"Fast" Plasmons Propagating in Graphene Plasmonic Waveguides with Negative Index Metamaterial Claddings

We propose the monolayer graphene plasmonic waveguide (MGPW), which is composed of graphene core sandwiched by two graphene metamaterial (GMM) claddings and investigate the properties of plasmonic modes propagating in the waveguide. The effective refraction index of the GMMs claddings takes negative (or positive) at the vicinity of the Dirac-like point in the band structure. We show that when the effective refraction index of the GMMs is positive, the plasmons travel forward in the MGPW with a positive group velocity (vg > 0, vp > 0). In contrast-for the negative refraction index GMM claddings-a negative group velocity of the fundamental mode (vg < 0, vp > 0) appears in the proposed waveguide structure when the core is sufficiently narrow. A forbidden band appears between the negative and positive group velocity regions, which is enhanced gradually as the width of the core increases. On the other hand, one can overcome this limitation and even make the forbidden band disappear by increasing the chemical potential difference between the nanodisks and the ambient graphene of the GMM claddings. The proposed structure offers a novel scheme of on-chip electromagnetic field and may find significant applications in the future high density plasmonic integrated circuit technique.