Plasmon modes in extrinsic graphene: ab initio simulations vs semi-classical models

Excitation and propagation of surface plasmons in extrinsic graphene are analyzed from the fundamental point of view, using time-dependent density functional theory in linear response regime. Density functional calculations, being set up from first principles, naturally include anisotropic effects in the unique electronic structure of graphene that cause remarkable consequences even on the THz band. The main signature of this anisotropy is the occurrence of two distinct plasmon modes over a frequency band of 1 to 300 THz, where most photonic devices currently operate with large bandwidths and low losses. Further anisotropic features are inherent to the different electromagnetic response of graphene to positive and negative doping concentrations. The Dirac-cone approximation provides a simplified insight, assuming an isotropic graphene band structure near the Fermi level, which is found to be reliable at probing frequencies below 20 THz, and doping levels associated to Fermi energy shifts below/above \pm 0.3 eV. In these limits, a continuous integral expression derived from the Kubo formula represents an easy-to-use tool capable of catching the main essence of the process.