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

The Gaussian beam diffraction by a thin amplitude grating with a dislocation shifted relative to the beam axis is considered. The first-order diffracted beam with an off-axis optical vortex is represented as a superposition of Laguerre-Gauss modes. The optical scheme permitting the spatial separation of modes with even and odd mode indices is proposed and realised experimentally. The method of separation is based on the difference in Gouy phase shifts for focused beams. The possibility of separating photons with zero and nonzero orbital angular momentum is discussed.