Scattering of guided waves in a waveguide with a slightly rough boundary: Stochastic functional approach

The guided normal waves or modes in a waveguide would be perturbed if the boundaries of the waveguide were to become statistically irregular or rough. Due to the accumulation effects of multiple scattering along the entire propagation path, even very slight boundary irregularities can give rise to a considerable influence on the propagation characteristics of the guided modes. In this paper, a way is proposed to treat the scattering problem of guided waves in a waveguide with a slightly rough boundary by applying the stochastic functional approach, which has been used successfully in the scattering problems of a plane scalar or electromagnetic wave in free space from various shaped random rough surfaces and has been shown to be good for treating the multiple scattering effects. As a prototype of the basic theory, only the planar structure of the waveguide and the Dirichlet boundary condition are considered. The waveguide's Green's function is expanded in terms of the Wiener-Hermite stochastic functionals of a homogeneous Gaussian random surface. Expressions for the modified normal waves (modes) of the average or coherent Green's function are given for the Dirichlet boundary condition. A mass operator is derived which contains the information of the multiple scattering of the modes from the rough boundary and can be evaluated in an iterative way. The second order statistical moment or the correlation function of the Green's function is also considered. Some numerical examples are given for illustration. It has been shown that our approach gives more thorough results than those given by the graphical or Feynman diagram method