Existence conditions for bulk large-wavevector waves in metal-dielectric and graphene-dielectric multilayer hyperbolic metamaterials

Abstract

We theoretically investigate general existence conditions for broadband bulk large-wavevector (high- k ) propagating waves (such as volume plasmon polaritons in hyperbolic metamaterials) in arbitrary subwavelength periodic multilayers structures. Treating the elementary excitation in the unit cell of the structure as a generalized resonance pole of 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 metaldielectric 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-dielectricmultilayers tend to support high- k waves and explore the range of parameters, where this is possible, confirming the prospects of using graphene for materials with hyperbolic dispersion. The suggested formalism is applicable to a large variety of structures, such as continuous or structured microwave, terahertz (THz) and optical metamaterials, optical waveguide arrays, 2D plasmonic and acoustic metamaterials.