Investigation of the nonlinear optical properties of metamaterials by second harmonic generation

Nonlinear optical spectroscopy is applied to two types of metamaterials: (i) variations of split-ring resonators fabricated as periodic two-dimensional arrays of gold on SiO2, and (ii) gratings of periodically spaced straight wires of gold on multiferroic hexagonal single crystals from the RMnO3 family. Optical second harmonic generation (SHG) on samples of type (i) is used to characterize the nonlinear response of metamaterials in dependence of the photon energy and the size, shape, and symmetry of the nanoscopic building blocks constituting the metamaterials. We find a complex dependence of the SHG spectra on the design parameters that requires an in-depth theoretical analysis. SHG is applied to samples of type (ii) to enhance the nonlinear optical performance of functional materials by writing a metamaterial acting as optical catalyst on top. We observe an enhancement of the SHG signal induced by the ferroelectric order of the RMnO3 crystals, yet with pronounced variations between samples. Measurements of both types, (i) and (ii), show that a comprehensive understanding of the nonlinear optical properties of metamaterials requires one to go beyond a macroscopic symmetry treatment. In fact, structural inhomogeneities on the level of the nanoscopic building blocks have a major impact.