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

In a semiconductor illuminated by a strong terahertz field, optically excited electron-hole pairs can recombine to emit light in a broad frequency comb evenly spaced by twice the terahertz frequency. Such high-order terahertz 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 kVcm-1), an obstacle for technological applications. Here we predict that bi-layer graphene generates high-order sidebands at much weaker terahertz fields. We find that a terahertz field of strength 1 kVcm-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 terahertz frequencies, facilitating ultrafast optical communications.