Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere

The so-called Generalized Bessel–Laguerre–Gaussian (GBLG) beam is introduced, in this paper, and an approximate formula of the average axial intensity of its propagation through a turbulent atmosphere is investigated using the extended Huygens–Fresnel diffraction integral in the paraxial approximation and on the Rytov theory. The analytical expression elaborated is regarded as the main result of this work. Several above studies are derived here as special cases from our research. The impact of some parameters, including incident beam parameters and turbulence strength, on the distribution of the axial intensity of the GBLG beam and on the profiles of some particular beams through a turbulent atmosphere are carried out numerically in the paper. From our numerical results-, the propagation of Gaussian beams, Laguerre–Gaussian beams and Bessel–Gaussian beams through the considered medium are deduced as particular cases.