Theory of nonlinear s-polarized plasmon-polariton and phonon-polariton modes in dielectric superlattices

The propagation of nonlinear s-polarized polariton waves (TE modes) in an infinitely extended superlattice is considered. The periodic system is composed of two different components where the layers are arranged in an alternating fashion so that each layer of material 1 is bounded by two layers of material 2 and vice versa. In general, each of the individual layers may be characterized by a Kerr-type nonlinear dielectric function with a frequency-dependent characteristic of either the plasmons in a metal/semiconductor or the optical phonons in an ionic crystal. To investigate the propagation of polariton modes in such a system, a theoretical model is formulated leading to Jacobi elliptic functions for the electric field amplitude across the layers. Subsequently, the application of boundary conditions at the interfaces gives rise to dispersion relations. Numerical examples are given for plasmon-polariton and phonon-polariton modes and a comparison is made with phonon-polariton modes propagating in a three layered system.