Selective active resonance tuning for multi-mode nonlinear photonic cavities

Resonant enhancement of nonlinear photonic processes is critical for the scalability of applications such as long-distance entanglement generation. To implement nonlinear resonant enhancement, multiple resonator modes must be individually tuned onto a precise set of process wavelengths, which requires multiple linearly-independent tuning methods. Using coupled auxiliary resonators to indirectly tune modes in a multi-resonant nonlinear cavity is particularly attractive because it allows the extension of a single physical tuning mechanism, such as thermal tuning, to provide the required independent controls. Here we model and simulate the performance and tradeoffs of a coupled-resonator tuning scheme which uses auxiliary resonators to tune specific modes of a multi-resonant nonlinear process. Our analysis determines the tuning bandwidth for steady-state mode field intensity can significantly exceed the inter-cavity coupling rate if the total quality factor of the auxiliary resonator is higher than the multi-mode main resonator. Consequently, over-coupling a nonlinear resonator mode to improve the maximum efficiency of a frequency conversion process will simultaneously expand the auxiliary resonator tuning bandwidth for that mode, indicating a natural compatibility with this tuning scheme. We apply the model to an existing small-diameter triply-resonant ring resonator design and find that a tuning bandwidth of 136 GHz ~ 1.1 nm can be attained for a mode in the telecom band while limiting excess scattering losses to a quality factor of 10^6. Such range would span the distribution of inhomogeneously broadened quantum emitter ensembles as well as resonator fabrication variations, indicating the potential for the auxiliary resonators to enable not only low-loss telecom conversion but also the generation of indistinguishable photons in a quantum network.