Orbital angular momentum of the vortex beams through a tilted lens

Properties of orbital angular momentum (OAM) of a linearly polarized vortex beam traversing a tilted lens is investigated in detail, where the influences stemming from the tilted angle of the lens and the separation between the beam and the lens are mainly focused on. It was shown that such an optical system can invert the sign of the topological charge of the incident vortex beam. The possibility of reversing the sign of OAM was discussed and it was found that it only depends on the elements of the ray transfer matrix of this optical system. Finally, a simple experiment was carried out to verify the theoretical results.