Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

In this paper, the principal resonance response of a stochastically driven elastic impact(EI) system with time-delayed cubic velocity feedback is investigated. Firstly, based on the method of multiple scales, the steady-state response and its dynamic stability are analyzed in deterministic and stochastic cases, respectively. It is shown that for the case of the multivalued response with the frequency island phenomenon, only the smallest amplitude of the steady-state response is stable under a certain time delay, which is different from the case of the traditional frequency response. Then, a design criterion is proposed to suppress the jump phenomenon, which is induced by the saddle-node bifurcation. The effects of the feedback parameters on the steady-state responses, as well as the size, shape, and location of stability regions are studied. Results show that the system responses and the stability boundaries are highly dependent on these parameters. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.     

Optimization of Yb3+-doped double-clad fiber lasers using a new approximate analytical solution

We investigated the properties of continuous wave (CW) Yb³⁺-doped double-clad fiber lasers (DCFLs) with linear-cavities theoretically and numerically using the rate equations. Under steady-state conditions, a new approximate analytical solution for CW Yb³⁺-doped double-clad fiber lasers (DCFLs) with consideration of the scattering losses were deduced. Good agreement between the proposed solution and the numerical simulation was demonstrated. Compared with the known approximate solutions published in the literature, the proposed solution has a briefer expression, higher accuracy and wider scope of application, which extends the applicable range of the analytical result to low reflective feedback mirror configurations. The solution provides a clear physical understanding of the optimal design of the CW Yb³⁺-doped DCFLs and can be applied to different pump and output configurations. Using the proposed solution, the optimal design of the CW Yb³⁺-doped DCFLs was discussed. If cavity reflectivities are given in advance, the optimal fiber length is found to be independent of the pump power. When the pump power and reflectivity of the feedback end are known in advance, the results show that the optimal fiber length increases and the optimal reflectivity of output mirror decreases with increase in pump power. Furthermore, when the feedback mirror is highly reflective, there exists a certain tolerance of the optimal parameters, in which the conversion efficiency decreases only slightly. But the conversion efficiency is sensitive to reflectivity of output mirror if feedback mirror has low reflectivity.     

激光回馈波片位相延迟测量的误差源及消除方法

激光回馈法是一种新型的波片位相延迟测量方法。将波片放置在激光器与回馈镜之间,可使激光回馈波形产生偏振90°旋转（即跳变）现象,而两偏振态所占的周期比（占空比）与波片的位相延迟相关。通过测量占空比即可由计算机自动给出波片位相延迟。采用双向扫描回馈镜,2次获得并测出占空比,这样可以很好地消除两偏振态损耗的波动造成的测量误差,提高了该方法长期测量的稳定性。测量的重复性达到0.5°。该方法结构简单,在线测量精度高,满足工业化生产的需要。     

Stability of racemic and chiral steady states in open and closed chemical systems

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived.     

Effect of the External Mirror Feedback Strength in the Dynamics and Spectrum of the Injected Semiconductor Lasers

We analytically investigate the effect of an external mirror on the stability of an injected semiconductor laser, the latter treated as injected damped oscillators. In the studied configuration, the injected semiconductor laser with an external mirror is under the influence of a chaotic oscillating optical signal that is generated by a similar semiconductor master laser. We derive our results in terms of the damping rate and resonance frequency. We show that the external mirror can eliminate the unstable modes of the injected laser at low frequencies. Furthermore, the mirror can enhance the damping of the oscillation modes of the injected semiconductor laser; consequently, the driven response of the injected laser may have a broad spectrum, even wider than that of the chaotic driving signal. We also show results for the bandwidths of the injection amplitude and phase increment as functions of the injection rate and feedback strength of the external mirror. In addition, we use bifurcation and time-series curves to describe the dynamical behavior of the injected laser. We identify the feedback strength of injected laser, relative to that of the master laser, which induces synchronization between the injected-laser oscillation modes and the master laser.     

外腔镜非线性运动对激光回馈应力测量系统精度的影响及修正

基于激光的回馈效应可实现光学材料应力分布的测量, 而系统外腔镜的非线性运动会引起测量结果的误差, 影响系统的精度. 利用高精度Nd:YAG激光回馈干涉仪对外腔镜的位移随时间的变化进行测量, 采用高次拟合的方式得到位移与时间函数关系, 并利用三镜腔等效模型的调谐曲线方程, 对非线性运动引入的应力测量误差进行计算, 实现对系统精度的修正. 结果表明: 外腔镜运动方向不同, 引起的误差呈现相反的变化趋势; 将不同方向的测量结果进行平均, 可减小系统的测量误差. 分析了外腔镜非线性运动带来的误差对系统测量精度的影响, 提出了测量误差修正方法, 对提高系统的测量精度具有重要意义.     

