Spontaneous symmetry breaking of dissipative optical solitons in a two-component Kerr resonator

Spontaneous Symmetry Breaking in Diffraction

We demonstrate spontaneous symmetry breaking in the diffraction of a laser-driven grating with memory in its nonlinear response. We observe, experimentally and theoretically, asymmetric diffraction even when the grating and illumination are symmetric. Our analysis reveals how diffracted waves can spontaneously acquire momentum parallel to the lattice vector in quantities unconstrained by the grating period. Our findings point to numerous opportunities for imaging, sensing, and information processing with nonlinear periodic systems, which can leverage a much richer diffractive response than their linear counterparts.

Real-time imaging of standing-wave patterns in microresonators

Real-time characterization of microresonator dynamics is important for many applications. In particular, it is critical for near-field sensing and understanding light-matter interactions. Here, we report camera-facilitated imaging and analysis of standing wave patterns in optical ring resonators. The standing wave pattern is generated through bidirectional pumping of a microresonator, and the scattered light from the microresonator is collected by a short-wave infrared (SWIR) camera. The recorded scattering patterns are wavelength dependent, and the scattered intensity exhibits a linear relation with the circulating power within the microresonator. By modulating the relative phase between the two pump waves, we can control the generated standing waves' movements and characterize the resonator with the SWIR camera. The visualized standing wave enables subwavelength distance measurements of scattering targets with nanometer-level accuracy. This work opens broad avenues for applications in on-chip near-field (bio)sensing, real-time characterization of photonic integrated circuits, and backscattering control in telecom systems.

Nonlinear topological symmetry protection in a dissipative system

We investigate experimentally and theoretically a system ruled by an intricate interplay between topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator where photons interact through the Kerr nonlinearity. In presence of a phase defect, the modal structure acquires a synthetic Möbius topology enabling the realization of spontaneous symmetry breaking in inherently bias-free conditions without fine tuning of parameters. Rigorous statistical tests confirm the robustness of the underlying symmetry protection, which manifests itself by a periodic alternation of the modes reminiscent of period-doubling. This dynamic also confers long term stability to various localized structures including domain walls, solitons, and breathers. Our findings are supported by an effective Hamiltonian model and have relevance to other systems of interacting bosons and to the Floquet engineering of quantum matter. They could also be beneficial to the implementation of coherent Ising machines.

Bifurcation analysis of complex switching oscillations in a Kerr microring resonator

Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the past two decades due to their compact sizes, unprecedented measurement capabilities, and widespread applications. The increasingly high finesse (or Q factor) of such resonators means that nonlinear effects are unavoidable even for low power, making them attractive for nonlinear applications, including optical comb generation and second harmonic generation. In addition, light in these nonlinear resonators may exhibit chaotic behavior across wide parameter regions. Hence, it is necessary to understand how, where, and what types of such chaotic dynamics occur before they can be used in practical devices. We study here the underlying mathematical model that describes the interactions between the complex-valued electrical fields of two optical beams in a single-mode resonator with symmetric pumping. Recently, it was shown that this model exhibits a wide range of fascinating behaviors, including bistability, symmetry breaking, chaos, and self-switching oscillations. We employ here a dynamical system approach to perform a comprehensive theoretical study that allows us to identify, delimit, and explain the parameter regions where different behaviors can be observed. Specifically, we present a two-parameter bifurcation diagram that shows how (global) bifurcations organize the observable dynamics. Prominent features are curves of Shilnikov homoclinic bifurcations, which act as gluing bifurcations of pairs of periodic orbits or chaotic attractors, and a Belyakov transition point (where the stability of the homoclinic orbit changes). In this way, we identify and map out distinctive transitions between different kinds of chaotic self-switching behavior in this optical device.

