Period-one characteristic in an optoelectronic delayed feedback semiconductor laser and its application in sensing

Nonlinear dynamics in an optoelectronic delayed feedback semiconductor laser and its application in sensing are studied. We analyze the theories of stability and period of the laser. A route to quasi-periodic bifurcation or a stochastic state from stability is numerically analyzed by shifting the feedback level. The induced dynamics are found to be in one of four distributions(stable, periodic pulsed, period-three pulsed, and undamping oscillating).An external injection into the laser results in the process being more or less the opposite with the conventional optical injection cases. Based on this process or the dynamic regimes, we present a modeling of the incoherent detection sensor using the nonlinear period-one characteristic of the laser. The sensor discriminates the injection light variation as a sensing signal via detecting the behaviors from the period-one laser.     

Dynamic characteristics in an external-cavity multi-quantum-well laser

This paper outlines our studies of bifurcation, quasi-periodic road to chaos and other dynamic characteristics in an external-cavity multi-quantum-well laser with delay optical feedback. The bistable state of the laser is predicted by finding theoretically that the gain shifts abruptly between two values due to the feedback. We make a linear stability analysis of the dynamic behavior of the laser. We predict the stability scenario by using the characteristic equation while we make an approximate analysis of the stability of the equilibrium point and discuss the quantitative criteria of bifurcation. We deduce a formula for the relaxation oscillation frequency and prove theoretically that this formula function relates to the loss of carriers transferring between well regime and barrier regime, the feedback level, the delayed time and the other intrinsic parameters. We demonstrate the dynamic distribution and double relaxation oscillation frequency abruptly changing in periodic states and find the multi-frequency characteristic in a chaotic state. We illustrate a road to chaos from a stable state to quasi-periodic states by increasing the feedback level. The effects of the transfers of carriers and the escaping of carriers on dynamic behavior are analyzed, showing that they are contrary to each other via the bifurcation diagram. Also,we show another road to chaos after bifurcation through changing the linewidth enhancement factor, the photon loss rate and the transfer rate of carriers.     

Controlling Chaos of a Delayed Optical Bistable System

High-dimensional chaos was controlled with the occasional proportional feedback technique in a delayed optical bistable system which consists of a laser diode interferometer with a delayed opto-electronic feedback loop. Both the experiment and the numerical simulation showed that a large number of periodic orbits can be stabilized by controlling the chaotic attractor. The transient state of the trajectory under control was demonstrated.     

Instability control in microwave-frequency microplasma

This paper introduces comprehensive large-signal analyses of modulation dynamics and noise of a chaotic semiconductor laser. The chaos is induced by operating the laser under optical feedback (OFB). Control of the chaotic dynamics and possibility of suppressing the associated noise by sinusoidal modulation are investigated. The studies are based on numerical solutions of a time-delay rate equation model. The deterministic modulation dynamics of the laser are classified into seven regular and irregular dynamic types. Variations of chaotic dynamics and noise with sinusoidal modulation are examined in both time and frequency domains over wide ranges of the modulation depth and frequency. The results showed that chaotic dynamics can be converted into five distinct dynamic types; namely, continuous periodic signal (CPS), continuous periodic signal with relaxation oscillations (CPSRO), periodic pulse (PP), periodic pulse with relaxation oscillations (PPRO) and periodic pulse with period doubling (PPPD). The relative intensity noise (RIN) of these types is characterized when the modulation frequencies are much lower, comparable to, and higher than the resonance frequency. Suppression of RIN to a level 8 dB/Hz higher than the quantum limit was predicted under the CPS type when the modulation frequency is 0.9 times the resonance frequency and the modulation depth is 0.14.     

Theoretical modeling of the dynamics of a semiconductor laser subject to double-reflector optical feedback

We theoretically model the dynamics of semiconductor lasers subject to the double-reflector feedback. The proposed model is a new modification of the time-delay rate equations of semiconductor lasers under the optical feedback to account for this type of the double-reflector feedback. We examine the influence of adding the second reflector to dynamical states induced by the single-reflector feedback: periodic oscillations, period doubling, and chaos. Regimes of both short and long external cavities are considered. The present analyses are done using the bifurcation diagram, temporal trajectory, phase portrait, and fast Fourier transform of the laser intensity. We show that adding the second reflector attracts the periodic and perioddoubling oscillations, and chaos induced by the first reflector to a route-to-continuous-wave operation. During this operation, the periodic-oscillation frequency increases with strengthening the optical feedback. We show that the chaos induced by the double-reflector feedback is more irregular than that induced by the single-reflector feedback. The power spectrum of this chaos state does not reflect information on the geometry of the optical system, which then has potential for use in chaotic (secure) optical data encryption.     

