Universal symmetry-breaking dynamics for the Kerr interaction of counterpropagating light in dielectric ring resonators

Abstract

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry breaking mechanism in electrodynamics occurs between counter-propagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counter-propagating light in bi-directionally pumped microresonators finds application in the realisation of optical non-reciprocity (for optical diodes), studies of PT -symmetric systems, and the generation of counter-propagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr-interaction of counter-propagating light in a dielectric ring resonator. In particular, we study discontinuous behaviour in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realise, for example, highly sensitive near-field or rotation sensors. We then generalise to a time-dependent model, which predicts new types of dynamical behaviour, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarisation in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations.

Effects of self- and cross-phase modulation on the spontaneous symmetry breaking of light in ring resonators

“…This condition is the generalization of the critical point presented in Ref. [12] for A = 1 and B = 2.…”

“…This solution set is plotted in Fig. 2(a), along with its analogous graph, 2(b) , reported in [12]. Figs.…”

“…We note that symmetry breaking phenomena have a wide range of applications in nonlinear optics: enhancing the Sagnac effect [7,11]; realising isolators, circulators [10], and all-optical oscillators [12] (for use in integrated photonic circuits); and the development of enhanced near-field detectors [17]. A possible area of further application is the generation of temporal cavity solitons (TCS).…”

A nonlinear enhanced microresonator gyroscope

“…This symmetry breaking is illustrated in Fig. 1 [17,19] and the transmitted powers, indicative of the circulating powers, are detected on two photodiodes (PD). Rotation in the plane of the resonator causes a difference between the readings on PD1 and PD2.…”

Dissipative Polarization Domain Walls in a Passive Coherently Driven Kerr Resonator

“…Resonant build-up then occurs, and the intracavity fields interact through Kerr cross-phase modulation. A key phenomenon that can occur in this bidirectionally pumped system above a certain threshold is a spontaneous symmetry breaking of the circulating field intensities-i.e., the sudden change from equal intensities (a state that becomes unstable) to a situation in which the intensity of one field becomes dominant while the other is suppressed [1][2][3][4][5][6][7][8][9][10]. Microresonators can additionally exhibit oscillatory behaviors due to a variety of mechanisms, such as thermal instabilities [11] or external forcing [12].…”