Laser Beam Atmospheric Propagation in Presence of Temperature Gradients: Anisotropy of Scintillation Index Field and Beam Centroid Variances

Optical systems play a vital role in free-space communications, remote sensing, and other atmospheric applications. Their performance is strongly influenced by atmospheric effects, which depend on optical path length, turbulence characteristics, and system design. Numerical simulations provide a controlled environment for studying these effects and testing diverse system configurations. Conventional models typically account only for turbulence, but field observations show that vertical temperature gradients from solar heating can also alter refractivity, causing significant beam energy redistribution and centroid trajectory deflection. To capture both turbulence and refractivity contributions, we employ the split-step method for solving the parabolic wave equation, representing phase shifts with a sequence of phase screens. We validated our software by comparing beam propagation simulations with published data, performing laser beam propagation over distances of 1–20 km and using Gaussian beams with radii from 5 mm to 20 cm, under both turbulent and non-turbulent conditions. The simulation results showed strong agreement with analytical predictions across weak and moderate scintillation regimes. Our research focuses on characterizing atmospheric optical effects in the presence of temperature gradients: we demonstrate anisotropy in the scintillation index field, with up to a 50% difference in beam centroid variance between vertical and horizontal directions at a 2 km propagation distance.