In this paper, an optimal design approach for the diffractive phase element
s (DPE's) that implement rotationally symmetric Gaussian beam shaping in th
e fractional Fourier transform (FRFT) domain is presented. Simulation desig
n results for converting a rationally symmetric Gaussian beam into a unifor
m 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.