Second order optical nonlinearity of graphene due to electric quadrupole   and magnetic dipole effects
  We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order op- tical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference fre- quency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response. 
J. L. Cheng, N. Vermeulen, J. E. Sipe
cond-mat.mtrl-sci physics.optics