  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.
