Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell model beams

Abstract

By adopting a new tensor method, we derive an analytical transform formula for the cross-spectral density matrix of partially coherent and partially polarized Gaussian–Schell model (GSM) beams through a fractional Fourier transform (FRT) optical system. Using the formula derived, we study the polarization and intensity distribution properties of partially coherent and partially polarized GSM beams in the FRT plane. The results show that the polarization and intensity distribution properties in the FRT plane are closely related to the fractional order of the FRT optical system and the initial coherence of the partially coherent beam. The transformation properties of an ordinary scalar GSM beam and partially coherent and partially polarized GSM beams are compared and discussed. Our method provides a simple and convenient way to study the FRT of partially coherent and partially polarized GSM beams.