Fractional Fourier transform of flat-topped multi-Gaussian beams based on the Wigner distribution function

By using the Wigner distribution function (WDF), the fractional Fourier transform (FRFT) of flat-topped multi-Gaussian(FTMG) beams is studied. Analytical expressions for the intensity distribution, beam width, far-field divergence angle, M² factor and K parameter of FTMG beams are derived. The influence of fractional order on transformation properties of FTMG beams in the FRFT plane is illustrated with numerical examples.