Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates

We present methods for generating and for sorting specific orbital angular momentum (OAM) eigenmodes of a light beam with high efficiency, using a liquid crystal birefringent plate with unit topological charge, known as \qo{q-plate}. The generation efficiency has been optimized by tuning the optical retardation of the q-plate with temperature. The measured OAM $m=\pm2$ eigenmodes generation efficiency from an input TEM$_{00}$ beam was of 97%. Mode sorting of the two input OAM $m=\pm2$ eigenmodes was achieved with an efficiency of 81% and an extinction-ratio (or cross-talk) larger than 4.5:1.