Radiation of twisted photons in elliptical multifrequency undulators

TL;DR

This paper develops a comprehensive theory for the generation of twisted photons in elliptical multifrequency undulators, enabling controlled production of photon states with specific angular momentum properties.

Contribution

It introduces explicit formulas for radiation amplitude, analyzes energy spectra and selection rules, and links the results to virtual photon interactions, advancing the understanding of twisted photon generation in complex undulators.

Findings

Explicit radiation amplitude expressions derived.

Energy spectrum and TAM projection selection rules established.

Symmetry properties and virtual photon interpretation provided.

Abstract

The theory of radiation of twisted photons in elliptical multifrequency undulators is developed. It is shown that helical multifrequency undulators can be employed as a bright and versatile source of photons in the states that are superpositions of the modes with definite projection of total angular momentum (TAM), amplitude, and relative phase. All these parameters of the state are readily controlled by the undulator design. The explicit expression for the amplitude of radiation of a twisted photon from a charged particle in the multifrequency undulator is derived. The energy spectrum of radiation and the selection rules for the TAM projection of radiated photons are described. The symmetry properties of the spectrum with respect to the TAM projection are established. The interpretation to the energy spectrum and to the selection rules is given in terms of virtual photons mediating between the charged particle and the undulator. The results obtained are also applicable to radiation of twisted photons produced by ultrarelativistic charged particles moving in plane multifrequency electromagnetic waves.