  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.
