The Fractional Fourier Transform of Hypergeometric-Gauss Beams Through the Hard Edge Aperture

Abstract

Abstract-Based on the Collins integral formula and Lohmann optical system, we expand the hard edge aperture into complex Gauss function and derive an approximate analytic expression of intensity distribution theoretically for Hypergeometric-Gauss beams through the fractional Fourier transform (FRT) optical systems with hard edge aperture. The influences of FRT order, aperture size and other optical parameters on the light intensity distribution of Hypergeometric-Gauss beams passing through the FRT optical systems are discussed in detail. The results show that the FRT is an excellent beamshaping method.

Evolution properties of Laguerre higher order cosh-Gaussian beam propagating through fractional Fourier transform optical system

“…Since then, researchers have employed the technique in various applications including laser optics, signal processing, and image encryption (Mendlovic and Ozaktas, 1993;Ozaktas and Mendlovic, 1993;Lohmann, 1993;Mendlovic et al, 1994;Dorsch et al, 1995;Zhang et al 1998;Kutay and Ozaktas, 1998;Xue, 2001;Torre, 2002;Hannelly and Sheridan, 2003;Wang and Zhao, 2013). Researchers have explored the possibility of investigating the fractional Fourier transform of various models for light beams, such as elliptical Gaussian beams (Cai and Lin, 2009) Lorentz and Lorentz Gaussian beams (Zhou, 2009a,b), Anomalous hollow beam (Wang and Zhao, 2009), four-petal Gaussian beams (Tang 2009), Airy beam (Zhou et al 2012), confluent hypergeometric beams (Tang et al 2012), hollow sinh-Gaussian beams (Tang et al 2014), hypergeometric-Gaussian beams (Qu et al 2015), double-half inverse Gaussian hollow beams (Saad et al 2018), circular cosine hyperbolic-Gaussian beams (El Halba et al 2022) among others. In addition, many papers have been reported to study the propagation of vortices beams in FRFT including, Lorentz-Gauss vortex beams (Zhou et al 2013) vortex cosine hyperbolic-Gaussian beams (Hricha et al 2020), four-petal Gaussian vortex (Dai et al 2021), vortex Hermite-cosh-Gaussian beams (El Halba, 2021).…”