Propagation in Statistically Irregular Waveguides—Part II: Second Order Statistical Moments

The correlation function of a point-source field is shown to be governed by the Bethe-Salpeter equation which reduces to the transfer equations for the eigenwave intensities. Because of the boundary irregularities the initial energy distribution among the modes undergoes substantial changes at great distances. In the case of a multimode waveguide the radiation transfer equation takes the form of the diffusion equation in the mode number domain, with the role of time played by the distance along the waveguide. In the framework of the multiple scattering theory developed, the propagation of a time-dependent quasi-monochromatic signal is also discussed. The wall roughness manifests in distortions of the signal shape. In a number of cases explicit expressions have been obtained for the pulse shape as a function of time and coordinates. Typical distances are estimated at which an amplitude modulation is effectively “washed away” by the influence of the multiple scattering.