摘要
随着现代通信技术的不断发展,通信容量的不断增加,迫切需要研究开发具有高速、高保密性的新一代信息安全保密技术。近来,国际上对基于半导体激光器的光混沌及其在保密通信中应用的研究急剧升温,其技术的突破,必将对保密通信,特别是对军事保密通信产生革命性的影响。而相对于常规的边发射半导体激光器,作为新型量子阱半导体激光器的典型代表,垂直腔表面发射激光器(VCSLEs)具有低阈值电流,易于单纵模输出,大的调制带宽,易于集成等优点而受到人们的广泛关注。但目前人们对VCSELs的混沌同步特性及其在保密通信中的应用还缺乏深入的研究。
本文针对VCSELs输出存在两个可能正交偏振态的特点,提出了两种实现单向双信道混沌通信系统方案：一种是基于平行光反馈和平行光注入下单向耦合VCSELs同步系统(简称平行系统),另一种是基于旋转光反馈和注入下单向耦合VCSELs系统(简称旋转系统)。对这两种系统中的两个正交线偏振模和总输出的混沌同步特性和混沌保密通信性能,内部参数失配对混沌同步质量的影响,以及电流变化时两个线偏振模式强度差值的变化等进行了深入研究。研究结果表明：在固定其他参数的情况下,在阈值电流附近时,平行系统中x模占主导地位,y模极弱,随着电流的增大,平行系统中两个线偏振模式的强度差值逐渐减小,而旋转系统中两个线偏振模式的强度始终相当；平行和旋转系统中两个线偏振模式和总输出之间都能实现完全同步,但是旋转系统对内部参数失配表现出更好的容忍性；在旋转系统中,分别加载在两个线偏振模式的传输信号能分别很好的解调出来,但是在平行系统中,当电流较小时(X模占主导地位),加载在x模式上的信号能很好的解调出来,而加载在y模式上的解调结果比较差。但随着电流的增大,y模逐渐增强,加载在y模式上的信号也能被成功解调。
The security of the information transmission has become more and more important with the development of modern communication technology. In recent years, chaos and chaos synchronization of semiconductor lasers (SLs) has attracted much attention for its potential applications in secure communications. The break-though of this technology will bring about revolutions on secure communications, especially on martial secure communications. Compared to the conventional edge-emitting semiconductor lasers, the vertical-cavity surface-emitting lasers, as a new type and typical representative of quantum-well semiconductor lasers (VCSELs), exhibit several desirable characteristics such as a small threshold current, circular beam profile with narrow divergence, single longitudinal mode emission, wafer-scale testing and array capabilities. These great advantages have stimulated their development and use in applications. However, at present, the deep physical insight into chaos synchronization of VCSELs and its applications in secure communications are lacking.
In this paper, two dual-channel chaotic synchronization configurations are proposed, taking the two orthogonal linear polarization (LP) states of the output of VCSELs into consideration. Two systems are constructed on the basis of two unidirectionally coupled VCSELs. One is called the polarization-preserved coupled system or the parallel coupled system for short, where a VCSEL subjected to polarization-preserved optical feedback is used as a transmitter and the other VCSEL subjected to polarization-preserved optical injection is used as a receiver. The other is called the polarization-rotated coupled system for short, where a VCSEL subjected to polarization-rotated optical feedback is used as a transmitter and the other VCSEL subjected to polarization-rotated optical injection is used as a receiver. The synchronization and communication performances of these two systems are numerically investigated. The results show that, the averaged intensity of x LP mode is always equivalent to that of y LP mode for the case of polarization-rotated optical feedback. But for the case of polarization-preserved optical feedback, the average intensities of these two LP modes are very different; the difference between the average intensities of two orthogonal LP modes becomes smaller with the current increase, In these two systems, complete synchronization can be achieved for each pair of corresponding LP modes and the total output, respectively. However, compared with the parallel coupled system system, the polarization-rotated coupled system has higher tolerance to mismatched parameters. Furthermore, in the polarization-rotated coupled system, the encoded messages can be successfully extracted for both of orthogonal LP modes. But in the parallel coupled system, only the encoded messages modulated on x LP mode can be successfully demodulated when the current is small. The message modulated on y LP mode cann't be successfully extracted until the current increase to some value.
