Numerical Simulations of Fractional Fourier Transform of Hypergeometric-Gaussian Beam

The fractional Fourier transform (FRFT) of a new type of laser beams called the hypergeometric-Gaussian beam (HyGGB) is investigated in detail. The analytical expression for the FRFT of a HyGGB is derived. The properties of a HyGGB in the FRFT plane with different parameters are illustrated. The results show that the intensity distribution of a HyGGB in the FRFT plane strongly depends on the fractional order, the lens focal length and the initial beam width.