Extremely efficient terahertz high harmonic generation in graphene by hot Dirac fermions

Multiple optical harmonics generation—the multiplication of photon energy as a result of nonlinear interaction between light and matter—has become one of the key technologies in modern electronics and optoelectronics. Owing to its unique electronic band structure featuring massless Dirac fermions, graphene has been repeatedly predicted to have high efficiency of optical harmonics generation in the technologically important terahertz frequency range. So far, experiments have failed to confirm these predictions under technologically relevant operation conditions. Here we report the generation of terahertz harmonics up to the seventh order in single-layer graphene at room temperature and under ambient conditions, driven by terahertz fields of only tens of kilovolts per centimetre, and with field conversion efficiencies in excess of 10⁻³, 10⁻⁴ and 10⁻⁵ for the third, fifth and seventh terahertz harmonics, respectively. The key to such highly efficient harmonics generation in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The generated terahertz harmonics were observed directly in the time domain as electromagnetic field oscillations at these newly synthesized frequencies. The effective nonlinear optical coefficients of graphene for the third, fifth and seventh harmonics exceed the respective nonlinear coefficients of typical solids by 7–18 orders of magnitude. Our results provide a direct pathway to highly efficient terahertz frequency synthesis that is within the capabilities of the present generation of graphene electronics operating at fundamental frequencies of only a few hundreds of gigahertz.