引文
[1].潘立登等,《网络通信中的基本安全技术》,电子技术应用,2000年第3期。
[2].关新平,范正平,陈彩莲等.混沌控制及其在保密通信中的应用.国防工业出版
社.2002
[3].方锦清.驾驭混沌与发展高新技术.北京：原子能出版社.2002
[4]. L. M. Pecora, T. L. Carroll. "Synchronization in chaotic systems," Phys. Rev. Lett., 1990,64(8):821-824.
[5]. L. M. Pecora, T. L. Carroll. "Driving systems with chaotic signals," Phys. Rev. A, 1991,44(8):2347-2388.
[6]. T. L. Carroll, L. M. Pecora. "Synchronization chaotic circuits," IEEE Trans. Circuits Syst.,1991, CAS-38,453-456.
[7]. B. A. Huberman, E. Lumer. "Dynamics of adaptive systems," IEEE Trans Circuits Syst.,1990,37(4):547-550;
[8].K. Pyragas, "Continuous control of chaos by self-controlling feedback," Phys. Rev. A,1992,170,421-428.
[9].胡岗.混沌控制.上海：科学教育出版社.2000
[10]. M. K. Ali, J. Q. Fang. "Synchronization of chaos and hyperchaos using linear and nonlinear feedback i:unctions," Physical Review E.1997,55(5):5285-5290
[11]. L. Koraev, K. S. Halle, K. Eckert, L. O. Chua, and U. Parlitz, "Experimental demonstration of secure communication via chaotic synchronization," Int.Bifurcation chaos,1992,2,709-714.
[12]. J. A. K. Suykens, P. F. Curran,-and L. O. Chua, "Robust synthesis for master-slave synchronization of Lur's systems," IEEE Trans Circuits Syst.,1999,46(7):841-878.
[13]. K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, "Synchronization of Lorenz-based chaotic circuit with application to communications", IEEE Trans Circuits Syst-Ⅱ,1993,40(10):626-633.
[14]. A. Uchida, S. Yoshimori et al, "Chaotic on-off keying for secure communications," Opt. Lett.,26(12):866-868.
[15]. T. Heil, J. Mulet, I. Fischer, C. R. Mirasso et al, "On/off phase shift-keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron.,2002,38,1162-1170.
[16]. T. Stojanovski, L. Kocarev and U. Parlitz, "Driving and synchronization by chaotic impulsive," Phys. Rev E,1996,54(2):2128-2138.
[17]. T. yang and L. O. Chua, "Impulsive synchronization of Lorenz systems," Phys. Rev. A,1997,26,349-354.
[18].J. M. Liu, H. F. Chen, S. Tang. "Synchronized chaotic optical communications at high bit rates," IEEE Quantum Electron.,2002,38(9):1141-1154.
[19]. J. Paul, S. Sivaprakasam, P. S. Spencer, et al. "GHz bandwidth message transmission using chaotic diode lasers," Electronics Lett.,2002,38(1):28-29.
[20]. H. G Winful, L. Rahman. "Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers," Phys. Rev. Lett.,1990,65(13):1575 — 1578
[21]. R. Roy, K. Sthornburg. "Experimental synchronization of chaotic lasers," Phys. Rev. Lett.,1994,28(22):2009-2011
[22].刘增基,周洋溢,胡辽林等.光纤通信.西安：西安电子科技大学出版社.2001
[23]. P Colet, R. Roy, "Digital communication with synchronized chaotic lasers," Opt. Lett.,1994,19(24).
