived closed-form expressions for beam propagation

Confirmed transverse rotations of superposed Bessel Gauss beams experimentally

Demonstrated the method's speed and practicality as an alternative to diffraction integrals

Abstract

We introduce a compact operator-based technique that solves the paraxial wave equation for a broad class of structured light fields. Using the spatial evolution operator to propagate two families of physically apodized inputs, Gaussian apodized Whittaker integrals and Gaussian apodized Helmholtz fields, we derive closed form expressions that retain the Gaussian width and therefore describe finite energy beams. The method unifies and extends the Helmholtz Gauss families and readily generalizes to nonseparable nondiffracting architectures. Experiments on superposed Bessel Gauss beams confirm the predicted transverse rotations, demonstrating that this operator approach is a fast, transparent, and practical alternative to standard diffraction ntegral treatments