We show that the optical properties of a metal-nonlinear dielectric grating can be precisely described by a uniform nonlinear dielectric slab. Based upon such a metamaterial mapping, we show that the effective optical nonlinearity in a metal-dielectric grating can be enhanced by orders of magnitude higher than that of the underlying nonlinear dielectric material, is broadband, and can be operated at a low quality-factor regime so as to have an extremely short intrinsic temporal response of a few picoseconds. Furthermore, we demonstrate extraordinary harmonic generation efficiency enhancement and large threshold-power reduction in bistability.
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