Graphene plasmonics

Macroscopic Approach to Graphene Plasmonics To introduce graphene plasmons, we first consider the simple case of an infinite graphene sheet contained inside an electromagnetic medium that is translationally symmetric along the in-plane axes. This allows a simple decomposition into Fourier modes with in-plane wavevector k = (k ^x, k ^y) and with a fixed frequency, so that each field varies as exp(ik ^xx + ik^y y - iωt). In the following, we consider, without loss of generality, waves directed along, that is, fixed k ^xwith k^y = 0. Electromagnetic modes in this situation may be transverse electric or transverse magnetic, however, charged oscillations like plasmons occur only in the latter (and in the x, z plane). We focus on the transverse magnetic modes. The graphene plasmon is an oscillation with inertia provided by free charge carriers in the graphene, and restoring forces provided by the Coulomb interactions between the electrons (which are also influenced by the dielectric environment around the graphene). In a linear response, the electrodynamics of graphene in this situation can be completely described by its optical conductivity function.