论文研究 Chaos Generation in a Semiconductor Ring Laser with an Optical Injection.pd

一种基于半导体环形激光器的混沌信号产生技术的研究，袁国慧，张鑫，提出了两种基于光注入半导体环形激光器的混沌信号的产生方案，注入光分别是来自独立的分布反馈激光器输出的不变光和具有反馈回路国武技论文在线http:/www.paper.edu.cn75 current of 81 mAFig 2 gives a mapping of different dynamic states in the srl subject to a constant externalinjection as a function of the injection coefficient and detuning frequency. The wathet blue, blue,red purple and rose red regions represent the stable, periodic, multi-periodic and chaotic80 oscillation rcspcctivcly Clcarly, chaos can bc gencratcd in thC Srl subjcct to a constant cxtcrnalinjection with appropriate injection coefficient and detuning frequency, such as 0. 071 and 3. 9GHz.Tab. I SRL device parametersSymbolDescriptionⅤaluecircular ring radius100uain coefticient1.l7×10velocity of light in the ring resonate8.57×10m/sLlinewidth enhancement factorcarrier density at the transparency7.6×1023threshold current21.5×10Acurrent injection effi1.6×10self-gain saturation coefficient3.16×10-23cross-gain saturation coelficientphoton lifetil5.17×10carrier lifetime3.15×10d-trin time12volume of the ring resonator cavity of 2.58x10 16mSRLT optical confinement factor 0.2260.250.20.150.0585detuning frequency /GHZFig. 2. Dependence of the dynamic state on the detuning frequency and injection coefficient.By setting the injection coefficient to 0.071, the dependence of the dynamic states in the SrLon the detuning frequency is investigated. Fig. 3(a) is the bifurcation diagram with the detuningfrcqucncy as the control paramctcr. Thcrc is no chaotic oscillation in the srl when the detuningfrequency is less than-10 GHz. As the detuning frequency varies from-10 to-5 GHz, lockingregion appears. The reason why the locking region does not appear near the zero detuningfrequency is that the induced change of the carrier density due to the optical injection changes the95 refractive index of ring resonator and finally results in a shift of the cigenfrcqucncy of the SriSRL experiences period oscillation routes to chaos when the detuning frequency is-15GHzFollowing the intermittent chaotic region( the chaos region disturbed by other dynamicschperiod and period-double dynamics), the period-doubling oscillation appears when the detuningfrequency is greater than 12 GHz. Fig. 3(b) shows the largest Lyapunov exponent spectrum which100 is approximately bascd on thc Classic wolf s algorithm. Bccausc a positive Lyapunov exponent3国武技论文在线http:/www.paper.edu.cnis regarded as an indication of chaos, Fig. 3(b) shows the chaotic region as a function of thedetuning frequency0.060.040.02≥detuning frequency /GHzdetuning frequency/ GHz105Fig 3. Numerical results of the output of the Srl with the detuning frequency as the control parameter (aBifurcation diagram. (b) Largest Lyapunov exponent spcctrum110Fig. 4(a) is the bifurcation diagram with the injection coefficient as the control parameter,which indicates that the srl experiences period-doubling bifurcation routes to chaos. In additionwhen the injcction coefficient is grcatcr than 0.074, thc chaotic output of the systcm is suppressed.Fig 4(b)shows the largest Lyapunov exponent spectrum as a function of the injection coefficientThe regions with posilive largesT Lyapunov exponent which is laken as a sign of chaos in Fig 4(b)115 agree well with the chaotic oscillation regions in Fig 4(a)o5o0>苏0.0200.0400.050.10.15020.25如00.050.10.1502injection coef f icientjection coeff ioFig 4. Numcrical results of the output of thc srl with the injcction cocfficicnts as the control parameter(a)Bifurcation diagram. (b)Largest Lyapunov exponent spectrum(a).(b),(c)in Fig. 5 show the time series, attractors and power spectra of the Srl when theinjection coefficients is 0.071 and the detuning frequency is 3. 9GHz Random-like time series and125 the strange attractor, as well as the relatively flat power spectrum indicate a chaotic system that isconsistent with the above analysis0282848.6889time t/nscarries Ns ie+23detuning frequency /GH130Fig. 5. Time series, attractors and power spectrum of SRI, the injection coefficients is 01.071, the detuningfrequency is 3.9 GHz4国武技论文在线http:/www.paper.edu.cnFig 6 is the schematic diagram for the improved scheme of bandwidth-enhanced chaos135neration, in which part of the chaotic output from the dFb laser with an optical feedback isinjcctcd into the SRLDFB LaserSRLFig. 