Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of strong scintillations

We investigate analytically and numerically correlation functions of the phase of light waves that propagate through turbulent media. We examine the case of strong scintillations that occur at large values of the Rytov dispersion, $σ^2_R$. Then, it is possible to relate the pair correlation function of phase gradients to the known pair correlation function of the envelope dependent on the distance $r$ assuming Gaussianity of the envelope of the beam. Our direct numerical simulations show that the profile of the pair correlation function for phase gradients gradually approaches the theoretical expression as the value of $σ_R^2$ increases, if $r<r_0$ where $r_0$ is the Fried length. For larger $r$ the behavior of the computed correlation function is quite different because of destroying the Gaussianity.