title: 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.
authors: NSF Nanoscale Science and Engineering Center (NSEC), University of California, Berkeley 3112 Etcheverry Hall, UC Berkeley, California 94720, USA.
authors: Kevin
authors: K
authors: O'Brien
authors: 1] NSF Nanoscale Science and Engineering Center (NSEC), University of California, Berkeley 3112 Etcheverry Hall, UC Berkeley, California 94720, USA [2] Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
authors: Haim
authors: H
authors: Suchowski
authors: 1] NSF Nanoscale Science and Engineering Center (NSEC), University of California, Berkeley 3112 Etcheverry Hall, UC Berkeley, California 94720, USA [2] Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
authors: Junsuk
authors: J
authors: Rho
authors: NSF Nanoscale Science and Engineering Center (NSEC), University of California, Berkeley 3112 Etcheverry Hall, UC Berkeley, California 94720, USA.
authors: Alessandro
authors: A
authors: Salandrino
authors: NSF Nanoscale Science and Engineering Center (NSEC), University of California, Berkeley 3112 Etcheverry Hall, UC Berkeley, California 94720, USA.
authors: Boubacar
authors: B
authors: Kante
authors: 1] NSF Nanoscale Science and Engineering Center (NSEC), University of California, Berkeley 3112 Etcheverry Hall, UC Berkeley, California 94720, USA [2] Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
authors: Xiaobo
authors: X
authors: Yin
authors: 1] NSF Nanoscale Science and Engineering Center (NSEC), University of California, Berkeley 3112 Etcheverry Hall, UC Berkeley, California 94720, USA [2] Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA [3] Kavli Energy NanoSciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors: Xiang
authors: X
authors: Zhang