Two-Dimensional Nonlinear Mixing Between a Dissipative Kerr Soliton and Continuous Waves for a Higher-Dimension Frequency Comb

Dissipative Kerr solitons (DKSs) intrinsically exhibit two degrees of freedom through their group and phase rotation velocity. Periodic extraction of the DKS into a waveguide produces a pulse train and yields the resulting optical frequency comb's repetition rate and carrier-envelope offset, respectively. Here, we demonstrate that it is possible to create a system with a single repetition rate but two different phase velocities by employing dual driving forces. By recasting these phase velocities into frequencies, we demonstrate, experimentally and theoretically, that they can mix and create new phase-velocity light following any four-wave mixing process, including both degenerately pumped and non-degenerately pumped effects. In particular, we show that a multiple-pumped DKS may generate a two-dimensional frequency comb, where cascaded nonlinear mixing occurs in the phase velocity dimension as well as the conventional mode number dimension, and where the repetition rate in each dimension differs by orders of magnitude.