Behavior of Bessel–Whittaker–Gaussian beams through a paraxial optical system

Abstract

In this document, an original family of laser beams, referred to as Bessel–Whittaker–Gaussian beams (BWGBs), is presented as a general form of the Bessel–Gaussian and Whittaker–Gaussian beams. The analytical propagation expression of the BWGBs traveling through a paraxial ABCD optical system is developed on the basis of the Collins formula. Several graphical representations are used to explore the influence of the beams’ initial parameters, for instance beam orders (m, \(\xi\)), on the intensity distribution of the BWGBs as they propagate. The results show that m and \(\xi\) have a significant effect on the beams characteristics in free space. For a thin lens, the focal length modifies the shape of the beams. In a Fourier transform system, the intensity profile of the BWGBs becomes more focused as the focal length decreases. In contrast, in a fractional Fourier transform system, the effect of the parameter p is well noted. This work can be employed in light communications and optical trapping.