Surface Bloch waves in metamaterial and metal-dielectric superlattices

We study the properties of electromagnetic Bloch waves in semi-infinite periodic structures created by alternating metamaterial and dielectric layers. We derive and analyze the dispersion relations in the long-wavelength limit for both TE- and TM-polarized surface Bloch modes for magnetic metamaterials with negative refraction and metal-dielectric plasmonic superlattices. We reveal that in the subwavelength regime, the bulk modes are characterized by three different refractive indices (trirefringence), while the surface modes can propagate parallel to the Bloch wavevector and along the interface between superlattice and semi-infinite dielectric.