A new design approach for the diffractive phase elements (DPE’s) that implement beam shaping in the fractional Fourier transform (FRFT) domain is presented. The new algorithm can successfully achieve the design of DPE’s for beam shaping in both unitary and nonunitary transform systems. The unitarity transform condition of the FRFT domain is discussed. Modeling designs of the DPE’s are carried out for several fractional orders and different parameters of the beam for converting a Gaussian profile into a uniform beam. Our approach can realize beam shaping well for a nonunitary transform system in the FRFT domain.
© 1998 Optical Society of America
Original Manuscript: September 4, 1997
Revised Manuscript: December 1, 1997
Manuscript Accepted: November 17, 1997
Published: May 1, 1998
Yan Zhang, Bi-Zhen Dong, Ben-Yuan Gu, and Guo-Zhen Yang, "Beam shaping in the fractional Fourier transform domain," J. Opt. Soc. Am. A 15, 1114-1120 (1998)