A new approach that can predict the nonlinear light scattering properties of nanostructures could help turn optical metamaterials to more practical uses. The unique electromagnetic properties of metamaterials stem from their physical structure rather than their chemical composition. This structure, for example, provides certain metamaterials with a negative refractive index. Efforts to engineer such properties remain in their infancy, however, with no general conclusion on the relationship between linear and nonlinear properties. Confocal microscopy confirmed that the nonlinear optical properties of metamaterials can be predicted using a theory about light passing through nanostructures. Images courtesy of Xiang Zhang/Berkeley Lab. Researchers at Lawrence Berkeley National Laboratory and the University of California, Berkeley, attacked the problem by combining Miller’s rule, a technique for estimating the nonlinear optical properties in natural crystals developed by Robert Miller, with a theory of nonlinear light scattering developed for nanostructures by Dutch scientist Sylvie Roke. “From the linear properties, one calculates the nonlinear polarization and the mode of the nanostructure at the second harmonic,” said doctoral candidate Kevin O'Brien. “We found the nonlinear emission is proportional to the overlap integral between these, not simply determined by their linear response.” The researchers used confocal microscopy to observe the second harmonic generation from metamaterial arrays whose geometry was gradually shifted from a symmetric bar shape to an asymmetric U shape. “We’ve shown that the relative nonlinear susceptibility of large classes of metamaterials can be predicted using a comprehensive nonlinear scattering theory,” said professor Dr. Xiang Zhang. “This will allow us to efficiently design metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.” The U.S. Department of Energy provided the funding. The work was published in Nature Materials (doi: 10.1038/nmat4214). For more information, visit www.lbl.gov. Metamaterial arrays whose geometry varies gradually from a symmetric bar to an asymmetric U shape were used to compare the predictive abilities of Miller's rule and a nonlinear light scattering theory.