Multilayer graphene waveguides

We study dispersion properties of TM-polarized electromagnetic waves guided by a multilayer graphene metamaterial. We demonstrate that both dispersion and localization of the guided modes can be efficiently controlled by changing the number of layers in the structure. Remarkably, we find that in the long wavelength limit, the dispersion of the fundamental mode of the $N$-layer graphene structure coincides with the dispersion of a plasmon mode supported by a single graphene layer, but with $N$ times larger conductivity. We also compare our exact dispersion relations with the results provided by the effective media model.