Zhukovsky, Sergei1; Andryieuski, Andrei3; Sipe, John E.5; Lavrinenko, Andrei1
1 Department of Photonics Engineering, Technical University of Denmark2 Plasmonics and Metamaterials, Department of Photonics Engineering, Technical University of Denmark3 Nanophotonics, Department of Photonics Engineering, Technical University of Denmark4 University of Toronto5 University of Toronto
We theoretically investigate general existence conditions for broadband bulk large-wave-vector (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-wave-vector 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 parameteres 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, and optical metamaterials.
Physical Review B Condensed Matter, 2014, Vol 90, Issue 15