title: Fractional Fourier transform for partially coherent Gaussian-Schell model beams.
abstract: The fractional Fourier transform (FRT) is applied to partially coherent twisted anisotropic Gaussian-Schell model (GSM) beams based directly on the cross-spectral density. An analytical and concise formula is derived for the cross-spectral density of partially coherent twisted anisotropic GSM beams passing through a FRT system in terms of the tensor method. The corresponding tensor ABCD law for performing a FRT is obtained. The connection between the FRT formula and the generalized Collins formula for partially coherent beams is discussed. The formulas derived provide a powerful tool for analyzing and calculating the FRTs of partially coherent beams.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Lin
authors.forename: Yangjian
authors.initials: Y
authors.lastname: Cai