Competitive relaxation of the lumped-distributed feedback intensity in dye lasers

Relaxation oscillations of intensity in lumped-distributed feedback dye lasers are observed. These are caused by a competition between distributed feedback (DFB) and a feedback caused by an external mirror cavity. The effect is interpreted in terms of rate equations which include the time delay of radiation reflected from external mirrors relative to radiation due to periodic structure.     

双光反馈半导体激光混沌系统中外腔延时反馈特征的抑制

在一个双光反馈半导体激光混沌系统中,固定其中一个反馈腔镜(固定腔M₁)的反馈延迟时间以及反馈强度,实验研究了另一个反馈腔镜(可变腔M₂)的反馈延迟时间以及反馈强度对系统混沌输出的延时反馈特征的影响.研究结果表明:在可变腔M₂与固定腔M₁的反馈强度相等的条件下,改变M₂的腔长,当其腔长约等于(但不能严格等于)M₁的腔长或者腔长的一半时,系统将呈现较好地抑制延时反馈特征效果;当M 关键词： 半导体激光器 双光反馈 混沌输出 延时特征     

外反馈He—Ne激光器的非稳特性研究

报道了平面镜和自泵浦相位共轭镜反馈Ｈｅ－Ｎｅ激光器的非稳特性，观测了反馈镜位置对激光光强起伏及波动频率的影响，即在半腔长的整数倍附近，激光光强具有较大的起伏和秒量级的准周期振荡，并对其产生机理进行了分析。     

Y模型四能级原子辅助光力学系统的多稳现象

本文对Y模型四能级原子辅助光力学系统的稳态特性进行了研究.结果发现,构成复合光力学系统的振动腔镜和被束缚在腔内的原子系综将随着弹簧劲度系数的减小,由单稳态过渡到多稳态.在劲度系数很大时,振动腔镜对整个光力学系统几乎无作用,光力学系统和处在腔中的原子系综都将出现一个稳态解.而当劲度系数足够小时,振动腔镜的稳态位移出现了多稳现象,随之对处于光力学腔中的原子系综的稳态行为也产生了影响,不但使得原子系综的极化率呈现出多个稳态解,同时使得腔中的原子系综对探测光的吸收和色散也发生了相应的变化.同时发现,通过调节劲度系数的取值可以控制整个系统稳态解的个数.这些研究结果在精密测量或量子信息处理等方面具有潜在应用价值.     

Mode profiles in resonators with a near 90° roof-top mirror

The transverse modes of a laser resonator comprising a near 90° roof-top mirror and a feedback mirror are studied theoretically. We relate this configuration to an almost plane roof-top resonator and apply the Fox and Li technique to compute the lowest-order symmetric and antisymmetric modes. The effects of perturbations to the vertex angle of the roof-top mirror, misalignments of the feedback mirror and curved feedback mirrors are examined.     

Feedback coupling loss in single mode fiber lasers

Based on the expansion of the fundamental mode LP₀₁ in single mode fiber in terms of Laguerre-Gaussian free space modes, the feedback coupling losses for two different types of cavity mirror, i.e., a curvature mirror and a combing mirror of a lens and a plane mirror, are numerically calculated for the first time. The results show that, for the curvature mirror, the lowest coupling loss is obtained when its curvature radius matches the wavefront curvature. In particular, if a plane mirror is used as the cavity mirror, it has to be placed close to the fiber end to obtain the low coupling loss. For the combing mirror, the lowest coupling loss can be obtained when the plane mirror is placed at the back focal plane of the lens, and the variation of the coupling loss is insensitive to the mirror positions for the lens with longer focal length. Finally, the plane mirror and the combing mirror of a lens and a plane mirror are suggested to be the cavity mirror in the practical construction of the high power fiber lasers.     

A laser feedback interferometer with an oscillating feedback mirror

A method is proposed to solve the problem of direction discrimination for laser feedback interferometers.By vibrating the feedback mirror with a small-amplitude and high-frequency sine wave,laser intensity is modulated accordingly.The modulation amplitude can be extracted using a phase sensitive detector(PSD).When the feedback mirror moves,the PSD output shows a quasi-sine waveform similar to a laser intensity interference fringe but with a phase difference of approximately ±π/2.If the movement direction of the feedback mirror changes,the phase difference sign reverses.Therefore,the laser feedback interferometer offers a potential application in displacement measurement with a resolution of 1/8 wavelength and in-time direction discrimination.Without using optical components such as polarization beam splitters and wave plates,the interferometer is very simple,easy to align,and less costly.     

