Electric-field-induced optical second-harmonic generation in doped graphene

• Graphene's potential for optical second-harmonic generation (SHG).
• Electric-field-induced (EFI) mechanism of SHG in doped graphene.
• Resonant structures in the EFISHG spectrum of doped graphene.

A graphene layer interacting with an incident electromagnetic wave of frequency ω   will produce dipole radiation at frequency 2ω2ω in the presence of an in-plane electric field breaking the spatial inversion symmetry of the graphene. Here, we develop a theory that describes such electric-field-induced second-harmonic generation (EFISHG) from doped graphene. We derive an analytic expression for the relevant third-order nonlinear optical (NLO) susceptibility χ(3)(−2ω;ω,ω,0)χ(3)(−2ω;ω,ω,0) and numerically evaluate the absolute magnitude of the χ(3)χ(3) for various values of the system's parameters. We find that the |χ(3)||χ(3)| spectrum is dominated by the resonant peak structure located at the incident photon energy ℏωℏω equal to the Fermi energy EFEF of charge carriers in the doped graphene. We also show that the possibility to tune the doping level of graphene by an external gate voltage allows one to maximize the radiated EFISHG power at ℏω=EFℏω=EF, which may be of practical interest for the designs of the NLO devices based on employing a SHG-signal.