  An optical ring resonator with third-order, or Kerr, nonlinearity will
exhibit symmetry breaking between the two counterpropagating circulating powers
when pumped with sufficient power in both the clockwise and counterclockwise
directions. This is due to the effects of self- and cross-phase modulation on
the resonance frequencies in the two directions. The critical point of this
symmetry breaking exhibits universal behaviors including divergent responsivity
to external perturbations, critical slowing down, and scaling invariance. Here
we derive a model for the critical dynamics of this system, first for a
symmetrically-pumped resonator and then for the general case of asymmetric
pumping conditions and self- and cross-phase modulation coefficients. This
theory not only provides a detailed understanding of the dynamical response of
critical-point-enhanced optical gyroscopes and near-field sensors, but is also
applicable to nonlinear critical points in a wide range of systems.
