# Discontinuities in the Electromagnetic Fields of Vortex Beams in the Complex Source/Sink Model

## TL;DR

This paper investigates unexpected discontinuities in the electromagnetic fields of vortex beams modeled by the complex source/sink approach, revealing their origin and proposing a method to avoid them, which impacts the physical realism of such models.

## Contribution

It identifies the source of discontinuities in nonparaxial vortex beam models and offers a simple method to eliminate these nonphysical features.

## Key findings

- Discontinuities occur for all odd orbital angular momentum modes.
- Discontinuities lead to nonphysical electromagnetic fields.
- A method to avoid these discontinuities is proposed.

## Abstract

An analytical discontinuity is reported in what was thought to be the discontinuity-free exact nonparaxial vortex beam phasor obtained within the complex source/sink model. This discontinuity appears for all odd values of the orbital angular momentum mode. Such discontinuities in the phasor lead to nonphysical discontinuities in the real electromagnetic field components. We identify the source of the discontinuities, and provide graphical evidence of the discontinuous real electric fields for the first and third orbital angular momentum modes. A simple means of avoiding these discontinuities is presented.