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 ("tri-refringence") while the surface modes can propagate parallel to the Bloch wavevector and along the interface between superlattice and semi-infinite dielectric.