Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications

A few years ago the possibility of coupling and inter-converting the spin and orbital angular momentum (SAM and OAM) of paraxial light beams in inhomogeneous anisotropic media was demonstrated. An important case is provided by waveplates having a singular transverse pattern of the birefringent optical axis, with a topological singularity of charge q at the plate center, hence named 'q-plates'. The introduction of q-plates has given rise in recent years to a number of new results and to significant progress in the field of orbital angular momentum of light. Particularly promising are the quantum photonic applications, because the polarization control of OAM allows the transfer of quantum information from the SAM qubit space to an OAM subspace of a photon and vice versa. In this paper, we review the development of the q-plate idea and some of the most significant results that have originated from it, and we will briefly touch on many other related findings concerning the interaction of the SAM and OAM of light.