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Multiple nonlinear optical interactions with arbitrary wave vector differences.

We present a novel method for simultaneously phase matching several nonlinear optical interactions within a single crystal. Quasiperiodic modulation of the nonlinear coefficient enables one to achieve high frequency mixing efficiencies for interactions with arbitrary wave vector differences. Doubling of two different frequencies as well as direct frequency tripling is experimentally demonstrated. The temperature- and wavelength-dependent properties of these interactions are explored. We discover that periodic approximation to the quasiperiodic structure shifts the phase-matched wavelengths.