Selection rules for the scattering of twisted photons by helical media

In the present paper, we study the mechanism of interaction of twisted photons with helically symmetric dielectrics. In the framework of quantum electrodynamics in a dispersive medium, the problem of scattering of twisted photons by a slab made of a helical medium is solved. High orders of perturbation theory are considered. The selection rules for the scattered wave are revealed. It is shown that the medium imparts a longitudinal momentum to the photon as well as an additional projection of the total angular momentum onto the axis of helical symmetry of the medium. It is shown that the selection rules are satisfied for all orders of the perturbation theory and, therefore, are valid in the nonperturbative regime, i.e., they are a general property of the scattering of electromagnetic waves on plates made of a helical medium placed into a homogeneous isotropic transparent dielectric.