Stochastic mirage phenomenon in a random medium

Abstract

In the framework of geometric optics, we consider the problem of characterizing the ray trajectory in a random medium with a mean refractive index gradient. Such a gradient results in the mirage phenomenon where an object's observed location is displaced from its actual location. We derive formulas for the mean ray path in both the situation of isotropic stochastic fluctuations and an important anisotropic case. For the isotropic model, the mean squared displacement is also given by a simple formula. Our results could be useful for applications involving the propagation of electromagnetic waves through the atmosphere, where larger-scale mean gradients and smaller-scale stochastic fluctuations are both present.

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

“…In this paper we present a method for describing longrange propagation through inhomogeneous, multiscale, and stochastic variations in the atmospheric refractive index. This paper extends the work of [27,28], in which we developed a novel approach consisting of the following steps: (i) identify critical regions containing large gradients, curvature, or local extrema of the refractive index profile (ii) locally approximate the refractive index using linear, quadratic, and stochastic terms These local approximations can capture, for example, scintillation-producing irregularities such as those formed at the edges of turbulent Rayleigh-Taylor ionospheric plasma bubbles and atmospheric layers [8]. This method is able to resolve the non-paraxial effects associated with the bending of the guiding ray path, including the phenomena of mirages and focusing/defocusing in long-range EM wave propagation through the inhomogeneous, turbulent atmosphere.…”

Non-Classic Atmospheric Optical Turbulence: Review

“…Recent measurements of this turbulent mirage phenomenon [44] indicate that over the 13-15 km path, the vertical image shift might reach several meters. See also [45,46] for related analytical and numerical calculations.…”

Coupling of paraxial and white-noise approximations of the Helmholtz equation in randomly layered media

“…The backward Kolmogorov equation for the limiting density ρ 0 will follow from the solvability condition (23).…”

“…Many technologies that rely on electromagnetic wave propagation through various regions of the atmosphere are significantly affected by atmospheric turbulence. In the troposphere, tropopause, and lower stratosphere, random fluctuations in temperature, pressure, and humidity give rise to random refractive index fluctuations, referred to as refractive turbulence (see, e.g., [9,26,27,23,22]). The ionosphere is another turbulent region, where electron density fluctuations lead to fluctuations in the refractive index.…”