"Analytical Continuation'' of Flattened Gaussian Beams

TL;DR

This paper introduces an analytical method to extend flattened Gaussian beams to any beam order, enabling closed-form solutions for their propagation through complex optical systems using special functions.

Contribution

It provides a novel analytical extension of flattened Gaussian beams applicable to any beam order, facilitating exact propagation analysis in optical systems.

Findings

Closed-form solutions for flat-top beam propagation

Use of bivariate confluent hypergeometric functions

Applicable to arbitrary $ABCD$ optical systems

Abstract

A purely analytical extension of the flattened Gaussian beams [Opt. Commun. \textbf{107,} 335 (1994)] to any values of the beam order, is here proposed. Due to it, the paraxial propagation problem of axially symmetric, coherent flat-top beams through arbitrary $ABCD$ optical systems can definitely be solved in closed form via a particular bivariate confluent hypergeometric function.