  We investigate frequency comb generation in the presence of polarization
effects induced by nonlinear mode coupling in microresonator devices. A set of
coupled temporal Lugiato-Lefever equations are derived to model the propagation
dynamics, and an in-depth study is made of the modulational instability of
their multistable homogeneous steady-state solutions. It is shown that new
kinds of instabilities can occur for co-propagating fields that interact
through nonlinear cross-phase modulation. These instabilities display
properties that differ from their scalar counterpart, and are shown to result
in the generation of new types of incoherently coupled frequency comb states.
