# Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

## TL;DR

This paper develops a Bessel series expansion based on the exact Helmholtz solution in cylindrical coordinates, enabling accurate and straightforward modeling of low-numerical-aperture focal waves in electromagnetic scattering.

## Contribution

It introduces a novel Bessel series expansion method for precise description of paraxial waves, facilitating easier implementation in scattering problems.

## Key findings

- Validated with Gaussian beams and focused fields
- Achieves accurate wave field evaluation in the paraxial regime
- Facilitates implementation in electromagnetic scattering simulations

## Abstract

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.