Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: I

In this paper, the modal expansion theory is presented as a new analytical approach together with the resulting new physical parameters. In particular, the features of an arbitrary power-law structure function are investigated. The exact expression for the Gaussian spectrum is rederived. An approximate analytical expression for the two-frequency coherence function evaluated at equal positions for the Kolmogorov spectrum is presented and comparison with the numerical solution in the literature exhibits a remarkable agreement. As a result of the modal decomposition, general properties for a transversally homogeneous and isotropic medium are demonstrated, such as the exponential decay of the amplitude of the solution and the linear phase behaviour at large propagation distances.