Tunable phase matching for efficient four-wave-mixing Bragg scattering in microrings

We propose and theoretically study a tunable frequency matching method for four-wave-mixing Bragg-scattering frequency conversion in microring resonators. A tunable coupling between the clockwise and counterclockwise propagating modes in the resonators was designed to introduce adjustable mode splitting, thus compensating for the frequency mismatching under different wavelengths. Using a silicon nitride ring resonator as an example, we showed that the tuning bandwidth approaches 35 number of FSRs. Numerical simulations further revealed that the phase-matching strategy is valid under different wavelength combinations and is robust to variations in waveguide geometry and fabrication. These results suggest promising applications in high-efficiency frequency conversion, integrated nonlinear photonics, and quantum optics.