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Integrated nonlinear wavelength converters transfer optical energy fromlasers or quantum emitters to other useful colors, but chromatic dispersionlimits the range of achievable wavelength shifts. Moreover, because ofgeometric dispersion, fabrication tolerances reduce the accuracy with whichdevices produce specific target wavelengths. Here, we report nonlinearwavelength converters whose operation is not contingent on dispersionengineering; yet, the output wavelengths are controlled with high accuracy. Inour scheme, coherent coupling between counter-propagating waves in a photoniccrystal microresonator induces a photonic bandgap that isolates (in dispersionspace) specific wavenumbers for nonlinear gain. We first demonstrate the wideapplicability of this strategy to parametric nonlinear processes, by simulatingits use in third harmonic generation, dispersive wave formation in Kerrmicrocombs, and four-wave mixing Bragg scattering. In experiments, wedemonstrate Kerr optical parametric oscillators in which suchwavenumber-selective coherent coupling designates the signal mode. As a result,differences between the targeted and realized signal wavelengths are <0.3percent. Moreover, leveraging the bandgap-protected wavenumber selectivity, wecontinuously tune the output frequencies by nearly 300 GHz without compromisingefficiency. Our results will bring about a paradigm shift in howmicroresonators are designed for nonlinear optics, and they make headway on thelarger problem of building wavelength-accurate light sources using integratedphotonics.

Wavelength-Accurate Nonlinear Conversion through Wavenumber Selectivity in Photonic Crystal Resonators