From surface to volume plasmons in hyperbolic metamaterials: General   existence conditions for bulk high-k waves in metal-dielectric and   graphene-dielectric multilayers
  We theoretically investigate general existence conditions for broadband bulk large-wavevector (high-k) propagating waves (such as volume plasmon polaritons in hyperbolic metamaterials) in subwavelength periodic multilayer structures. Describing the elementary excitation in the unit cell of the structure by a generalized resonance pole of a reflection coefficient, and using Bloch's theorem, we derive analytical expressions for the band of large-wavevector propagating solutions. We apply our formalism to determine the high-k band existence in two important cases: the well-known metal-dielectric, and recently introduced graphene-dielectric stacks. We confirm that short-range surface plasmons in thin metal layers can give rise to hyperbolic metamaterial properties, and demonstrate that long-range surface plasmons cannot. We also show that graphene-dielectric multilayers tend to support high-k waves and explore the range of parameters for which this is possible, confirming the prospects of using graphene for materials with hyperbolic dispersion. The approach is applicable to a large variety of structures, such as continuous or structured microwave, terahertz (THz) and optical metamaterials. 
Sergei V. Zhukovsky, Andrei Andryieuski, J. E. Sipe, Andrei V.   Lavrinenko
physics.optics cond-mat.mes-hall