Quantum Theory of Surface Polaritons on a Rough Surface11The project supported by National Natural Science Foundation of China through Grant No. 68977017 and 9687006-01

Abstract

In this paper, we present the quantum field theory of the surface phonon-polaritons on a rough polar crystal surface. The dispersion relations of the surface phonon-polaritons and the dispersion relations of polariton leaking modes owing to the interaction between bulk TO mode with the surface effect and photons are derived. We also study the -dependence of the electric field strength in each polariton branch. The numerical calculations for the dispersion relations and the -dependence of the electric field strength are carried out for a stepped GaP surface. The results show that the surface roughness depressed the frequency of the surface phonon-polariton below its values in the absence of the surface roughness. For the frequencies of the polariton leaking modes, the photon-like one is enhanced by the surface roughness and the phonon-like one is depressed. Our evaluations also illustrate that the surface roughness introduces a strong dependence on the -dependence of the electric field strength in each polariton branch.