  We theoretically investigate the second harmonic generation and photon drag
effect induced by an incident plane wave to a doped graphene placed on a
two-dimensional diffraction grating. The relevant nonlinear conductivity of the
graphene is obtained by a semi-classical treatment with a phenomenological
relaxation. The grating acts not only as a plasmon coupler but also as a
dispersion modulator of the graphene plasmon. As a result, the second harmonic
generation is strongly enhanced by exciting the graphene plasmon polariton of
the first- and/or second-harmonic frequencies. The photon drag effect is also
strongly enhanced by the excitation of the plasmon at the first-harmonic
frequency. The direct current induced by the photon drag effect flows both
forward and backward directions to the incident light, depending on the
modulated plasmon mode concerned.
