Direct and cascaded collective nonlinear processes on metasurfaces

  Ofer Doron [1-3]  ,  Lior Michaeli [1-3]  ,  Tal Ellenbogen [1,3]  
[1] Department of Physical Electronics, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 6779801, Israel
[2] Raymond and Beverly Sackler School of Physics & Astronomy, Tel-Aviv University, Tel-Aviv 6779801, Israel
[3] Tel Aviv Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 6997801, Israel

We use collective interactions on metasurfaces to manipulate the interplay between direct and cascaded third-harmonic generation and demonstrate complete elimination of third-harmonic generation.


Third-harmonic generation (THG) can be achieved by either direct interaction of three pump photons to produce a photon at the third-harmonic, or by a cascaded process in quadratic nonlinear materials that enables second-harmonic generation (SHG) followed by sum-frequency generation (SFG) involving the second harmonic (SH) and the pump waves. Conventional schemes to control these two separate THG mechanism mostly rely on selective phase matching of the different process, i.e. SHG, SFG, or THG [1]. Here we show that in nanostructured nonlinear metasurfaces collective interactions facilitate a new route to independently control and enhance both the direct and cascaded THG processes. This gives rise to intriguing interference effects of the two, enabling to enhance or even completely eliminate the THG process.

Recently it was shown that collective nonlinear dynamics of metallic metasurfaces can play a significant role in their total nonlinear optical response. Specifically, for the case of SHG it was demonstrated that the coherent scattering of either the fundamental frequency (FF) or the SH, i.e. at the linear or nonlinear Rayleigh anomalies (RAs), may substantially enhance the total conversion efficiency [2,3]. These observations were phenomenology explained by extension of the conventional coupled dipole approximation (CDA) to the nonlinear case [3]. Very recently it was shown by simulations that the cascaded THG process can be favored over the direct process by enhancing the collective SH on metasurfaces [4]. Here, by leveraging the degree of freedom accessible in the close relation between localized surface plasmon resonances and the coherent lattice scattering, we show that the interaction can result in a Fano-like asymmetrical spectral line shape of the total THG process.

In order to study the nonlinear plasmonic array response to incident light we used the nonlinear CDA for the case of THG. We found that the effective cubic hyperpolarizability is separated into its two contributions, one describes the direct process and the other describes the cascaded process. The main difference between the two contributions is a geometrical factor controlling the collective interaction at the SH and appears solely in the cascaded term. This term supports enhanced SH under the nonlinear RA condition [3]. The separation between the direct and cascaded terms allows to obtain control on the relative phase and amplitude of the two contributions, which can lead to either constructive or destructive interference. In the meeting we will present the complete calculations and discuss the dynamics at the different points of interest including the intriguing phenomena of THG elimination.



1. Y. Tagaki and S. Muraki, "Third-harmonic generation in a noncentrosymmetrical crystal: direct third-order or cascaded second-order process?", Journal of luminescence, 87, 865-867 (2000).

2. R. Czaplicki, A. Kiviniemi, J. Laukkanen, J. Lehtolahti, M. Kuittinen and M. Kauranen, "Surface lattice resonances in second-harmonic generation from metasurfaces", Optics Letters, 41, 2684 (2016).

3. L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, "Nonlinear Surface Lattice Resonance in Plasmonic Nanoparticle Arrays", Phys. Rev. Lett. 118, 243904 (2017).

4. M. J. Huttunen, P. Rasekh, R. W. Boyd, and K. Dolgaleva, "Using surface lattice resonances to engineer nonlinear optical processes in metal nanoparticle arrays", PRA, 97, 053817 (2018).