Analytical Investigation of TM Surface Waves in 1D Photonic Crystals Capped by a Self-Focusing Left-Handed Slab

In this paper, the localized TM surface waves of a nonlinear self-focusingleft-handed slab sandwiched between a uniform medium and a one-dimensionalphotonic crystal (1D PC) is analytically investigated. Our method is based on the firstintegral of the nonlinear Maxwell's equations. For the TM surface waves, the presenceof two electric field components makes the analysis difficult. Therefore, we used theuniaxial approximation for the nonlinear slab. The considered 1D PC can be a lefthandedPC (made of alternate left-handed (LH) and right-handed material) or a usualPC. In these structures, we find that the nonlinear LHM slab allows to control thedispersion properties of p-polarized surface waves. It is shown that there are no surfacemodes in the linear regime in the conventional PC and by increasing the intensity ofelectromagnetic field to higher value, the surface modes are emerged. To confirm ourachievements, we also compared