线性延时反馈Josephson结的Hopf分岔和混沌化

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌. 关键词： 约瑟夫森结 线性延时反馈 Hopf分岔 混沌     

Stable route-tracking synchronization between two chaotically pulsing semiconductor lasers

Stable route-tracking synchronization is experimentally demonstrated in two semiconductor lasers with delayed optoelectronic feedback. When the two lasers are stably synchronized, the receiver laser is observed to track the route to chaotic pulsing of the transmitter laser. The stability of the route-tracking synchronization is examined by calculation of the transverse Lyapunov exponents of the coupled system.     

Periodic and chaotic oscillations in mutual-coupled mid-infrared quantum cascade lasers

Dynamic states in mutual-coupled mid-infrared quantum cascade lasers (QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang—Kobayashi equations model. Three types of period-one states were found, with different periods of injection time delay τ_inj, 2τ_inj, and reciprocal of the detuning frequency. Besides, square-wave, quasi-period, pulse-burst and chaotic oscillations were also observed. It is concluded that external-cavity periodic dynamics and optical modes beating are the mainly periodic dynamics. The interaction of the two periodic dynamics and the high-frequency dynamics stimulated by strong injection induces the dynamic states evolution. This work helps to understand the dynamic behaviors in QCLs and shows a new way to mid-infrared wide-band chaotic laser.     

Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback

We report an experimental study of ultra-high-frequency chaotic dynamics generated in a delay-dynamical electronic device. It consists of a transistor-based nonlinearity, commercially-available amplifiers, and a transmission-line for feedback. The feedback is band-limited, allowing tuning of the characteristic time-scales of both the periodic and high-dimensional chaotic oscillations that can be generated with the device. As an example, periodic oscillations ranging from 48 to 913 MHz are demonstrated. We develop a model and use it to compare the experimentally observed Hopf bifurcation of the steady-state to existing theory [Illing and Gauthier, Physica D 210, 180 (2005)]. We find good quantitative agreement of the predicted and the measured bifurcation threshold, bifurcation type and oscillation frequency. Numerical integration of the model yields quasiperiodic and high dimensional chaotic solutions (Lyapunov dimension approximately 13), which match qualitatively the observed device dynamics.     

Chaos in a multimode solid-state laser system

When a nonlinear crystal is placed within a multimode solid-state laser cavity, deterministic fluctuations are induced in the output intensity. In this paper, the results of our studies of the intensity noise in a diode pumped, intracavity frequency doubled Nd:YAG (neodymium doped yttrium aluminum garnet) laser will be presented. First, a novel technique to eliminate these fluctuations is described. Second, the observation of antiphase states in the laser output is discussed. These states are characterized by a cyclic periodic pulsing of the individual longitudinal mode intensities. Finally, the statistical properties of chaotic intensity fluctuations are characterized. It is be demonstrated that it is possible to accurately model the laser dynamics by a system of globally coupled, nonlinear oscillators.     

Characterizing bifurcations and chaos in multiwavelength lasers with intensity-dependent loss and saturable homogeneous gain

We consider the nonlinear dynamics of multiwavelength laser cavities with saturable transmitter and saturating homogeneous gain using a simple and general discrete model. Saturable transmitter is an intensity dependent loss in which the transmittance decreases when the incident optical power increases. We determine the condition under which the saturable transmitter will generate behaviors such as stable steady-state lasing states, periodic lasing states, and chaotic lasing states. Indeed, for sufficiently large power, steady-state operation is first destabilized through a Hopf bifurcation which generates periodic lasing solutions. This is followed by a sequence of period doubling bifurcations to chaotic lasing. The bifurcation structure leading to chaos is characterized by three key methods of dynamical systems: a Feigenbaum series, the calculation of Lyapunov exponents and the computation of the correlation dimension of the system. We found that even single wavelength operation can exhibit complex nonlinear dynamics if the loss element is a saturable transmitter.     

Experimental control of a chaotic semiconductor laser

We have experimentally controlled the chaotic output of a single-mode semiconductor laser pumped near threshold and subject to optical feedback. We used a novel technique called dynamic targeting, which was theoretically proposed by Wieland et al. [Opt. Lett. 22, 469 (1997)]. Optical feedback causes the semiconductor laser to undergo a bifurcation cascade that exhibits regions of stability, periodicity, chaos, and coherence collapse. By adjusting the feedback phase simultaneously as the feedback strength was varied we steered the laser into the stable maximum gain mode, and thus we stabilized the system at maximum intensity.     