[24]. V. Annovazzi-Lodi, S. Donati, A. Scire, "Synchronization of chaotic injected-laser systems and its application to optical cryptography", IEEE J. Quantum Electron., 1996,32,953-959.
[25]. V. Annovazzi-Lodi, S. Donati, A. Scire, "Synchronization, of chaotic lasers by optical feedback for cryptographic applications," IEEE J. Quantum Electron,1997, 33(9):1449-1454.
[26]. A. Uchida, M. Shinozuka, T. Ogawa, et al. "Experiments on chaossynchronization in two separate microchip lasers," Optics Letters.1999,28(1):19-21.
[27]. L. G Luo, P. L. Chu, H. F. Liu, "1-GHz optical communication system using chaos in erbium-doped fiber lasers," IEEE Photonics Technology Letters.2000, 12(3):269-271.
[28]. R. Wang, K.Shen, "Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to driver them," Physical Review E. 2001,65(12):016207-1-4.
[29]. C. Juang, T. M. Hwang, J. Juang, and W. W. Lin, "Optical chaotic AM demodulation by asymptotic synchronization," IEEE Photon Technol Left,2000,36(1):179-181.
[30]. S. Sivaprakasam, k. A. Shore, "Message encoding and decoding using chaotic external-cavity diode lasers," IEEE J. Quantum Electron,2000,36,(1):35-38.
[31]. A. Uchida, Y. Liu, L. Fischer, et al, "Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers," Phys. Rev. A,2001,64(2): 023801-1-6.
[32]. S. Sivaprakasam, K. A. Shore, "Cascaded synchronization of external-cavity laser diodes", Opt. Lets,2001,26(5):253-254.
[33]. J. M. Liu, H. F. Chen, S. Tang, "Optical-communication based on chaos in semiconductor lasers," IEEE Trans Circuits Syst-1,2001,48(12):1475-1483.
[34]. J. M. Buldu, J. Garcia-Ojalvo, M. C. Torrent, "Demultiplexing chaos from multimode semiconductor lasers," IEEE J Quantum Electronics.2005, 41(2):164-170.
[35]. L. Wu, S. Zhu, "Mufti-channel communication using chaotic synchronization of mufti-mode lasers," Phys. Rev. A,2003,157-161.
[36]. J. M. Buldu, J. Garcia-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using un-directionally coupled semiconductor lasers," IEEE J. Quantum.,2004,40(6):640-650.
[37]. J. Paul, S. Sivapralcasam, K. A. Shore, "Dual-channel chaotic optical communication using external-cavity semiconductor lasers," J. Opt. Soc. Am. B., 2004,21(3).
[38]. T. Wipiejewski, K. Panzlaf, E. Zeeb, et al., "Submilliamp vertical cavity laser diode structure with 2.2 run continuous tuning," 18# European Conf..on Opt. Commun., ECOC' 92,1992, No. PDII-4.
[39]. P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical of chaotic external-cavity VCSELs," IEEE J. Quantum Electron.,1998, 34(9):1673-1679.
[40]. P. S. Spencer, C. R. Mirasso, "Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSEL's". IEEE J. Quantum Electron.,1998, 35(5):803-809.
[41]. S. F Yu, P Shun, N. Q. Ngo. "Performance of optical chaotic communication system using multimode vertical cavity surface emitting lasers. Opt. Commua.,2001, 200:143-152.
[42]. N. Fujiwara, Y. Takiguchi, J. Ohtsubo. "Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers," Opt. Lett.,2003,28(18):1677-1679.
[43]. M. S. Torre, C. Masoller, K. A. Shore, "Synchronization of unidirectionally coupled multi-transverse-mode vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 21,1772-1780(2004).
[44]. Y. H. Hong, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore. "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Optics Lett,2004,29(11):1215-1217.
[45]. Y. H. Hong, M. W. Lee, P. S. Spencer, K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,"
Opt Lett.,2004,32,1215-1217.
