We develop a numerical model for the calculation of the average field intensity of surface-phonon polaritons in the presence of random roughness. The average field intensity is related to the average two-particle Green function, which is computed within the framework of diagrammatic theory. The field of surface-phonon polaritons decays exponentially from the incident beam center on the surface. Particular emphasis is placed on examining effects of the localization of surface-phonon polaritons due to random roughness. It is found that the localization occurs in a limited frequency range near the maximum frequency of surface-phonon polaritons. The decaying length in the extended region is much larger than that in the localized region. In the extended region the field intensity of surface-phonon polaritons is usually smaller than the incident intensity, while in the localized region it can be enhanced. The numerical results demonstrate that localization effects can reduce the intensity enhancement by the order of ${10}^3$. Further, the intensity enhancement decreases as the roughness amplitude increases. We conclude that the localization of surface-phonon polaritons is due to the destructive interference between waves scattered from the rough surface.

• Received 5 December 1994

DOI:https://doi.org/10.1103/PhysRevB.51.10017