Hopf bifurcations in time-delay systems with band-limited feedback

We investigate the steady-state solution and its bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed feedback. We show that the steady state is globally stable for small feedback gain and that local stability is lost, generically, through a Hopf bifurcation for larger feedback gain. We provide simple criteria that determine whether the Hopf bifurcation is supercritical or subcritical based on the knowledge of the first three terms in the Taylor-expansion of the nonlinearity. Furthermore, the presence of double-Hopf bifurcations of the steady state is shown, which indicates possible quasiperiodic and chaotic dynamics in these systems. As a result of this investigation, we find that AC-coupling introduces fundamental differences to systems of Ikeda-type [K. Ikeda, K. Matsumoto, High-dimensional chaotic behavior in systems with time-delayed feedback, Physica D 29 (1987) 223–235] already at the level of steady-state bifurcations, e.g. bifurcations exist in which limit cycles are created with periods other than the fundamental “period-2” mode found in Ikeda-type systems.     

Development of narrow-linewidth diode lasers by use of volume holographic transmission gratings

We present two diode laser setups that employ volume holographic transmission gratings to provide optical feedback. The advantage of this kind of grating is high diffraction efficiency and the possibility to place optical elements on both sides of the grating. This allows for advanced external cavities and adjustable feedback efficiency. The first setup is a diode laser in the Littman configuration with the transmission grating replacing the conventional reflection grating. The second setup improves the frequency selectivity by substituting the feedback mirror with a passive resonator. This grating-enhanced external cavity diode laser (GECDL) achieves excellent frequency stability. A prototype of the GECDL setup demonstrates an intrinsic linewidth of 7 kHz and an operation range that covers the full amplification profile of the laser diode.     

Generation of Steady-State Entanglement in Quadratically Coupled Optomechanical System Assisted by Two-Level Atoms

We propose a scheme for the realization of a hybrid, strongly entangled system formed of an atomic ensemble surrounded by a quadratically coupled optomechanical cavity with a vibrating mirror. We firstly investigate the steady-state bipartite entanglement between the movable mirror and the cavity mode with the help of an atomic media. It shows that the introduction of the atomic medium can greatly improve the entanglement between the movable mirror and the cavity mode. Secondly, steady-state tripartite entanglement including the movable mirror, the cavity and atom media are investigated. We find the robust tripartite entanglement persists in the present system.     

ITER装置中等离子体旋转和反馈控制对电阻壁模影响的数值研究

在托卡马克等离子体中,电阻壁模是非常重要的磁流体不稳定性,特征时间在毫秒量级.对长时间稳态运行下的先进托卡马克,电阻壁模限制着聚变装置的运行参数空间(放电时间和比压),影响经济效益,所以研究电阻壁模稳定性至关重要.本文使用MARS程序,针对ITER装置上9 MA先进运行平衡位形,研究了等离子体旋转和反馈控制对电阻壁模的...     

Spatial soliton-like structures in a thin-film system with a transverse photonic crystal in the feedback loop

The problem of existence and stability of soliton-like structures in a system consisting of a thin layer with resonance nonlinearity, a feedback mirror, and a photonic crystal located between them is studied. It is shown that, depending on the parameters of the photonic crystal, its presence can lead both to a change in the background on which localized structures are excited and to an increase in the interval of test pulse amplitudes necessary for the excitation of these structures.     

Axial feedback stabilization of flute modes for mirror machines

A novel scheme of feedback stabilization of the m=1 flute mode for axisymmetric mirror machines is proposed that has potential for reactor extrapolation. A three-region plasma model is analyzed, consisting of a hot core surrounded by a warm transition annulus, which in turn is surrounded by a warm halo annulus that is in contact with segmented annular feedback plates at the two end walls. For plasma parameters characteristic of the TMX-U and MFTF-B devices at the Lawrence Livermore National Laboratory and the MMX device at the University of California, Berkeley, the required feedback power is calculated. The results show that stability can be achieved in the MMX and TMX-U devices with a modest feedback gain and power. The power requirement for the near-reactor conditions of MFTF-B is more severe, but can be reduced by a modified choice of plasma parameters     

Stability of power grids: An overview

Transient stability and steady-state (small signal) stability in power girds are reviewed. Transient stability concepts are illustrated with simple examples; in particular, we consider three methods for computing region of attraction: time-simulations, extended Lyapunov function, and sum of squares optimization method. We discuss steady state stability in power systems, and present an example of a feedback control via a communication network for the 10?Unit 39 Bus New England Test system.