Saddle-point exciton signature on high-order harmonic generation in two-dimensional hexagonal nanostructures

Abstract

The disclosure of basic nonlinear optical properties of graphene-like nanostructures with correlated electron-hole nonlinear dynamics over a wide range of frequencies and pump field intensities is of great importance for both graphene fundamental physics and for the expected novel applications of two-dimensional (2D) hexagonal nanostructures in extreme nonlinear optics. In the current paper, the nonlinear interaction of 2D hexagonal nanostructures with the bichromatic infrared driving field taking into account the many-body Coulomb interaction is investigated. Numerical investigation in the scope of the Bloch equations within the Houston basis that take into account $e\text{--}e$ and $e\text{--}h$ interactions in the Hartree-Fock approximation reveals significant excitonic effects in the high-harmonic generation process in 2D hexagonal nanostructures such as graphene and silicene. It is shown that, due to the correlated electron-hole nonlinear dynamics around the van Hove singularity, spectral caustics in the high-harmonic generation spectrum are induced near the saddle-point excitonic resonances.