Effects of a turbulent atmosphere on an apertured Lommel-Gaussian beam

Abstract

In this paper, based on the generalized Huygens-Fresnel diffraction integral, the expansion of the hard aperture function into a finite sum of complex Gaussian functions and the Rytov theory method, we develop an approximate analytical expression of the on-axis intensity of Lommel–Gaussian beams passing through a turbulent atmosphere. The corresponding closed-forms for the unapertured Lommel–Gaussian, the aperture Lommel, the apertured/unapertured Bessel–Gaussian, the apertured Bessel and the apertured/unapertured fundamental Gaussian beams are derived in the work as special cases. Some of these theoretical results provide more accordance with other studies elaborated in the literature. Some numerical calculations are carried out to illustrate the effects of some parameters, such as the waist width, the wavelength, and the turbulence strength, on the on–axis intensity of Lommel–Gaussian at a z-plane of a turbulent atmosphere.