Noise induced oscillations in time delayed semiconductor laser system

The paper reports a detailed analysis of the chaotic dynamics of a theoretical model of a time delayed semi conductor laser. The periodic, quasi-periodic and chaotic nature is investigated with phase-plots, bifurcation analysis and lyapunov exponents. The effect of the system when induced by colored and bounded sine-Wiener noise has been examined extensively. The nature of the noise-induced propagating waves is investigated with the help of wavelet power spectra. It has been observed that the additive noise can suppress the chaotic dynamics of the system. Also the system is more chaotic in the presence of multiplicative noise. Moreover, the additive and multiplicative noise can modulate the output power upto a certain level, with constant input parameters.     

Delay control of coherence resonance in type-I excitable dynamics

We consider a simple paradigmatic system of type-I excitability subject to noise and time-delayed feedback. This system is governed by a global bifurcation, namely a saddle-node bifurcation on a limit cycle. In the absence of noise, delay can induce complex dynamics including multiple stable and unstable periodic orbits. Random fluctuations result in coherence resonance in dependence on the noise strength. We show that this effect can be enhanced by delayed feedback control with suitably chosen feedback strength and time delay.     

非即变相位共轭反馈对半导体激光器动态特性的影响

从四波混频产生相位共轭的物理原因出发,定义了相位共轭镜（PCM）的响应时间．建立起非即变相位共轭反馈条件下半导体激光器的外腔模型。以响应时间及频率失调为参变量,对其分岔及噪声等动态行为进行数值分析。结果表明,不考虑噪声影响时,增加相位共轭镜响应时间会使混沌带出现的次数和范围得到较大的抑制,当响应时间增大到1．5ns时,混沌带消失,半导体激光器保持稳定的单周期状态;考虑噪声影响后,随若响应时间的相对强度噪声（RIN）可减小几dB甚至十几dB,产生突变需要的反馈量也增大一个数量级以上,且其频谱的峰值向高频方向移动;另外,由于共轭反馈引起的频率失调低于半导体激光器激射频率3个数量级以上．它只对分岔特性有影响．对相对强度噪声的影响几乎为零。     

Performance characteristics of positive and negative delayed feedback on chaotic dynamics of directly modulated InGaAsP semiconductor lasers

The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers with nonlinear gain reduction in its optimum value range is investigated using bifurcation diagrams. The results are confirmed by calculating the Lyapunov exponents. A negative delayed optoelectronic feedback configuration is found to be more effective in inducing chaotic dynamics to such systems with nonlinear gain reduction factor in the practical value range.      

延时反馈半导体激光器双劈控制混沌方法研究

提出延时反馈半导体激光器双劈控制混沌方法,建立有劈控制的激光动力学物理模型.通过调节激光器外腔光路中的光器件劈去控制反馈光光程,改变了反馈光的延时时间和反馈强度,在物理上实现了延时时间和反馈强度的双参数混沌控制.数值结果证明该方法可以控制激光混沌到周期态,能使激光器输出光脉冲平均功率增加. 关键词： 混沌 控制 劈 双参数     

Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation

This Letter is concerned with bifurcation and chaos control in scalar delayed differential equations with delay parameter τ. By linear stability analysis, the conditions under which a sequence of Hopf bifurcation occurs at the equilibrium points are obtained. The delayed feedback controller is used to stabilize unstable periodic orbits. To find the controller delay, it is chosen such that the Hopf bifurcation remains unchanged. Also, the controller feedback gain is determined such that the corresponding unstable periodic orbit becomes stable. Numerical simulations are used to verify the analytical results.     

Low frequency fluctuations in a multimode semiconductor laser with optical feedback

We study a multimode semiconductor laser subject to a moderate optical feedback. The steady state is destabilized by either a simple Hopf bifurcation leading to in phase dynamics or by a degenerate Hopf bifurcation leading to antiphase dynamics. The degenerate bifurcation is also a source of multiple coexisting attractors. We show that a simple interpretation of the low frequency fluctuations in the multimode regime is provided by a chaotic itinerancy among the many coexisting unstable attractors produced by the degenerate Hopf bifurcation.     

Bifurcation,chaotic phenomena and control of chaos in a one—dimensional discrete Josephson lattice

We have investigated the fluxon dynamical behaviour in a one-dimensional parallel array of small Josephson junctions in the presence of an externally applied magnetic field. In the case of high damping,the system is in stable state. On the contrary, in the case of low damping, bifurcation and chaotic phenomena have been observed. Control of chaos is achieved by a delayed feedback mechanism, which drives the chaotic system into a selected unstable periodic orbit embadded within the associated strange attractor. It is attractive to control chaos to a periodic state, rather than operating always outside the device parameter space where chaos dominates.