Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects

摘要

We present a practical scheme to separate the contributions of the electricquadrupole-like and the magnetic dipole-like effects to the forbidden secondorder optical nonlinear response of graphene, and give analytic expressions forthe second order op- tical conductivities, calculated from the independentparticle approximation, with relaxation described in a phenomenological way. Wepredict strong second order nonlinear effects, including second harmonicgeneration, photon drag, and difference fre- quency generation. We discuss indetail the controllability of these effects by tuning the chemical potential,taking advantage of the dominant role played by interband optical transitionsin the response.