Calculations of wave propagation through statistical random media, with and without a waveguide

Simulations of laser-beam propagation through atmospheric turbulence and acoustic pulse propagation though ocean internal waves in the presence of a transverse waveguide are described. Both these problems are amenable to the parabolic wave equation for propagation in the forward direction. In the optical case, the question treated is the irradiance variance and spatial spectrum. In the ocean case, pulse propagation over long ranges is investigated. Determining the travel time of a pulse requires expanding the numerical simulation in a broadband, multifrequency calculation that takes even more time. Much effort has been expended in approximating the propagation by rays, so that the trajectory of the energy propagating from a given source to a given receiver can be tracked, and coherence calculations can be ray-based, using semi-classical formulas. This paper reviews the comparisons of several analytic ray-based approximations with numerical parabolic-equation simulations to determine their accuracies.