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

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 $l=\pm 1$ 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.

arXiv comment20 pp., 5 figs; 22 pp., 6 figs, some misprints corrected

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Cited by in corpus (8)

• Geometric theory of topological defects: methodological developments and new trends
• Scattering of plane-wave and twisted photons by helical media
• Angular momentum transfered by the field of a moving point charge
• Observation of transition radiation carrying orbital angular momentum
• Short wavelength band structure of photons in cholesteric liquid crystals
• Multichannel scattering for the Schrödinger equation on a line with different thresholds at both infinities
• Exploring spatial dispersion in helical wired media: An effective field theory approach
• Radiation of twisted photons in elliptical multifrequency undulators