Optimizing third-harmonic generation at terahertz frequencies in graphene

We model third-harmonic generation in doped monolayer graphene at terahertz frequencies by employing a nearest-neighbor tight-binding model in the length gauge. We show that for a given incident-field amplitude there is an optimum Fermi level that maximizes the emitted third-harmonic field. The optimum Fermi level depends very strongly on the incident-field amplitude as well as on the scattering time and increasing either enhances the third-harmonic response. We consider the general case of Fermi-level-independent scattering as well as three different scattering mechanisms that are Fermi-level dependent: phonon, long-range impurity, and short-range impurity scattering. For each case, we determine the optimal Fermi level as well as the amplitude of the optimized third-harmonic response for single-cycle incident fields with central frequencies of 1 THz and amplitudes in the range of 25-75 kV/cm. We find that although nonlinear processes beyond third order suppress third-harmonic generation, we still obtain third-harmonic amplitudes as large as 1.6% of the fundamental of the transmitted field.