Integral transformation solution of free-space cylindrical vector beams and prediction of modified-Bessel-Gaussian vector beams

TL;DR

This paper introduces a unified integral transformation approach to describe free-space cylindrical vector beams, including known and new modified-Bessel-Gaussian vector beams, based on solutions to the vector Helmholtz equation.

Contribution

It provides a novel, unified integral transformation framework for cylindrical vector beams, predicting new beam types beyond existing solutions.

Findings

Includes known $J_1$ Bessel-Gaussian and Laguerre-Gaussian vector beams

Predicts two new modified-Bessel-Gaussian vector beams

Offers a flexible amplitude spectrum for beam design

Abstract

A unified description of the free-space cylindrical vector beams is presented, which is an integral transformation solution to the vector Helmholtz equation and the transversality condition. The amplitude 2-form of the angular spectrum involved in this solution can be arbitrarily chosen. When one of the two elements is zero, we arrive at either transverse-electric or transverse-magnetic beam mode. In the paraxial condition, this solution not only includes the known $J_1$ Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wave equations, but also predicts two new kinds of vector beam, called the modified-Bessel-Gaussian vector beam.