Role of Plasmon Modes on the Optical Reflectivity of Graphene-Metallic Structures: A Theoretical Approach

In recent years, the tunable plasmon modes in the terahertz region of a multilayer graphene structure interacting with a metallic film substrate have attracted significant interest motivated by the graphene´s unique optical and electronic properties and the possibility to enhance light-matter interaction. In this work, the plasmon waves in graphene layered systems on a conducting thin film are investigated, the hybrid graphene-metal metamaterialis surrounded by two semi-infinite materials with different dielectric constants ε₁andε₂, respectively. The dispersion relations of electronic collective excitations are calculated by the zeros of an effective dielectric constant obtained from a recursive relation for the amplitudes associated with the electric field between graphene layers in the metamaterial. Long-range Coulomb interactions based on the hybrid layered graphene-metal structure lead new set spectra of collective excitations. At long wavelength (q®0) the optical modes (w~q^1/2)depend on the two-dimensional carrier density, the metallic thickness, the metallic substrate plasmon frequency, the number of the graphene layers and the dielectric constants in which the hybrid graphene-metal structure is embedded. This latter plays an important role in a wide range of applications such as a surface plasmon resonance biological sensors and terahertz surface plasmons in optically pumped graphene metamaterials.