Binding dynamics of cavity solitons in a Kerr resonator with high order dispersion

Cavity solitons are persistent light pulses arising from the externally driven Kerr resonators. Thanks to the passive parametric gain, cavity soliton has been endowed with the natural advantage of the chip-scaled integration since it was first experimentally generated in the fiber-based platform. Deterministic single soliton with smooth spectrum is a preferred state for numerous applications. However, multiple solitons are more common in the resonators with anomalous dispersion. In this condition, adjacent solitons are easily perturbed to attract and collide with each other. Some experimental observations deviated from the aforementioned description have recorded the stable soliton intervals that can last for a long time scale. This phenomenon is known as soliton binding and is attributed to the presence of narrow resonant sidebands in the spectrum. While the stationary configuration of two binding solitons has been investigated, the dynamical evolution remains an area for further exploration. In this paper, we discuss the binding dynamics of the cavity solitons in the presence of high-order dispersion. The proposed theoretical predictions match well with the numerical results, encompassing both the stationary stable intervals and dynamic trajectories. Our research will provide a comprehensive insight into the soliton motion induced by the internal perturbations.

Random number generation using spontaneous symmetry breaking in a Kerr resonator

We demonstrate an all-optical random number generator based on spontaneous symmetry breaking in a coherently driven Kerr resonator. Random bit sequences are generated by repeatedly tuning a control parameter across a symmetry-breaking bifurcation that enacts random selection between two possible steady-states of the system. Experiments are performed in a fiber ring resonator, where the two symmetry-broken steady-states are associated with orthogonal polarization modes. Detrimental biases due to system asymmetries are suppressed by leveraging a recently discovered self-symmetrization phenomenon that ensures the symmetry-breaking dynamics act as an unbiased coin toss, with a genuinely random selection between the two available steady-states. We optically generate bits at a rate of 3 MHz without post-processing and verify their randomness using the National Institute of Standards and Technology and Dieharder statistical test suites.

Inter-mode soliton linear-wave scattering in a Kerr microresonator

Soliton microresonator frequency combs (microcombs) have recently emerged as an attractive new type of optical comb source with a wide range applications proposed and demonstrated. To extend the optical bandwidth of these microresonator sources, several previous studies have proposed and studied the injection of an additional optical probe wave into the resonator. In this case, nonlinear scattering between the injected probe and the original soliton enables the formation of new comb frequencies through a phase-matched cascade of four-wave mixing processes. In this work, we expand the relevant analyses to consider soliton-linear wave interactions when the soliton and the probe fields propagate in different mode families. We obtain an expression for the phase-matched idler locations as a function of the dispersion of the resonator and the phase detuning of the injected probe. We confirm our theoretical predictions in experiments performed in a silica waveguide ring microresonator.

Passive symmetry breaking of the space-time propagation in cavity dissipative solitons

Dissipative solitons are fundamental wave-pulses that preserve their form in the presence of periodic loss and gain. The canonical realization of dissipative solitons is Kerr-lens mode locking in lasers, which delicately balance nonlinear and linear propagation in both time and space to generate ultrashort optical pulses. This linear-nonlinear balance dictates a unique pulse energy, which cannot be increased (say by elevated pumping), indicating that excess energy is expected to be radiated in the form of dispersive or diffractive waves. Here we show that Kerr-lens mode-locked lasers can overcome this expectation. Specifically, by breaking the spatial symmetry between the forward and backward halves of the round-trip in a linear cavity, the laser can modify the soliton in space to incorporate the excess energy. Increasing the pump power leads therefore to a different soliton solution, rather than to dispersive/diffractive loss. We predict this symmetry breaking by a complete numerical simulation of the spatio-temporal dynamics in the cavity, and confirm it experimentally in a Kerr-lens mode-locked Ti:Sapphire laser with quantitative agreement to the simulation. The simulation opens a window to directly observe the nonlinear space-time dynamics that molds the soliton pulse, and possibly to optimize it.

