Self-induced Switching Research Articles

Self-induced switching and chimera states in spatially weighted neuronal networks

Self-induced switching and chimera states in spatially weighted neuronal networks

Results on hybrid control of self-oscillating resonant converters

Abstract A unified set of input-dependent coordinates is proposed for the description of parallel and series resonant converters. The description naturally leads to a hybrid feedback control strategy for self-oscillating behavior. We show through a hybrid representation that the ensuing dynamics admits a unique almost globally attractive hybrid limit cycle. A tuning parameter, the switching angle, is then numerically shown to lead to monotonic variation of the peak output current/voltage and of the self-induced switching frequency. Numerical simulations with high-accuracy software illustrate the desirable behavior of the self-oscillating scheme, and it robustness to unmodeled phenomena.

Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching

We delineate critical issues for ``controlling light with light'' in photonic crystal (PC) waveguides coupled to Kerr-nonlinear microresonators. These arise from (a) fundamental trade-off between switching speed and switching intensity threshold inherent in high-quality $Q$-factor cavities and (b) the dynamical nonlinear oscillation of such cavities in response to incident light pulses. Using finite-difference time-domain simulations of electromagnetic pulse propagation, we consider both (i) a nonlinear Fabry-Perot microresonator (embedded within a PC waveguide) exhibiting a narrow transmission resonance and (ii) a nonlinear point defect (side-coupled to a PC waveguide) exhibiting a narrow reflection spectrum. We describe self-induced switching from transmission to reflection induced by pulse intensity tuning as well as control of pulse transmission induced by the secondary, continuous (cw) laser field propagating through the same PC waveguide. For the Fabry-Perot microresonator, a well-defined self-switching threshold is obtained. However, this is accompanied by considerable temporal and spectral distortion of the pulse caused by the oscillatory nonlinear response of the microresonator. When the quality factor of the microresonator is increased, the switching intensity threshold can be lowered but the pulse transit (switching) time and the pulse distortion are increased. For the side-coupled microresonator, a gradual (not sharp) self-switching behavior as a function of incident intensity is obtained. For both the Fabry-Perot and side-coupled nonlinear microresonators, control of pulse transmission can be achieved by means of a secondary cw laser field. The cw power required for switching with realistic Kerr nonlinearities is in excess of $1\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕\ensuremath{\mu}{\mathrm{m}}^{2}$ and may cause optical damage to the semiconducting PC backbone. Both instantaneous and noninstantaneous Kerr-response models are considered. Our results underscore the limitations and trade-offs inherent in the possible control of light with light using Kerr-nonlinear microresonators.

Dynamical characterization of chaotic itinerancy in a three-mode laser subjected to frequency-shifted optical feedback

We investigated chaotic dynamics in a microchip three-mode solid-state laser subjected to frequency-shifted optical feedback. When the frequency shift was tuned to harmonic frequencies of the relaxation oscillation, a bifurcation from a periodic sustained relaxation oscillation ("soft-mode") state to a chaotic spiking ("hard-mode") state via a chaotic itinerancy was observed as the feedback intensity was increased. Dynamic characterizations of modal interplay and self-induced switching between the soft- and hard-mode chaotic states over times (i.e., chaotic itinerancy) were carried out by the information circulation analysis and joint time-frequency analysis of long-term experimental time series. Drastic changes in information transfer rates among oscillating modes and occasional frequency locking among periodicities of two chaotic states associated with switchings were identified in chaotic itinerancy. Essential dynamical behaviors were reproduced by numerical simulation.

Noise-driven switching and chaotic itinerancy among dynamic states in a three-mode intracavity second-harmonic generation laser operating on a Lambda transition.

We studied the antiphase self-pulsation in a globally coupled three-mode laser operating in different optical spectrum configurations. We observed locking of modal pulsation frequencies, quasiperiodicity, clustering behaviors, and chaos, resulting from the nonlinear interaction among modes. The robustness of [p:q:r] three-frequency locking states and quasiperiodic oscillations against residual noise has been examined by using joint time-frequency analysis of long-term experimental time series. Two sharply antithetical types of switching behaviors among different dynamic states were observed during temporal evolutions; noise-driven switching and self-induced switching, which manifests itself in chaotic itinerancy. The modal interplay behind observed behaviors was studied by using the statistical dynamic quantity of the information circulation. Well-organized information flows among modes, which correspond to the number of degeneracies of modal pulsation frequencies, were found to be established in accordance with the inherent antiphase dynamics. Observed locking behaviors, quasiperiodic motions, and chaotic itinerancy were reproduced by numerical simulation of the model equations.

Nonstationary chaotic oscillations in lasers with frequency-shifted feedback

The nonlinear dynamics of lasers with frequency-shifted delayed feedback are investigated. Resonant excitation of sustained relaxation oscillations by harmonic resonance is demonstrated. Self-induced switching between sustained relaxation oscillation and spiking oscillation is observed as the feedback coefficient is increased. Observed instabilities are well reproduced by numerical simulations of proposed model equations. A statistical analysis of this switching phenomenon is carried out numerically, and the results indicate that an inverse-power relation with the feedback coefficient determines the periods over which the system dwells in its relaxation-oscillation state.

Clustering, grouping, self-induced switching, and controlled dynamic pattern generation in an antiphase intracavity second-harmonic-generation laser

Antiphase dynamics in globally coupled optical systems are investigated numerically in the model of intracavity second-harmonic generation in multimode lasers. Clustering, grouping of antiphase motions, and self-induced chaotic switching among a factorial number of coexisting grouping states, leading to antiphase periodic states, are found to occur when a pump parameter is increased. Dynamical characterization of grouping behavior and self-induced switching is carried out by global intensity circulation analysis. Nonreciprocal independence of intensity flow in grouping states and switching-path formation process among coexisting grouping states are presented. The controlled switching-path formation between different periodic grouping states by perturbation-pulse injections is demonstrated.

Chaotic itinerancy in antiphase intracavity second-harmonic generation

The emergence of local chaotic antiphase states and self-induced switching among the ruins of local chaotic antiphase attractors (i.e. chaotic itinerancy) leading to fully developed global chaos have been demonstrated by numerical simulations in a model of intracavity second-harmonic generation in multimode lasers. Dynamical characterization of chaotic itinerancy has been carried out using circulation analysis.

Dynamical spatial-pattern memory in globally coupled lasers.

The chaotic dynamics found in globally coupled modulated laser systems have been switched into stable orbits, including antiphase periodic states and clustered states, by an injection-seeding method. Direct assignment to desired factorial periodic orbits has been demonstrated. Self-induced switching among destabilized clustered states (chaotic itinerancy) in the transition process from clustered states to global chaos has also been found.

COMPLEX DYNAMICS IN COUPLED NONLINEAR ELEMENT SYSTEMS

This paper reviews complex dynamics which arise through the interaction of simple nonlinear elements without chaotic response, including self-induced switching among local attractors (chaotic itinerancy) and related phenomena. Several realistic physical systems consisting of coupled nonlinear elements are considered on the basis of computer experiments: coupled nonlinear oscillator (e.g., discrete complex time-dependent Ginzburg-Landau equation) systems, coupled laser arrays, and a coupled multistable optical chain model.