6. Schematic diagram for a Srl with a chaotic optical injectionUnder appropriate working conditions, bandwidth-enhanced chaos occurs in the Srl biasedin the chaotic region. In this scheme, the feedback coefficient is set to 0.044, the detuningfrequency is 10.5GHz, the injection coefficient is 0. 35, and the bias current of Srl is 81mA. Thepower spectra of the chaos generated in two schemes are depicted in Fig. 7. By using two sets ofparamelers lo reach the maximum bandwidths in both cases separalely, the bandwidth of the145 bandwidth-enhanced chaos generated can reach 12GHz, which achieves approximately atwo-fold increase compared with the previous scheme. Here, the definition of bandwidth is thefrequency span where 80% of the energy is contained, because using the conventional 3-dBbandwidth definition to describe the fluctuant power spectrum of chaos is not very suitable150requency/GHzFig. 7. Power spectra of chaos: gray curve is the power spectrum of chaos in the former scheme; the detuningfrcqucncy is 3. 9GHz, thc injcction cocfficicnt 0.071, bias currcnt of srl &l mA. Black curvc is thc powcrspectrum of bandwidth-enhanced chaos in the improved scheme; the feedback coefficient is 0.044, the detuningfrequency 10.5 GHz, the injection coefficient 0.35, and the bias current of srl&ImA155In this paper, two chaos generation schemes are demonstrated numerically based on aemiconductor ring laser (SRL) with either a constant optical injection or a chaotic opticalinjection from an external dFB laser. Effects of operating parameters on the output of the srlare160 also investigated. Bandwidth-enhanced chaos generation is successfully realized based on thechaotic optical injcction schcmc. The bandwidth of the chaos achieves approximately a two-foldincrease compared with the former scheme. The results show that srls are suitable for interestingoplical chaos applications1651J. Liu, H. Chen, S. Tang, Optical-Communication Systcms Bascd on Chaos in Semiconductor Lasers[J], IEEETrans. Circuits and Systems, 2001, 48(12): 1475-1483[2J. Sacher, D. Baums, P. Panknin, Elsasser, W, Gobel, E.O., Intensity instabilities of semiconductor lasersunder current modulation, external light injection, and delayed feedback[J], Phys. Rev. A, 1992, 45(3): 1893-1905国武技论文在线http:/www.paper.edu.cnS M. Sorel, G. giulianiScire, Miglierina, R, Donati, S, Laybourn, P.J. R, Operating Regimes ofGaAs-AlGaAs Semiconductor Ring Lasers: Experiment and Model], IEEE Journal of Quantum Electronics,2003,39(10):1187-95[4]G. Yuan, S. Yu, Bistability and Switching Properties of Semiconductor Ring Lasers With External OpticalInjcction J], IEEE Journal of Quantum Elcctronics, 2008, 44(1): 41-48175 [5] B. Zhang, L Mao. S. Xie, Wei-Lian Guo, Yan Chen, Xin Yul, Xian-Jie Li, Li-Fang Qi, The study onNonlinear bifurcation Dynamics of a semiconductor ring laser[], Proceedings of the SPIE, 2009,7382:738213-1-738213-5[6W.Coomans, S. Beri, G. Van der Sande, Gelens, L, Danckaert, J, Optical injection in semiconductor ringlaser[J,Phys.Rev.A,2010,81(3):033802180[7] A. Uchida, T. Heil, Y Liu, Aida, T, High-Frequency Broad-Band Signal Generation Using a SemiconductorLascr with a Chaotic Optical Injcction, IEEE Journal of Quantum Electronics, 2003, 39(11): 1462-1467[8] Wolf, A, Swift, J B, Swinney, H L,, Vastano. J. A l, Determining Lyapunov exponents from a time series,Physica D,1985,16D(3):285-317185一种基于半导体环形激光器的混沌信号产生技术的研究袁国慧,张鑫,王卓然(电子科技大学光电信息学院,成都610054)摘要:提出了两种基于光注入半导体环形激光器的混沌信号的产生方案,注入光分別是来自1∞0独立的分布反馈激光器输出的不变光和具有反馈囻路的分布反馈激光器输岀的混沌光、调节来自独立的分布反馈激光器不变光的注入系数和失谐频率,可以使环形激光器产生混沌振荡。模拟的参数图展示了环形激光器输岀状态对注入系数和失谐频率的依赖关系,分岔图和李雅普诺夫指数谱描述了外界扰动条件下的环形激光器通向混沌振荡的路径。同时,提出的带宽増强型混沌信号的产生方案,是将具有反馈回路的分布反馈瀲光器蝓岀的笮带混沌光注195入到环形激光器中,产生了宽带混沌信号,带宽约为12GHL的、大约是前一种方案的两倍关键词:混沌信号;半导体环形激光器;光注入;光反馈;分岔图中图分类号:TN929