Transformation of a generalized Bessel–Laguerre–Gaussian beam by a paraxial ABCD optical system

Abstract

An analytical expression of a Generalized Bessel–Laguerre–Gaussian (GBLG) beam passing through a paraxial ABCD optical system is developed by using the generalized Huygens–Fresnel diffraction integral. This result is regarded as the main finding of this paper. Several studies such as the propagation of fundamental Gaussian, flat-topped Gaussian, Bessel–Gaussian, Generalized Bessel–Gaussian and Laguerre–Gaussian beams, through an ABCD optical system, are derived as particular cases of our principle investigation. Numerical simulations are performed, in this work, to illustrate the propagation properties of GBLG beam through a free space, a thin lens, a Fractional Fourier transform system and a quadratic graded-index system.