Probability of radiation of twisted photons by classical currents

Abstract

The general formula for the probability of radiation of a twisted photon by a classical current is derived. The general theory of generation of twisted photons by undulators is developed. It is proved that the probability to record a twisted photon produced by a classical current is equal to the average number of twisted photons in a given state. The general formula for the projection of the total angular momentum of twisted photons with given the energy, the longitudinal projection of momentum, and the helicity is obtained. The symmetry property of the average number of twisted photons produced by a charged particle moving along a planar trajectory is found. The explicit formulas for the average number of twisted photons generated by undulators both in the dipole and wiggler regimes are obtained. It is established that, for the forward radiation of an ideal right-handed helical undulator, the harmonic number $n$ of the twisted photon coincides with its projection of the total angular momentum $m$. As for the ideal left-handed helical undulator, we obtain that $m=-n$. It is found that the forward radiation of twisted photons by a planar undulator obeys the selection rule that $n+m$ is an even number. It turns out that the average number of twisted photons produced by the undulator and detected off the undulator axis is a periodic function of $m$ in a certain spectral band of the quantum numbers $m$.

36 pp; some misprints corrected; formulas (48)-(51) changed

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• Probability of radiation of twisted photons by axially symmetric bunches of particles
• Probability of radiation of twisted photons in an inhomogeneous isotropic dispersive medium
• Generation of hard twisted photons by charged particles in cholesteric liquid crystals
• Probability of radiation of twisted photons by cold relativistic particle bunches
• Planar wiggler as a tool for generating hard twisted photons
• Probability of radiation of twisted photons in the infrared domain
• Radiation of twisted photons from charged particles moving in cholesterics
• Excitation of multipolar transitions in nuclei by twisted photons
• Generation of twisted photons by undulators filled with dispersive medium
• The angular momentum of electron radiation in a uniform magnetic field
• Radiative spin polarization in an ultrastrong magnetic field
• Proposal for the experimental observation of twisted photons in transition and Vavilov-Cherenkov radiations
• Emission of twisted photons by a scalar charged particle in a strong magnetic field
• Scattering of plane-wave and twisted photons by helical media
• Emission of twisted photons by a Dirac electron in a strong magnetic field
• Radiation of twisted photons in elliptical undulators
• Multiplexing signals with twisted photons by a circular arc phased array
• Observation of transition radiation carrying orbital angular momentum
• Production of twisted particles in heavy-ion collisions
• Angular momentum dynamics of vortex particles in accelerators
• Radiation of twisted photons in elliptical multifrequency undulators