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=±2 eigenmodes generation efficiency from an input TEM00 beam was of 97%. Mode sorting of the two input OAM m=±2 eigenmodes was achieved with an efficiency of 81% and an extinction-ratio (or cross-talk) larger than 4.5:1.
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