Multiplexing of RF-assisted fiber ring resonators based on phase-shift amplification

The multiplexing of fiber ring resonators (FRRs) for no crosstalk loss sensing is proposed and demonstrated experimentally. The difference between the parallel and series FRRs is theoretically elaborated to determine the multiplexing scheme. The frequency response properties of the cascaded FRRs at distinct radio frequency (RF) working points are compared and analyzed. The optical carrier-based microwave interferometry system is implemented to verify the numerical investigation and exhibit the multiplexing of phase-shift based demodulation at diverse RF working points. Enhanced by the phase-shift amplification and the series configuration, each FRR can be independently demodulated by recording the phase of frequency response at the specific RF working point. The experimental results indicate that the sensitivity of transmittance reaches -0.341 rad with the advantage of robustness and immunity to power fluctuation. Owing to the prominent contribution of insensitive points and the series strategy, the crosstalk of multiplexing for loss sensing between two FRRs is eliminated virtually, which matches well with the theory. The proposed scheme provides an innovative approach for multiplexing the phase-based FRRs sensors without additional expenditure.

Diverse Forms of Breathers and Rogue Wave Solutions for the Complex Cubic Quintic Ginzburg Landau Equation with Intrapulse Raman Scattering

This manuscript consist of diverse forms of lump: lump one stripe, lump two stripe, generalized breathers, Akhmediev breather, multiwave, M-shaped rational and rogue wave solutions for the complex cubic quintic Ginzburg Landau (CQGL) equation with intrapulse Raman scattering (IRS) via appropriate transformations approach. Furthermore, it includes homoclinic, Ma and Kuznetsov-Ma breather and their relating rogue waves and some interactional solutions, including an interactional approach with the help of the double exponential function. We have elaborated the kink cross-rational (KCR) solutions and periodic cross-rational (KCR) solutions with their graphical slots. We have also constituted some of our solutions in distinct dimensions by means of 3D and contours profiles to anticipate the wave propagation. Parameter domains are delineated in which these exact localized soliton solutions exit in the proposed model.

Breathing dynamics of symmetry-broken temporal cavity solitons in Kerr ring resonators

We investigate theoretically and experimentally the instabilities of symmetry-broken, vectorial, bright cavity solitons (CSs) of two-mode nonlinear passive Kerr resonators. Through comprehensive theoretical analyses of coupled Lugiato-Lefever equations, we identify two different breathing regimes where the two components of the vectorial CSs breathe respectively in-phase and out-of-phase. Moreover, we find that deep out-of-phase breathing can lead to intermittent self-switching of the two components, spontaneously transforming a soliton into its mirror-symmetric state. In this process, solitons are also sometimes observed to decay. All our theoretical predictions are confirmed in experiments performed in an optical fiber ring resonator, where CS symmetry breaking occurs across the polarization modes of the resonator. To the best of our knowledge, our study constitutes the first experimental report of breathing instabilities of multi-component optical solitons of driven nonlinear resonators.

Spontaneous Symmetry Breaking in a Coherently Driven Nanophotonic Bose-Hubbard Dimer

We report on the first experimental observation of spontaneous mirror symmetry breaking (SSB) in coherently driven-dissipative coupled optical cavities. SSB is observed as the breaking of the spatial or mirror Z_{2} symmetry between two symmetrically pumped and evanescently coupled photonic crystal nanocavities, and manifests itself as random intensity localization in one of the two cavities. We show that, in a system featuring repulsive boson interactions (U>0), the observation of a pure pitchfork bifurcation requires negative photon hopping energies (J<0), which we have realized in our photonic crystal molecule. SSB is observed over a wide range of the two-dimensional parameter space of driving intensity and detuning, where we also find a region that exhibits bistable symmetric behavior. Our results pave the way for the experimental study of limit cycles and deterministic chaos arising from SSB, as well as the study of nonclassical photon correlations close to SSB transitions.

A Kerr polarization controller

Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearly-polarized input field is converted into a left- or right-circularly-polarized field, controlled via the optical power. The observations are explained by Kerr-nonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The all-optical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effect-based polarization controllers is generic to high-Q Kerr-nonlinear resonators and could also be implemented in photonic integrated circuits. Beyond polarization control, the spontaneous symmetry breaking of polarization states could be used for polarization filters or highly sensitive polarization sensors when operating close to the symmetry-breaking point.