Generation of hard twisted photons by charged particles in cholesteric liquid crystals

TL;DR

This paper investigates the generation of twisted photons with specific angular momentum properties by charged particles crossing a cholesteric liquid crystal, providing explicit formulas and potential applications in X-ray and UV photon production.

Contribution

It introduces a quantum electrodynamics framework for calculating twisted photon radiation in cholesteric plates, revealing the angular momentum and polarization characteristics of the emitted photons.

Findings

Twisted photons with orbital angular momentum l=2n+1 are produced, with n being an integer.

Mainly linearly polarized photons with l=±1 are emitted at specific harmonics.

Explicit spectra and photon counts are derived for different particle energies and photon energies.

Abstract

We study the radiation from charged particles crossing a cholesteric plate in the shortwave approximation when the wavelength of photons is much smaller than the pitch of the cholesteric helix whereas the escaping angle of the photon and the anisotropy of the permittivity tensor can be arbitrary. The radiation of photons is treated in the framework of quantum electrodynamics with classical currents. The radiation of the plane-wave photons and the photons with definite projection of the angular momentum (the twisted photons) produced by charged particles crossing the cholesteric plate and moving rectilinearly and uniformly is considered. The explicit expressions for the average number of radiated photons and their spectra with respect to the energy and the projection of the angular momentum are obtained in this case. It turns out that in the paraxial approximation the projection of the orbital angular momentum, $l$, of radiated twisted photons is related to the harmonic number $n\in \mathbb{Z}$ as $l=2n+1$, i.e., the given system is a pure source of twisted photons as expected. It is shown that in the paraxial shortwave regime the main part of radiated photons is linearly polarized with $l=\pm1$ at the harmonics $n=\{-1,0\}$. The applicability conditions of the approach developed are discussed. As the examples, we consider the production of $6.3$ eV twisted photons from uranium nuclei and the production of X-ray twisted photons from $120$ MeV electrons.