Analogue simulation of stochastic parametric oscillators

The problem of a harmonic oscillator subject to both additive and multiplicative gaussian noise is solved analytically by means of an iteration procedure. Our solution agrees very closely with earlier predictions available in the literature. The reliability of perturbation approaches to stochastic systems that do not verify the detailed balance conditions is criticized by comparison with exact results worked out for this peculiar model. The effects due to finite correlation times of the fluctuations are also accounted for analytically. All of our predictions have been checked by means of analogue simulation.     

Phase bunching of oscillators in parametric resonance

Phase bunching in an ensemble of oscillators is considered by solving the Cauchy problem for the Mathieu equation using the asymptotic method of averaging in the third approximation for the zeroth resonance zone and in the fourth approximation for the first, second, third, and fourth zones in instability regions, as well as in stability regions near the boundaries with instability regions. It is shown that the existence and regularities of bunching follow from analysis of the well-known physical phenomenon, viz., beats of two oscillations. By way of example, parametric oscillations of charges at a node of the electric field of a standing wave are considered.     

High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators

This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.     

Rotating class of parametric resonance processes in coupled oscillators

We single out and elucidate basic features of strongly coupled parametric oscillators as opposed by symmetry to the type reducible to uncoupled Mathieu equations. The strongly coupled type is essential to the oscillations and waves in rotating structures and chiral systems. It exhibits only the main parametric resonance, no higher-order ones. As well, the relaxation–fluctuation behavior is unusual, characterized by a negative-energy oscillation mode that is, nonetheless, stable so the Gibbs statistics lose its force. The models presented are exactly solvable.     

A new definition of stochastic resonance

Summary Stochastic resonance in a bistable potential is characterized as a syncronization effect of the hopping mechanism induced by the external periodic bias. Most notably, syncronization is shown i) to attain a maximum with increasing the forcing frequency close to the relevant switching rate, thus revealing abona fide resonant process; ii) to occur even in the absence of symmetry breaking by the periodic forcing term. Paper presented at the International Workshop “Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena”, Elba, 5–10 June 1994.     

Pulsed optical parametric oscillators with intracavity optical parametric amplification: a critical study

It is known that the idler conversion efficiency of optical parametric oscillators (OPOs) can be increased by adding a second nonlinear crystal in the cavity. This crystal is pumped by the signal and acts as an optical parametric amplifier (OPA) for the idler. However, this technique unavoidably increases the oscillation threshold because of additional losses and increased build-up time due to cavity lengthening. In this paper, we investigate both theoretically and experimentally the benefits and drawbacks of this so called OPO–OPA configuration versus the singly resonant OPO (SRO) configuration. Calculations are found to be in agreement with an experimental study of a SRO and an OPO–OPA operating near 3.4 μm both pumped by a 90-mJ 27-ns Nd:YAG laser. Our study reveals that the OPO–OPA needs to be driven at least two times above threshold to produce more idler energy than the SRO. In addition, near 3 μm the OPO–OPA is particularly efficient given that the difference frequency wave generated in the second crystal is also output coupled. PACS 42.65.Yj; 42.65.Sf     

Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency

The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.     

随机共振研究新进展

介绍近10年来随机共振的几个重要研究方向取得的进展,对线性谐振子的随机共振研究,做了较详细的叙述.     

Continuous-wave optical parametric oscillators: recent developments and prospects

We review the progress in the development of continuous-wave optical parametric oscillators over the last decade. A recently developed theoretical analysis shows that their stability strongly depends on the group velocity dispersion of the nonlinear material used. Now, these devices generate not only near- and mid-infrared radiation, but also visible and terahertz light. Active locking to external references like atom transitions, resonators, or frequency combs enables mode-hop-free operation up to days. Furthermore, whispering-gallery-resonator-based devices enable the realization of millimeter-sized monolithic resonators with microwatt oscillation thresholds.     

Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

Solitons of singly resonant optical parametric oscillators

Single resonant parametric oscillators including intracavity quadratic and cubic nonlinearities are described in the mean-field limit with a cubic and quintic complex Ginzburg-Landau equation. Following our model, simple design criteria are derived for the generation of solitonlike pulses and beams for singly resonant optical parametric oscillators.     

Intensity noise of pump-enhanced continuous-wave optical parametric oscillators

4 (RTA), which provides a threshold pump power of 16 mW. The maximum signal wave power is 23 mW at a wavelength of 1243 nm. The spectral bandwidth of the signal wave is less than 750 kHz. Received: 3 February 1998     

双波长光参量振荡器的研究进展及应用

双波长光参量振荡器是一类非常新颖的激光器件。本文阐述了双波长光参量振荡器的工作原理,并总结了双波长光参量振荡器的研究进展,探讨了双波长光参量振荡器发展中存在的技术问题,介绍了双波长光参量振荡器的应用。     

Synchronization of coupled stochastic oscillators: The effect of topology

We study sets of genetic networks having stochastic oscillatory dynamics. Depending on the coupling topology we find regimes of phase synchronization of the dynamical variables. We consider the effect of time-delay in the interaction and show that for suitable choices of delay parameter, either in-phase or anti-phase synchronization can occur.      

Collective behavior of coupled nonuniform stochastic oscillators

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [K. Wood, C. Van den Broeck, R. Kawai, K. Lindenberg, Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators, Phys. Rev. Lett. 96 (2006) 145701], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter 0≤α≤1, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for α≤α^′<1. At α=1 the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.