“…In recent decades, the study of laser beam propagation through turbulent environments has gained significant traction due to its diverse applications in laser communications, remote sensing, laser radar, and optical weaponry, among other fields. A multitude of research endeavors have delved into various characteristics of laser beams in turbulent media, encompassing phenomena such as beam wander, beam spreading, scintillation index, intensity distribution, and field correlations (Wu et al 2016;Korotkova et al 2012;Hricha et al 2021;Baykal 2021;Nossir et al 2023;Saad et al 2023a;Schmidt, 2010;Andrews et al, 2001, Bayraktar, 2021aVoelz, 2011).…”