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The extraordinary properties of nonlinear optical propagation processes indouble-domain positive/negative index metamaterials are reviewed. Theseprocesses include second harmonic generation, three- and four-wave frequencymixing, and optical parametric amplification. Striking contrasts with theproperties of the counterparts in ordinary materials are shown. We also discussthe possibilities for compensating strong losses inherent to plasmonicmetamaterials, which present a major obstacle in numerous excitingapplications, and the possibilities for creation of unique ultracompactphotonic devices such as data processing chips and nonlinear-optical sensors.Finally, we propose similar extraordinary three-wave mixing processes incrystals based on optical phonons with negative dispersion.

Merging Nonlinear Optics and Negative-Index Metamaterials