Long-range Tamm surface plasmons in graphene metamaterials

Considering the Ohmic losses of graphene, we study linear Tamm surface plasmons supported by air-terminated graphene metamaterials composed of alternating layers of graphene and dielectric with thickness d and dielectric... [ view full abstract ]

Considering the Ohmic losses of graphene, we study linear Tamm surface plasmons supported by air-terminated graphene metamaterials composed of alternating layers of graphene and dielectric with thickness d and dielectric constant of 4. We theoretically prove that with sufficiently large thickness of the dielectric layers, i.e. 100 nm, the Tamm surface plasmons have considerably large (small) propagation (localization) length, comparable with those of a single layer of graphene. Neglecting the Ohmic losses of graphene, it has been demonstrated that similar to the metal-dielectric systems, multilayer graphene hyperbolic metamaterials are also capable of supporting long- and short-range surface plasmons (SPs) and also bulk modes, for transverse magnetic (TM) polarization of light. These systems are created by alternating graphene sheets separated by layers of dielectric with subwavelength-thickness. Moreover, TM Tamm surface plasmons localized at the surface of the system can also be realized in terminated graphene metamaterials. In realistic graphene-based plasmonic devices, the losses of the system can considerably affect the SPs propagation and localization characteristics. Therefore, in this abstract, considering the Ohmic losses of the graphene sheets, we investigate the normalized propagation length (PL) and localization length (LL) of the Tamm SPs in the graphene-dielectric metamaterials terminated with air. In this metamaterial, for d=10 nm, first the Tamm SPs are supported in a narrower range of frequency and, second, there is a considerable decrease (increase) in their PL (LL), as compared with those of a single layer graphene bounded with air and material with ε=4. Moreover, by increasing d to 100 nm, PL (LL) of the modes and the frequency range of their appearance will be increased (decreased) while there is still a large length of localization for Tamm SPs at lower frequencies. In conclusion, we have examined the propagation and localization characteristics of low-loss Tamm surface plasmons supported by graphene metamaterials. We have demonstrated that by taking the subwavelength thickness of the dielectric layers as 100 nm, Tamm SPs with long propagation and small localization lengths can be supported by the air-truncated graphene metamaterial at frequencies larger than 20 THz.