Local-field effects in the nonlinear optical response of metamaterials

We investigate optical second-harmonic generation from metamaterials that consist of two-dimensional arrays of lithographically designed T-shaped gold nanodimers, where the horizontal and vertical bars of the T are separated by a nanogap. The response is shown to depend in a nontrivial way on the gap size and to exhibit an unexpected dependence on the polarizations of the fundamental and second-harmonic light. The experimental results are explained by extensive calculations of the polarized local fields at the fundamental and second-harmonic frequencies. Due to the noncentrosymmetry requirement of second-order nonlinear processes, strong local fields in the gap region alone are not sufficient to drive the response efficiently. Instead, polarization properties of the local field and its asymmetric distribution around the dimer perimeters play the key role and enable efficient interaction with the surface nonlinearity of the metal. A small slant in the relative orientations of the vertical and horizontal bars of the dimer gives rise to second-harmonic signals that are forbidden for the ideal dimer with no slant. These signals are also explained by the local-field distributions, now modified by the slant.