  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.
