Generation of twisted photons by undulators filled with dispersive medium

We study the radiation of twisted photons by undulators filled with a homogeneous dielectric dispersive medium and obtain the general formulas for the average number of radiated twisted photons. We consider in detail the radiation of undulators in the dipole regime and the radiation of helical and planar wigglers. The selection rules for radiation of twisted photons by such undulators are found. These selection rules generalize the known ones for undulators in a vacuum. In the case of a medium with plasma permittivity, the lower undulator harmonics do not form. As a result, in such undulators, the main contribution to radiation coming from the lowest allowed harmonic possesses a nonzero projection of orbital angular momentum in the paraxial regime. We investigate the influence of the anomalous Doppler effect on the properties of radiated twisted photons and find the parameters of the system ensuring that the produced radiation, in particular, the Vavilov–Cherenkov radiation, is a pure source of twisted photons with a definite nonzero projection of orbital angular momentum. As the examples, we consider the radiation of twisted photons by beams of electrons and protons in the undulators filled with helium and xenon. The parameters are chosen so as to be achievable at the present experimental facilities.