Theory of low-power ultra-broadband terahertz sideband generation in bi-layer graphene

In a semiconductor illuminated by a strong terahertz (THz) field, optically excited electron–hole pairs can recombine to emit light in a broad frequency comb evenly spaced by twice the THz frequency. Such high-order THz sideband generation is of interest both as an example of extreme nonlinear optics and also as a method for ultrafast electro-optical modulation. So far, this phenomenon has only been observed with large field strengths (~10 kV cm(−1)), an obstacle for technological applications. Here we predict that bi-layer graphene generates high-order sidebands at much weaker THz fields. We find that a THz field of strength 1 kV cm(−1) can produce a high-sideband spectrum of about 30 THz, 100 times broader than in GaAs. The sidebands are generated despite the absence of classical collisions, with the quantum coherence of the electron–hole pairs enabling recombination. These remarkable features lower the barrier to desktop electro-optical modulation at THz frequencies, facilitating ultrafast optical communications.