Artificial structural nonlinearity of metallic nanoparticles has been shown recently to enable nonlinear optical conversion, e.g. second harmonic generation (SHG), with large effective nonlinear coefficients and in a variety of light manipulation schemes [1]. The ability to obtain controlled nonlinearity by modifying the geometry of nanostructured materials opens the door to new fundamental studies in the realm of nonlinear optics. Several studies have been performed in recent years on trying to unveil the fundamental mechanisms for the measured artificial nonlinearity, mainly focusing on the single plasmonic nanoparticle [2], or extended nearfield influence [3], where the influence of nonlinear coherent coupling of the plasmonic nanoparticles has remained unexplored.

In the linear regime it is well known that fulfilling the Rayleigh-anomaly (RA) condition in arrays of metallic nanoparticles at their localized surface plasmon resonance leads to excitation of so-called surface lattice resonances (SLRs), which substantially change the collective optical response of the plasmonic arrays [4]. Very recently, the Kauranen group has shown that excitation of SLR at frequency ω can lead to 10-fold enhancement of the SHG process at 2ω.

In this study we experimentally observe, for the first time to our knowledge, nonlinear SLR (NL-SLR) as a result of nonlinear RA (NL-RA) at 2ω coupled to a dark localized mode. The NL-SLR is manifested by sharp features of the SHG emission and attains more than 30-fold enhancement of the SHG with respect to normal incidence. By varying both the angle of incidence and the fundamental frequency wavelength, the correspondence between the NL-RA location and the sharp feature of the resonant response of the second harmonic were examined, and show very good agreement.

References 

[1]     N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics, vol. 9, n0 3, pp. 180-184, Feb, 2015.

[2]     K. OBrien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, X. Zhang, K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater., vol. 14, no.4, pp. 379-383, Feb.2015.

[3]     S. Linden, F. B. P. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener, “Collective Effects in Second-Harmonic Generation from Split-Ring-Resonator Arrays,” Phys. Rev. Lett., vol. 109, no. 1, p.015502, Jul. 2012.

[4]     B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. vol. 101, no. 14, 2008.