Dispersion of Bloch modes in a multilayer structure with alternating left-handed and right-handed materials

We study all-evanescent eigenmodes of a one-dimensional infinite periodic structure with alternating left-handed and right-handed materials that propagate perpendicularly to the Surface or guided eigenmodes. Investigation of dispersion properties of such Bloch modes is shown to be crucial for understanding of an efficient radiation energy transport across the periodic mltilayer structure. Frequency pass bands and gaps are found as a function of the two orthogonal wave vectors: the Bloch wave vector k(B) and the surface wave vector k(S). We demonstrate that pass bands of both TE- and TM-polarizations can exist and, under certain conditions, may overlap.