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

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