The discovery of optical second harmonic generation in 1961 started modern nonlinear
optics,,. Soon after, RC 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 …

The discovery of optical second harmonic generation in 1961 started modern nonlinear
optics1–3. Soon after, RC Miller found empirically that the nonlinear susceptibility could be
predicted from the linear susceptibilities. This important relation, known as Miller's Rule4, 5,
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 materials6, have shown novel nonlinear properties such as phase …