Optically nonlinear s-polarized electromagnetic waves in multilayered symmetric dielectrics

A theory is presented for the nonlinear s-polarized electromagnetic waves in multilayer systems with an arbitrary number of planar interfaces. Each of the individual layers may be characterized by either a linear or a Kerr-type nonlinear dielectric constant, and we examine the coupled nonlinear waves at both linear/nonlinear and nonlinear/nonlinear interfaces. An analysis of the phase trajectories (in terms of an electric field amplitude and its spatial derivative) is employed to enumerate the modes of the system in a systematic manner and to facilitate the derivation of dispersion relations. In particular, numerical examples are given for two-interface systems (for example, a thin film sandwiched between two semi-infinite media) and for periodic superlattices (with effectively infinite interfaces), thereby extending previous calculations.