Phase Mismatch–Free Nonlinear Propagation in Optical Zero-Index Materials

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Science  06 Dec 2013:
Vol. 342, Issue 6163, pp. 1223-1226
DOI: 10.1126/science.1244303

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Nonlinear Optics Made Easier

Nonlinear optical materials can change their optical properties in the presence of light. The nonlinearity results from the constructive addition of interacting photons, but the amount of nonlinear light produced is crucially dependent on meeting strict phase-matching conditions of the interacting photon fields. Suchowski et al. (p. 1223; see the Perspective by Kauranen) now show that metamaterials can be designed with optical properties that relax the phase-matching requirements. At a specific wavelength where the metamaterial exhibits zero refractive index, the photons are found to interact nonlinearly with the phasematching done automatically.


Phase matching is a critical requirement for coherent nonlinear optical processes such as frequency conversion and parametric amplification. Phase mismatch prevents microscopic nonlinear sources from combining constructively, resulting in destructive interference and thus very low efficiency. We report the experimental demonstration of phase mismatch–free nonlinear generation in a zero-index optical metamaterial. In contrast to phase mismatch compensation techniques required in conventional nonlinear media, the zero index eliminates the need for phase matching, allowing efficient nonlinear generation in both forward and backward directions. We demonstrate phase mismatch–free nonlinear generation using intrapulse four-wave mixing, where we observed a forward-to-backward nonlinear emission ratio close to unity. The removal of phase matching in nonlinear optical metamaterials may lead to applications such as multidirectional frequency conversion and entangled photon generation.

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