Title: The bandgap-detuned excitation regime in photonic-crystal resonators

Abstract: Control of nonlinear interactions in microresonators enhances access to classical and quantum field states across nearly limitless bandwidth. A recent innovation has been to leverage coherent scattering of the intraresonator pump as a control of group-velocity dispersion and nonlinear frequency shifts, which are precursors for the dynamical evolution of new field states. A uniform periodicity nanostructure addresses backscattering with one resonator mode, and pumping that mode enables universal phase-matching for four-wave mixing with control by the bandgap. Yet, since nonlinear-resonator phenomena are intrinsically multimode and exhibit complex modelocking, here we demonstrate a new approach to controlling nonlinear interactions by creating bandgap modes completely separate from the pump laser. We explore this bandgap-detuned excitation regime through generation of benchmark optical parametric oscillators (OPOs) and soliton microcombs. Indeed, we show that mode-locked states are phase matched more effectively in the bandgap-detuned regime in which we directly control the modal Kerr shift with the bandgaps without perturbing the pump field. In particular, bandgap-detuned excitation enables an arbitrary control of backscattering as a versatile tool for mode-locked state engineering. Our experiments leverage nanophotonic resonators for phase matching of OPOs and solitons, leading to control over threshold power, conversion efficiency, and emission direction that enable application advances in high-capacity signaling and computing, signal generation, and quantum sensing.