Quasi-phase matching in periodic nonlinear structures provides an efficient method to phase match a single nonlinear process. However, periodic modulation is not suitable for multiple-wavelength interactions, such as dual wavelength second harmonic generation, frequency tripling and frequency quadrupling. Multiple processes may be phase-matched by using aperiodic, rather than periodic, modulation of the nonlinear coefficient. We have developed a method to phase match any two arbitrary processes by quasi-periodic modulation of the nonlinear coefficient. This method was experimentally verified by performing dual wavelength second harmonic generation, as well as frequency tripling (based on simultaneous phase matching of frequency doubling, followed by sum frequency generation of the first and second harmonic waves) in a single quasi-periodically-poled KTP crystal. Additional degrees of freedom are obtained by using two dimensional periodic or quasi-periodic modulation of the nonlinear coefficient. We discuss frequency tripling by a 2D periodic structure, as well as the application of 2D quasi-periodic structures for nonlinear frequency conversion.
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