Mode separator for a beam with an off-axis optical vortex

The Gaussian beam diffraction by a thin amplitude grating with a dislocatio n shifted relative to the beam axis is considered. The first-order diffract ed beam with an off-axis optical vortex is represented as a superposition o f Laguerre-Gauss modes. The optical scheme permitting the spatial separatio n of modes with even and odd mode indices is proposed and realised experime ntally. The method of separation is based on the difference in Gouy phase s hifts for focused beams. The possibility of separating photons with zero an d nonzero orbital angular momentum is discussed.