Optically nonlinear phonon–polariton modes in a three-layered structure

A theory is presented for the propagation of phonon–polariton modes arising when phonons are coupled to electromagnetic waves in multilayered structures. A multi-layered structure consists of a thin film surrounded symmetrically by a bounding media. Numerical calculations are given for s -polarized phonon–polariton modes in the case where the bounding media are assumed to be semi-infinite layers with nonlinear dielectric functions of ionic crystal type supporting optical phonon modes and the thin film is characterized by a Kerr-type nonlinear dielectric function. The phonon–polaritons were found to have distinct branches characteristic of optical phonons and showing features that are different from those of plasmon–polaritons [S. Baher, M.G. Cottam, Surf. Rev. Lett. 10 (2003) 13]. The parameters that modify the modes are the in-plane wave vector, the thickness of the film, the phonon frequency and the nonlinearity of each layer. It was found that by increasing the film thickness and nonlinearity coefficient, the curves move to the left and the number of the branches increases without changing the pattern of the curves.