Long-range tamm surface plasmons supported by graphene-dielectric metamaterials

Abstract

Considering the Ohmic losses of graphene in the calculations and by obtaining exact dispersion relations of the modes, we theoretically study propagation and localization characteristics of Tamm surface plasmons supported by terminated graphene metamaterials. The metamaterials are composed of alternating layers of graphene and dielectric with subwavelength periods. We also examine the Tamm modes within the framework of long-wavelength approximation. It is shown that, in case the Ohmic losses of the graphene layers are taken into account, surface plasmons are not supported in a long-wavelength region, in which the graphene-dielectric multilayer structure behaves as a hyperbolic metamaterial. We prove that, when the metamaterial is truncated with air, by choosing sufficiently thick but still subwavelength dielectric layers, i.e., d = 300 nm, these surface waves will have a moderate propagation (localization) length that is comparable with those of a single layer of graphene. On the other hand, in case a miniaturized graphene metamaterial (10 < d(nm) < 100) is truncated by a thick cap layer (dcap = 5d) with εcap > εdielectric, it is possible to considerably improve the propagation and localization characteristics of the Tamm modes supported by the system within the 5.5-50 THz range of frequency, as compared to a single layer of graphene.