Massless Dirac electrons in graphene and surface states of topological insulators have peculiar optical properties and strong coupling to light. Surface plasmons in these materials may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the difference frequency generation (DFG) of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes monolayer graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a broad range of frequencies.
Graphene placed in a magnetic field possesses an extremely high mid/far-infared optical nonlinearity originating from its unusual band structure and selection rules for the optical transitions near the Dirac point. Based on quantum-mechanical density-matrix formalism, here we study the linear and nonlinear optical response of graphene in strong magnetic and optical fields. We calculate the power of coherent terahertz radiation generated as a result of four-wave mixing in graphene. We also show that even one monolayer of graphene gives rise to appreciable nonlinear frequency conversion efficiency and Raman gain for modest intensities of incident infared radiation.