Fractional Fourier transform of hollow Gaussian beam based on cylindrical coordinates

The analytic expression of the fractional Fourier transform (FRFT) based on cylindrical coordinates was derived. The transform relation between the lightintensity distribution on the fractional Fourier transform plane and the various beam parameters was discussed, and the numerical calculation was made. The transmission property of FRFT for the hollow Gaussian beam based on the on the cylindrical coordinates was obtained.