Refractive Effects Induced by Temperature Gradients in Short-Range Laser Beam Propagation

Accurately describing atmospheric effects requires incorporating atmospheric refractivity—the slowly varying, large-scale component of the refractive index. Spatial refractivity gradients modify optical trajectories and can induce anisotropy. Standard wave-optics methods often omit these contributions because of their complexity, relying instead on ray tracing to represent refractivity influences. This simplification, however, overlooks anisotropy effects driven by temperature-induced refractivity gradients. Existing treatments of optical anisotropy are largely ad hoc, and commonly used non-Kolmogorov turbulence models provide limited predictive capability in this context. To address this gap, we investigate how temperature gradients, and the resulting refractivity distributions, affect optical wave propagation in the atmosphere. We developed a Python-based split-step propagation code in which refractivity variations are incorporated through phase screens. The results reveal anisotropy in the long-exposure laser beam footprint caused by temperature gradients, with vertical and horizontal beam sizes differing by up to a factor of two after 2 km of propagation.