Plasmons and optical excitations in graphene rings.

A simple semiclassical drude-like conductivity of graphene is employed to describe plasmon excitations of graphene in the ring structures. A quasi-static self-consistent integral equation approach is performed, allowing the calculation of all the plasmon modes with different angular momentum l. Among them only the dipole modes (l = 1) will couple out to the radiation modes, which in turn can be excited optically by the plane waves, and the excitation energies as a function of the ratio of the radius of the inner hole to that of the outer ring have also been investigated. It is demonstrated that the energy of symmetric modes will monotonically decrease as the ratio rises, and the energy of antisymmetric modes does not exhibit a monotonically increasing behavior as in a three-dimensional metallic ring, but first reduces and then increases. These predictions are tested by full-wave simulations using the optical conductivity of graphene that was obtained from the random phase approximation (RPA).