Parametric conversion via second harmonic generation and two-hump solitons in phase-matched microresonators

Frequency conversion in microresonators has revolutionized modern-day nonlinear and quantum optics. Here, we present a theory of the multimode second harmonic generation in microresonators under conditions when the parametric conversion back to the pump spectrum dominates through the large domain in the resonator parameter space. We demonstrate that the spectral tunability of the sideband generation in this regime is governed by a discrete sequence of the so-called Eckhaus instabilities. We report the transition to mode locking and the generation of solitons, which have a double-pulse structure in the pump field. These solitons exist outside the bistability interval and on a slightly curved background.