Rotationally symmetric beam shaping in the fractional Fourier transform domain

In this paper, an optimal design approach for the diffractive phase elements (DPE's) that implement rotationally symmetric Gaussian beam shaping in the fractional Fourier transform (FRFT) domain is presented. Simulation design results for converting a rationally symmetric Gaussian beam into a uniform circular top-hat beam are detailed for several different orders of FRFT. The good uniformity and roll-off characteristics of the output beam can be obtained with our method.