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Register a new userUniversal Symmetry Breaking Dynamics for the Kerr Interaction of Counter-Propagating Light in Dielectric Ring Resonators
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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.
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Light is generally expected to travel through isotropic media independent of its direction. This makes it challenging to develop non-reciprocal optical elements like optical diodes or circulators, which currently rely on magneto-optical effects and birefringent materials. Here we present measurements of non-reciprocal transmission and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) light waves to circulate in the resonator. Equivalently, the symmetry breaking can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. This effect is expected to take place in any dielectric ring-resonator and might constitute one of the most fundamental ways to induce optical non-reciprocity. Our findings pave the way for a variety of applications including all optical switching, nonlinear-enhanced rotation sensing, optically controllable circulators and isolators, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors.
The realization of spontaneous symmetry breaking (SSB) requires a system that exhibits a near perfect symmetry. SSB manifests itself through a pitchfork bifurcation, but that bifurcation is fragile, and perturbed by any asymmetry or imperfections. Consequently, exploiting SSB for real-world applications is challenging and often requires cumbersome stabilization techniques. Here, we reveal a novel method that automatically leads to symmetric conditions, and demonstrate its practical application in coherently-driven, two-mode, passive Kerr resonators. More specifically, we show that introducing a $pi$-phase defect between the modes of a driven nonlinear resonator makes SSB immune to asymmetries by means of a period-doubled dynamics of the systems modal evolution. The two-roundtrip evolution induces a self-symmetrization of the system through averaging of the parameters, hence enabling the realization of SSB with unprecedented robustness. This mechanism is universal: all symmetry-broken solutions of driven Kerr resonators have a period-doubled counterpart. We experimentally demonstrate this universality by considering the polarization symmetry breaking of several different nonlinear structures found in normal and anomalous dispersion fiber cavities, including homogeneous states, polarization domain walls, and bright vector cavity solitons.
We report the experimental observation of oscillatory antiphase switching between counter-propagating light beams in Kerr ring microresonators, including the emergence of periodic behaviour from a chaotic regime. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging that restores the broken symmetry on average. Self-switching of counter-propagating light is robust for realising controllable, all-optical generation of waveforms, signal encoding and chaotic cryptography.
Strongly interacting solitons confined to an optical resonator would offer unique capabilities for experiments in communication, computation, and sensing with light. Here we report on the discovery of soliton crystals in monolithic Kerr microresonators-spontaneously and collectively ordered ensembles of co-propagating solitons whose interactions discretize their allowed temporal separations. We unambiguously identify and characterize soliton crystals through analysis of their fingerprint optical spectra, which arise from spectral interference between the solitons. We identify a rich space of soliton crystals exhibiting crystallographic defects, and time-domain measurements directly confirm our inference of their crystal structure. The crystallization we observe is explained by long-range soliton interactions mediated by resonator mode degeneracies, and we probe the qualitative difference between soliton crystals and a soliton liquid that forms in the absence of these interactions. Our work explores the rich physics of monolithic Kerr resonators in a new regime of dense soliton occupation and offers a way to greatly increase the efficiency of Kerr combs; further, the extreme degeneracy of the configuration space of soliton crystals suggests an implementation for a robust on-chip optical buffer.
Both the group velocity and phase velocity of two solitons can be synchronized by a Kerr-effect mediated interaction, causing what is known as soliton trapping. Trapping can occur when solitons travel through single-pass optical fibers or when circulating in optical resonators. Here, we demonstrate and theoretically explain a new manifestation of soliton trapping that occurs between counter-propagating solitons in microresonators. When counter-pumping a microresonator using slightly detuned pump frequencies and in the presence of backscattering, the group velocities of clockwise and counter-clockwise solitons undergo periodic modulation instead of being locked to a constant velocity. Upon emission from the microcavity, the solitons feature a relative oscillatory motion having an amplitude that can be larger than the soliton pulse width. This relative motion introduces a sideband fine structure into the optical spectrum of the counter-propagating solitons. Our results highlight the significance of coherent pumping in determining soliton dynamics within microresonators and add a new dimension to the physics of soliton trapping.
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