Propagation in Statistically Irregular Waveguides — Part I: Average Field

The Green's function technique is employed to investigate the influence of the boundary condition perturbations in a number of wave propagation problems. The method permits treatment of multiple scattering on random irregularities of a boundary surface which is of particular importance for waveguide applications. For an average Green's function the Dyson type equation has been obtained whose solution represents the coherent part of a point source field in a rough waveguide. The eigenfunction spectrum has also been calculated for such waveguides. By means of mutual wave transformation due to the scattering, the waveguide modes acquire additional (lossless) damping and altered phase velocities. Detailed calculations have been carried through for plane acoustical waveguides with statistically rough walls under the Dirichlet and Neumann conditions. The average field's damping has also been considered for some cases of more complex geometry. In the electromagnetic case the electrical and magnetic solutions are similarly influenced by the wall roughness. Owing to the scattering they acquire longitudinal components of E or H thus becoming guasi-electrical or quasi-magnetic. For these normal waves the damping coefficients (attenuation rates) have been derived. A particular attention is paid to cutoff frequencies in the presence of effective wave conversion to the resonant mode.