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Optoelectronics Instrumentation and Data Processing

Spontaneous Symmetry Breaking in Glass Microspheres with Cubic Nonlinearity and Rayleigh Scattering

Elena A. Anashkina, Alexander V. Andrianov

Published Feb 1, 2025• 1 citation
Publisher

Abstract

Abstract Spontaneous symmetry breaking in glass dielectric microspheres with Kerr nonlinearity was studied experimentally and theoretically, taking into account the linear Rayleigh scattering between counterpropagating waves under bidirectional symmetric optical pumping. It was shown that the higher the Rayleigh scattering coefficient, the higher the threshold power required to observe the effect. An increase in the Rayleigh coupling coefficient between counterpropagating waves leads to a narrowing of the pump frequency detuning region from the exact resonance frequency required for spontaneous symmetry breaking, and a decrease in the asymmetry of the light states

DOI
10.3103/s8756699025700086

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Abstract Spontaneous symmetry breaking in glass dielectric microspheres with Kerr nonlinearity was studied experimentally and theoretically, taking into account the linear Rayleigh scattering between counterpropagating waves under bidirectional symmetric optical pumping. It was shown that the higher the Rayleigh scattering coefficient, the higher the threshold power required to observe the effect. An increase in the Rayleigh coupling coefficient between counterpropagating waves leads to a narrowing of the pump frequency detuning region from the exact resonance frequency required for spontaneous symmetry breaking, and a decrease in the asymmetry of the light states
Spontaneous symmetry breaking is a concept of fundamental importance in many areas of physics, underpinning such diverse phenomena as ferromagnetism, superconductivity, superfluidity and the Higgs mechanism. Here we demonstrate nonreciprocity 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) states of light to circulate in the resonator. Equivalently, this effect 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. Our findings pave the way for a variety of applications including optically controllable circulators and isolators, all-optical switching, nonlinear-enhanced rotation sensing, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors.
We experimentally demonstrate symmetry breaking, symmetry restoring, and intensity switching of counterpropagating Raman waves in a microresonator with symmetric intracavity waves at the pump frequency. Stationary symmetric and asymmetric states of Raman waves are theoretically found within a symmetric system of equations, and asymmetric branches of solutions turned out to be unstable. To explain the experimental results, it is proposed that there is a weak asymmetry in the system that radically changes the system behavior, which has been confirmed by numerical simulations.
Spontaneous symmetry breaking can occur in the powers of two optical modes coupled into a ring resonator, described by a pair of coupled Lorentzian equations, and featuring tunable self- and cross-phase modulation terms. Investigated is a wide variety of nonlinear materials by changing the ratio of the self- and cross-phase interaction coefficients. Static and dynamic effects range from the number and stability of stationary states to the onset and nature of oscillations. Minimal conditions to observe symmetry breaking are provided in terms of the ratio of the self- and cross-phase coefficients, detuning, and input power. Different ratios of the nonlinear coefficients also influence the dynamical regime, where they can induce or suppress bifurcations and oscillations. A generalized description on this kind is useful for the development of all-optical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators.
A theoretical study of the polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect has been undertaken. When the incident light is circularly polarized, a striking difference in gain is found for the co- and counter-rotating senses of polarization of the scattered light---the former being suppressed and the latter being exceptionally favored. The analysis begins with a model for the Kerr effect, which involves the alignment of anisotropic molecules in an electric field, but the results can be immediately generalized to any light scattering process of tensor symmetry. The nonlinear problem of the propagation of an intense elliptically polarized light wave in a Kerr-active medium is shown to have a solution in which the vibrational ellipse undergoes self-precession and self-retardation. The stimulated scatterings or instabilities of such a self-precessing and self-retarding light wave are obtained for the backward and forward directions. Birefringence, optical activity, and linear and circular dichroisms are some of the phenomena which result, but the forward direction yields substantially different results from the backward direction because of Stokes-anti-Stokes coupling.
This thesis experimentally and theoretically investigates the applications of spontaneous symmetry breaking in nonlinear resonators. Symmetry breaking refers to the transition of an initially symmetric system into a pair of asymmetric states. In a resonator with two equally driven polarization components, the intensities of the two fields would typically be expected to remain equal. However, this symmetry can spontaneously break as a result of small changes to the input conditions, causing one polarization component to increase in intensity while the other decreases. In practice, the selection enacted by symmetry-breaking is not entirely random, due to experimental asymmetries that bias the outcome. In this thesis we will experimentally and numerically explore a remarkable technique which can eliminate said biases through a nonlinear symmetry protection mechanism. Operation in this symmetry protected regime allows for a truly random selection of states, even in the presence of experimental imperfections. We experimentally verified the efficacy of the symmetry-protection mechanism by constructing an all-optical random number generator. Using an optical fiber resonator coherently driven with a train of pulses, we have achieved optical random bit generation at rates exceeding 3 Mbit/s without post-processing. We evaluated the randomness of the system with a variety of metrics, demonstrating the high fidelity of the random number generator. We extended this platform further to develop a novel optical Ising machine, a computational platform demonstrated to offer efficient solutions to combinatorial optimization problems which arise in a variety of contexts. Our proof-of-concept experimental results demonstrate continuous operation with up to 100 coupled spins for over an hour, enabled by the symmetry-protection protocol that ensures highly robust operation. Furthermore, the ability to measure artificial spins through optical intensity offers advantages over existing phase-based Ising implementations. We support our experimental findings with numerical simulations, which highlight the platform’s future potential for scaling to larger systems, with all-to-all coupling.