Gyrator transform of phase-flipped Gaussian beams and conversion of an edge-dislocation into a vortex

Based on the Gyrator transform (GT) formula, the closed-form field expression of a phase-flipped Gaussian beam (PFGB) passing through a GT system is presented. It is proved that PFGBs with edge dislocation can be converted into dark hollow vortex error-Gaussian beams with topological charge 1 through GT optical systems. With the help of numerical method, the influences of Fresnel number FN and GT transform angle α on intensity and phase distributions of the vortex beam are investigated. Moreover, the optimum relation between Fresnel number FN and the corresponding transform angle α for realizing a perfect dark hollow pattern is obtained.