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.
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