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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.

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