Multi-color solitons and frequency combs in microresonators

Multi-color solitons that are parametrically created in dual-pumped microresonators generate interleaved frequency combs that can be used to obtain combs at new frequencies and, when synchronized, can be used for low-noise microwave generation and potentially as an element in a chip-scale clockwork. Here, we first derive three-wave equations that describe multi-color solitons that appear in microresonators with a nearly quartic dispersion profile. These solitons are characterized by a single angular group velocity and different angular phase velocities. We then use these equations to explain the interleaved frequency combs that are observed at the output of the microresonator. Finally, we used these equations to describe the experimentally-observed soliton-OPO effect. In this effect, the pump frequency color interacts nonlinearly with a signal frequency color to create an idler frequency color in a new frequency range, somewhat analogous to an optical parametric oscillation (OPO) process, but in which the Kerr nonlinearity plays a role in matching the angular group velocity, analogous to soliton formation. These three colors then create an interleaved frequency comb in the output waveguide. We determine the conditions under which we expect this effect to occur. We anticipate that the three-wave equations and their extensions will be of use in designing new frequency comb systems and determining their stability and noise performance.