Radiation of twisted photons from charged particles moving in cholesterics

TL;DR

This paper investigates the generation of twisted photons by charged particles passing through cholesteric plates, deriving explicit formulas and selection rules for the angular momentum of emitted photons in quantum electrodynamics framework.

Contribution

It provides a comprehensive quantum electrodynamics analysis of twisted photon radiation in anisotropic cholesteric media, including explicit solutions and new selection rules for angular momentum.

Findings

Derived explicit expressions for photon emission by charged particles in cholesterics.

Established selection rules for the angular momentum of radiated twisted photons.

Demonstrated potential of cholesteric plates as sources of twisted photons.

Abstract

The radiation of twisted photons by charged particles traversing a cholesteric plate is studied in the framework of quantum electrodynamics in an anisotropic inhomogeneous dispersive medium. The complete set of solutions to the Maxwell equations in the cholesteric plate is constructed in the paraxial and small anisotropy approximations. The explicit expressions for the average numbers of plane-wave and twisted photons created by a charged point particle crossing the cholesteric plate are derived. The selection rules for the twisted photons radiated at the harmonic $n\in \mathbb{Z}$ are established. In the paraxial regime, the projection of the orbital angular momentum of a radiated twisted photon obeys the selection rule $l=\pm(2n+1)$. In the approximation of a small anisotropy of the permittivity tensor, the selection rule becomes $m=\pm 2n$, where $m$ is the projection of the total angular momentum of a radiated twisted photon. The sign "$\pm$" in these selection rules is related to the choice of the forward or reflected waves in the cholesteric and is realized at the different energies of radiated photons. As the examples, the radiation of optical twisted photons by electrons with the Lorentz factors $\gamma=235$ and $\gamma=500$ and by uranium nuclei with $\gamma=2$ are considered. It is shown that charged particles traversing normally a cholesteric plate can be used as a pure source of twisted photons.