Guided TE-waves in a slab structure with lossless cubic nonlinear dielectric and magnetic material: parameter dependence and power flow with focus on metamaterials

Abstract

Abstract The parameter dependence and power flow of guided TE-waves in a lossless cubic nonlinear, dielectric, magnetic planar three-layer structure is studied as follows. Using a travelling wave ansatz with stationary amplitude, Maxwell’s equations are transformed to a system of ordinary nonlinear differential equations.The solutions of the system are presented compactly (in terms of hyperbolic and elliptic functions).The nonnegative and bounded (“physical”) solutions are determined by using a phase diagram condition (PDC) that is applied to express the continuity (transmission) conditions at the interfaces leading to the dispersion relation (DR).Based on the PDC, the parameter dependence and stability of the solutions to the DR and corresponding power flow are studied numerically for permittivities and permeabilities that may be appropriate to describe metamaterial.