Excitation of backward Tamm states at an interface between a periodic photonic crystal and a left-handed metamaterial

We study the excitation of electromagnetic surface waves in a slab of a left-handed metamaterial separating a one-dimensional periodic photonic crystal and a homogeneous dielectric medium, the so-called surface Tamm states. We show that such a layered structure can exhibit a giant lateral Goos-Hänchen shift of the scattered beam accompanied by a splitting of the reflected and transmitted beams due to the resonant excitation of surface waves at the interfaces between the left-handed metamaterial and photonic crystal. The beam shift can be either positive or negative, depending on the type of the surface Tamm states excited by the incoming beam.