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-focusing left-handed slab sandwiched between a uniform medium and a one-dimensional photonic crystal (1D PC) is analytically investigated. Our method is based on the first integral of the nonlinear Maxwell's equations. For the TM surface waves, the presence of two electric field components makes the analysis difficult. Therefore, we used the uniaxial approximation for the nonlinear slab. The considered 1D PC can be a lefthanded PC (made of alternate left-handed (LH) and right-handed material) or a usual PC. In these structures, we find that the nonlinear LHM slab allows to control the dispersion properties of p-polarized surface waves. It is shown that there are no surface modes in the linear regime in the conventional PC and by increasing the intensity of electromagnetic field to higher value, the surface modes are emerged. To confirm our achievements, we also compared the results obtained by this method and the attenuated total reflection (ATR) method.