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By using quantum electrodynamics in a dispersive medium, we describescattering of plane-wave and twisted photons by a slab made of a helicalmedium, the helix axis being normal to the slab plane and the medium being nottranslation invariant in this plane, in general. In the particular cases, thepermittivity tensor of a helical medium corresponds to cholesteric liquidcrystals, $C^*$-smectics, biaxial chiral nematics and smectics, $q$-plates,chiral sculptured thin films, and helical dislocations. Both perturbative andnonperturbative approaches are considered. The explicit expressions forscattering amplitudes, probabilities, and Stokes parameters of photons arefound taking into account the form of the photon wave packet. The selectionrules are established showing that the helical medium transfers the momentumand the angular momentum to scattered photons. This property can be employedfor production of twisted photons with large projection of the total angularmomentum. We describe the device for shifting the projection of the totalangular momentum of a photon and the principal scheme for signal coding interms of twisted photons.

Scattering of plane-wave and twisted photons by helical media