Modal theory for the two-frequency mutual coherence function in random media: point source

The recently introduced modal expansion representation for the two-frequency mutual coherence function is applied here to the solution of a point-source field in a random medium. This approach reduces the solution for any structure function to an eigenvalue problem for an ordinary differential equation. For the initial point source it is shown here that the modal expansion yields a result similar to that for the initial plane wave, modified by a spherical free-space phase which contains a weighted coordinate that does not interact with the medium. Having established these general characteristics, special attention is paid to power-law media and, in particular, to a quadratic medium, for which a new exact solution is derived. Via a collective summation of this new modal solution, we rederive the alternative exact solution which exists in the literature. We also discuss the new parameterization implied by the new modal solution.