Paraxial Wave Propagation in Random Media with Long-Range Correlations

We study the paraxial wave equation with a randomly perturbed index of refraction, which can model propagation beam in turbulent medium. The random perturbation is stationary and isotropic process general form covariance that may or not be integrable. focus attention mostly on nonintegrable case, corresponds to long-range correlations, is, relevant for through cloudy atmosphere. analysis carried out high-frequency regime where forward scattering approximation holds. It reveals randomization field multiscale: travel time front randomized at short distances propagation, it described by fractional Brownian motion. observed frame affected perturbations long distances, Schrödinger-type driven standard field. use these results quantify how leads decorrelation spatial spectral components deformation pulse emitted source. These are important questions applications, such as imaging free space communications pulsed laser beams also compare those used optics literature, based Kolmogorov turbulence. show explicitly commonly approximations appropriate but fail models correlations.