The scattering problem of an incident wave from a waveguide structure with a slightly rough surface is studied. The waveguide structure is considered to be a dielectric film deposited on a planar, perfectly conducting metal surface, and the top surface of the film is assumed to be a randomly rough surface. The stochastic scattered wave fields are represented in terms of orthogonal functionals with the Wiener coefficients. These coefficients are determined by applying the approximated boundary conditions expanded up to the third order of the random surface function. The analytical expressions for the coefficients of the first three terms are obtained rigorously up to the second order of the surface roughness so as to satisfy the reciprocity. It can be easily shown that our results are the same as those obtained by perturbation theory if we expand them in powers of the surface roughness. However, we have the so-called mass operator in the denominator of the coefficients, which can be used to determine the perturbed propagation constants of the guided waves in the presence of a rough surface and remove the divergence difficulty in the common perturbation theory. The numerical calculations show that there are some well-pronounced satellite peaks in the incoherent scattering distribution, in addition to the enhanced backscattering peak, when the waveguide structure can support two or more than two guided modes. This is caused by the interference of two double-scattering processes and is attributed to the existence of the guided waves in the scattering structure.

• Received 30 January 1995

DOI:https://doi.org/10.1103/PhysRevB.52.6027