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An optical ring resonator with third-order, or Kerr, nonlinearity willexhibit symmetry breaking between the two counterpropagating circulating powerswhen pumped with sufficient power in both the clockwise and counterclockwisedirections. This is due to the effects of self- and cross-phase modulation onthe resonance frequencies in the two directions. The critical point of thissymmetry breaking exhibits universal behaviors including divergent responsivityto external perturbations, critical slowing down, and scaling invariance. Herewe derive a model for the critical dynamics of this system, first for asymmetrically-pumped resonator and then for the general case of asymmetricpumping conditions and self- and cross-phase modulation coefficients. Thistheory not only provides a detailed understanding of the dynamical response ofcritical-point-enhanced optical gyroscopes and near-field sensors, but is alsoapplicable to nonlinear critical points in a wide range of systems.

Critical Dynamics of an Asymmetrically Bidirectionally Pumped Optical Microresonator