Effect of quadratic radial variation of phase on single slit diffraction of Laguerre-Gauss vortex beams

Effect of quadratic radial phase variation in the plane of the aperture on Fraunhofer diffraction of Laguerre-Gauss vortex beams by a slit is studied experimentally. For slit positions near the incident beam waist, its effect is to shear the diffraction pattern relative to that at the waist. The magnitude and sense of shear depend on the topological charge and slit location relative to the incident beam waist. For slit positions far from the waist, the diffraction pattern evolves to be significantly different and is dominated by two strong peaks. A closed form analytical expression for the diffraction pattern is presented, which reproduces experimental results quite well for all slit positions.