Renormalization of propagation in a waveguide with rough boundaries

A scheme is presented for computing the mean field in a waveguide with rough boundaries using nonperturbative half-space scattering amplitudes. It is shown that the presence of a second scattering surface renormalizes the mean half-space amplitudes even when surface roughness on the two bounding surfaces is uncorrelated. The method of ‘‘smoothing’’ is used to show how recent work on half-space scattering amplitudes might be incorporated into solutions of the wave equation in more realistic settings.