Long-range propagation through inhomogeneous turbulent atmosphere: analysis beyond phase screens

Many applications rely on the propagation of electromagnetic waves through extended regions of the atmosphere over which the refractive index can vary in a complex manner. Gradients and curvature of the mean refractive index profile result in ray bending and the associated phenomena of mirages, atmospheric lensing, and wave trapping in parabolic cavities. Stochastic refractive index fluctuations due to turbulence cause a random displacement of the trajectory and give rise to the wander, or spot dancing, of a propagating optical beam. In this paper we model these features of the refractive index profile locally and describe propagation through the corresponding regions. We derive formulas for the mean ray path that capture the effects of both atmospheric turbulence and variations in the mean refractive index profile, including the non-paraxial effects associated with the bending of the guiding ray path. We also give formulas for the mean-squared transverse displacement of a ray from the mean trajectory, which can provide for example an estimate of the magnitude of the beam wander due to turbulence.