Three-wave collinear difference-frequency mixing and terahertz coherent emission from gapped graphene

The second-order nonlinear optical susceptibility χ(2)(−ω3;ω1,ω2) corresponding to three-wave mixing of coherent radiation of the form ω3=ω1−ω2 is calculated for epitaxial graphene on a SiC substrate inducing the sublattice (inversion) asymmetry of the graphene and opening up a gap of about 0.26 eV in its π-electron-energy spectrum. The analytical treatment of the χ(2) is based on the tight-binding approximation for π electrons and the original Genkin-Mednis nonlinear-conductivity-theory formalism including mixed intra- and interband terms. It is found that throughout the transparency region of the graphene, the absolute magnitude of the χ(2) may be as large as 10−5 esu, which opens up new opportunities to generate terahertz (THz) coherent output from the graphene excited by two collinear mid-infrared ω1 and ω2 laser beams normally incident on its surface. The output power density produced at the difference frequency ω1−ω2 of 10 THz is estimated to be 0.1 μW/cm2 for 10 MW/cm2 pump peak intensities, and conditions are discussed under which a few orders of magnitude enhancement of the output power could be achieved in future experiments.