Backward surface electromagnetic waves in semi-infinite one-dimensional photonic crystals containing left-handed materials

We study the electromagnetic surface waves localized at an interface separating a homogeneous dielectric medium and a semi-infinite one-dimensional photonic crystal made of alternative left-handed metamaterial and right-handed material. An analytical direct matching procedure within the Kronig-Penney model was applied to analyze the dispersion properties of the localized surface states. We show that the presence of metamaterial in the photonic crystal structure can support the surface waves with a backward energy flow and allows a flexible control of dispersion properties of the surface modes. The surface states can be either forward or backward waves depending on the physical parameters of the photonic crystal, physical parameters of the cap layer, the position of the surface plane, and incident angle of the incoming beam.