  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.
