Impact of atmospheric turbulence on the propagation properties of elegant Hermite higher-order cosine-hyperbolic Gaussian beams

This study examines the propagation characteristics of an elegant Hermite Higher-order cosh-Gaussian beam (EHHOChGB) in atmospheric turbulence. Using the extended Huygens–Fresnel diffraction integral and Rytov method, a detailed analytical formulation for the average intensity of the EHHOChGB propagation in a turbulent is developed. Numerical illustrations and a discussion of the impact of turbulence strength on the intensity distribution under varying initial beam parameters conditions are presented. The obtained results show that the profile of the initial EHHOChGB remains essentially unchanged over short propagation distances. As the beam propagates further, a central peak in intensity gradually emerges at a specific propagation distance ultimately leading to a Gaussian-like profile in the far field. The speed of increase in the central peak intensity is observed to accelerate with higher turbulence strength or when beam parameters such as the beam order m and Gaussian waist width ω₀ are reduced. Furthermore, for small values of the decentered parameter b, the intensity of the central peak exhibits two distinct behaviors based on the parity of m. In contrast, the cosh power parameter N makes the beam more resistant to turbulence as it increases. The results could be valuable for practical applications of EHHOChGB in free-space optical communications and remote sensing.