  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.
