Spin-to-Orbital Optical Angular Momentum Conversion in Liquid Crystal "q-Plates": Classical and Quantum Applications

The angular momentum of light can be split into a spin and an orbital component (SAM and OAM). A few years ago, an optical process involving a conversion of angular momentum from one form to the other was conceived and experimentally demonstrated in a singular patterned liquid crystal cell, also known as "q-plate". In this paper, after reviewing the q-plate concept and technology, we will survey some of the most significant results that have originated from it, with particular attention to the possibility of realizing a physical one-to-one mapping between the polarization Poincaré sphere and an OAM subspace of an optical beam or of a single photon.