Predicting nonlinear properties of metamaterials from the linear response

Abstract

The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Miller's Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.

A review of metasurfaces: physics and applications

“…This seems to be also responsible for the recently observed broadband THz generation under femtosecond near-infrared laser excitation in an array of gold SRRs [237]. It was also shown that the geometry of resonators, particularly the asymmetry ratio, plays a critical role because of the mode overlap [238]. Although the nonlinear coefficients were enhanced by orders of magnitude, the absolute conversion efficiency is still rather low.…”

Controlling third harmonic generation with gammadion-shaped chiral metamaterials

“…Moreover, the third order nonlinear optical response of the proposed chiral metamaterials under illumination of a circularly polarized FW is numerically calculated using FEM method based on nonlinear scattering theory. 32 In the calculations, we first simulate the linear optical fields (E ω ) at the fundamental wavelength, which are assumed to be unaffected by the up-conversion process. The nonlinear polarization induced in the bulk of the nanostructure is then calculated by P 3ω = ε 0 χ (3) .…”

Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams

“…In metamaterials and nanostructures the application of Miller's rule is not straightforward. For example, it holds for third harmonic generation (THG), but fails for SHG, which can be explained by the nonlinear scattering model [28]. Examples of nonlinear near-field control in nanostructures have recently been reported [23,[28][29][30][31].…”

“…For example, it holds for third harmonic generation (THG), but fails for SHG, which can be explained by the nonlinear scattering model [28]. Examples of nonlinear near-field control in nanostructures have recently been reported [23,[28][29][30][31]. The nonlinear emission control is even more challenging in hybrid dielectric/plasmonic nanostructures, since the nonlinear optical generation can take place in the gap of the nanoantenna due to the presence of a nonlinear material, in the nonlinear dielectric surrounding the nanostructure, or in the nanostructure material itself [32].…”