  Graphene as a one-atom-thick platform for infrared metamaterial plays an
important role in optical science and engineering. Here we study the unique
properties of some plasmonic waveguides based on graphene nano-ribbon. It is
found that a graphene ribbon of finite width leads to the occurrence of coupled
edge mode. The single-mode region of a single freestanding graphene ribbon is
identified at a fixed frequency of 30 THz. A low-loss waveguide structure,
consisting of a graphene layer, a silica buffer layer and silicon substrate is
proposed to reduce the propagation loss and obtain a high figure of merit for
future integration of waveguide devices. Furthermore, two coupled ribbon
configurations, namely, side-side coupling and top-bottom coupling, are
investigated. As a device example, a nano-ring cavity of ultra-small size is
designed.
