Linearly polarized dipolar second harmonic generation from gold nano-antennas by controlling their radiation phase

A recurring theme in optics and photonics is the ability of metal nanostructures to imbue artificial materials with new functions. Metallic nano-antennas [1], so-called meta-atoms, are the building blocks of such metamaterials that boast unusual linear [2, 3] and nonlinear [4– 6] characteristics not observed in natural materials. Recently, nonlinear metamaterials have generated considerable excitement; while nonlinear effects in natural materials must gradually accumulate weak nonlinearity across macroscopic crystal dimensions, a small volume of metamaterial [7, 8], and even isolated antennas [9–11], can create a surprisingly strong effect. This capability stems from additional nanoscopic degrees of freedom that include couplings between the constituent nanoparticles within antennas or between antennas and material resonances [7, 9, 10]. Second harmonic generation (SHG) enables diversely coloured light sources through an energy exchange process between light at initial, ω, and final, 2ω, frequencies typically in optically thick non-linear crystals. Recently, metamaterials imbued with nonlinearity from their constituent nano-antennas have generated excitement by opening the possibility of wavelength-scale nonlinear optics. The nonlinear selection rules typically prevent dipole SHG from nano-antennas leading to much discussion concerning the best geometries. Following recent literature, we examine individual antennas that are designed to efficiently radiate SHG (η
SHG
> 10
⁻⁷
W
⁻¹
, corresponding to |χ
eff
⁽²⁾
| > 40pmV
⁻¹
) by incorporating simple resonant elements tuned to light at both ω and 2ω. We show that antennas exhibiting both non-centro-symmetry and a mirror symmetry plane exhibit the strongest normal incidence SHG emission with a high degree of linear polarization. We confirm this by direct measurement of SHG in the back focal plane of isolated nano-antennas in a variety of configurations. We also show that antennas incorporating multiple 2ω-elements provide greater flexibility to ensure that both symmetries are met. By interpreting the SHG emission patterns using a multi-dipole model we also identify the phase and the orientation of each antenna element as key design parameters to control SHG emission pattern and polarisation. Metamaterials incorporating such antennas could enable compact nonlinear photonic nanotechnologies.