Modal solution to the plane wave two-frequency mutual coherence function in random media

Pulse propagation in a random medium is mainly determined by the two-frequency mutual coherence function which satisfies the parabolic equation. It has been shown recently that this equation can be solved by separation of variables, thereby reducing the solution for any structure function into solutions of ordinary differential equations. Via a proper modal-expansion theorem, this representation may also be applied to any source problem. The modal approach also provides new physical interpretations for relevant physical parameters. This new solution approach is being reviewed here within the simplified framework of plane wave initial conditions. In particular, a general power law structure function is investigated, and the results are compared with the known exact solution for quadratic medium and a numerical solution for a Kolmogorov medium. Using the new modal approach, we present two alternative representations: a “mode series” and a “collective mode solution.” Both representations are suitable for extension into the time domain, giving a series of “wave front arrivals” and ‘collective resonance” contributions respectively.