Fractional Fourier transform of an elliptical dark-hollow beam

The fractional Fourier transform (FRT) of an elliptical dark-hollow beam (EDHB) is studied in detail. Based on the definition of FRT in the rectangular coordinate system, analytical formulae are derived for the FRT of an EDHB with the help of a tensor method. The properties of an EDHB in the FRT plane are illustrated numerically by use of the derived formulae. The results show that the properties of the EDHB in the FRT plane are closely related to the parameters of the beam and to the fractional order. The derived formula provides a convenient way for analyzing and calculating the FRT of an EDHB.