“…In the past few years, the fascinating properties of various kinds of laser beams propagating in turbulent atmosphere have received substantial interest (Nossir et al 2012, Chib et al 2023, Boufalah et al 2018, Shishter 2023, Saad et al 2017, Gbur 2014, Zhou 2011, 2009, Yaalou et al 2019, Ez-Zariy et al 2016and Zhong et al 2011). This attraction is due to their interesting applications in many areas of science and practical engineering including free-space optical communications (Navidpour et al 2007), remote sensing (Andrews and Phillips 1998), laser radar systems (Cai et al 2008), optical imaging (Hajjarian et al 2010), lattice spectroscopy (Han 2008) and so on. The turbulent atmosphere is considered as an inhomogeneous medium where small changes in the temperature occur thus causing the fluctuations in the refractive index, which induces beam dispersion, loss of spatial coherence and random fluctuations in light intensity and phase (Andrews and Phillips 1998).…”