  We present an analysis of wave propagation in a two step-index, parallel
waveguide system. The goal is to quantify the effect of scattering at randomly
perturbed interfaces between the guiding layers of high index of refraction and
the host medium. The analysis is based on the expansion of the solution of the
wave equation in a complete set of guided, radiation and evanescent modes with
amplitudes that are random fields, due to scattering. We obtain a detailed
characterization of these amplitudes and thus quantify the transfer of power
between the two waveguides in terms of their separation distance. The results
show that, no matter how small the fluctuations of the interfaces are, they
have significant effect at sufficiently large distance of propagation, which
manifests in two ways: The first effect is well known and consists of power
leakage from the guided modes to the radiation ones. The second effect consists
of blurring of the periodic transfer of power between the waveguides and the
eventual equipartition of power. Its quantification is the main practical
result of the paper.
