# Probability of radiation of twisted photons in an inhomogeneous isotropic dispersive medium

## TL;DR

This paper derives a general formula for the probability of twisted photon radiation by charged particles in inhomogeneous isotropic dispersive media, with applications to dielectric plates, helical media, and microbunched beams, revealing angular momentum properties.

## Contribution

It introduces a new general formula for twisted photon emission probability in complex media and explores its implications for various structured materials and beam configurations.

## Key findings

- Twisted photons have zero angular momentum projection when particles move along the detector axis.
- Helically microbunched beams can generate high angular momentum twisted photons.
- Charged particles in helical media produce pure twisted photon radiation.

## Abstract

The general formula for probability to record a twisted photon produced by a charged particle moving in an inhomogeneous isotropic dispersive medium is derived. The explicit formulas for probability to record a twisted photon are obtained for the radiation of a charged particle traversing a dielectric plate or an ideally conducting foil. It is shown that, in the case when the charged particle moves along the detector axis, all the radiated twisted photons possess a zero projection of the total angular momentum and the probability of their radiation is independent of the photon helicity. The radiation produced by helically microbunched beams of charged particles is also considered. The fulfillment of the strong addition rule for the projection of the total angular momentum of radiated twisted photons is demonstrated. Thus the helical beams allow one to generate coherent transition and Vavilov-Cherenkov radiations with large projections of the total angular momentum. The radiation produced by charged particles in a helical medium is studied. Typical examples of such a medium are metallic spirals and cholesteric liquid crystals. It is shown that the radiation of a charged particle moving along the helical axis of such a medium is a pure source of twisted photons.