[46]. M. W. Lee, Y. Hong, K. A. Shore, "Experimental demonstration of VCSEL-based chaotic optical communications," IEEE Photon. Technol. Lett.,2004, 16(10):2392-2394.
[47]. R. Ju, P. S. Spencer, K. A. Shore, "Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron.,2005,41(12):1461-1467.
[48]. X. F. Li, Wei Pan, Dong Ma, Bin Luo, "Chaos synchronization of unidirectionally injected vertical-cavity surface-emitting lasers with global and mode-selective coupling," Opt. Express,2006,8(14):3138-3151.
[49]. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, M. Y. Wang, "Separate polarization modes synchronization and synchronization switches between vertical-cavity surface-emitting lasers," Opt. Rev.2006,13,443-448.
[50]. W. L. Zhang, W. Pan, B. Luo et al. "Theoretical study on polarization dynamics of VCSELs with negative optoelectronic feedback," Appl. Opt.,2007,46(29): 7262-7266.
[51].钟东洲、夏光琼、王飞、吴正茂.基于光反馈的单向耦合注入垂直腔表面发射激光器的矢量混沌同步特性研究.物理学报,2007，56(6)：3279-3291.
[52]. M. Sciamanna, I. Gatare, A. Locquet, K. Panajotov, "Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection," Phys. Rev. E,2007,75,056213-1-10.
[53]. I. Gatare, M. Sciamanna, A. Locquet, K. Panajotov, "Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers," Opt. Lett.2007,32,1629-1631.
[54]. Y. H. Hong, P. S. Spencer, K. A. Shore, "Enhanced chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers with polarization-preserved injection," Opt. Lett.2008,33,587-589.
[55]. D. Z. Zhong, G Q. Xia, Z. M. Wu, X. H. Jia, "Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback," Opt. Commun.2008,281, 1698-1709.
[56]. D. Z. Zhong, Z. M. Wu, "Complete chaotic synchronization mechanism of polarization mode of VCSEL with anisotropic optical feedback," Opt. Commun. 2009,282,1631-1639.
[57]. A. T. Ryan, G P. Agrawal, G R. Gray, et al., "Optical-feedback-induced chaos and its control in multimode semiconductor lasers," IEEE J. Quantum Electron.,1994, 30(3):668-679.
[58]. Y. Liu, J. Ohtsubo, "Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer," IEEE J. Quantum Electron.,1997, 33(7):1163-1169.
[59].M. Yousefi, D. Lenstra, G Vemuri, et al., "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.-Optoelectron.,2001, 148(5):233-237.
[60]. R. J. Jones, P S. Spencer, K. A. Shore, "Controlling chaos in a semiconductor laser by external optical injection," IEE Proc.-Optoelectron.,2000,147(l):67-70.
[1]. K. Iga, "Surface-emitting laser-its birth and generation of new optoelectronics field," IEEE J. Select. Topics Quant. Electr.,2000,6(6):1201-1215.
[2].张存善,张延生,段晓峰等,垂直腔面发射激光器DBR结构反射特性分析.光电子·激光,2002,13(1)：34-36.
[3]. J. P Weber, K. Malloy, S. Wang. "Effect of layer thickness variations on vertical-cavity surface-emitting DBR semiconductor lasers," IEEE Photon. Technol. Lett.,1990,2(3):162-164.
[4].刘宝利,王炳桑,徐仲英.分布布拉格反射器(DBR)对半导体微腔一些特性的影响.半导体学报,2001,22(3)：335-339.
[5]. G P Agrawal, N. K. Dutta. Semiconductor lasers,2nd ed.. New York:Van Nostrand Reinhold,1993.
[6].周炳琨,高以智,陈调嵘等.激光原理第四版.北京：国防工业出版社,2002.
[7].潘炜,张晓霞,罗斌等.垂直腔面发射半导体微腔激光器.物理，1999,28(4)：210-216.
[8].伊贺健一,小山二三夫.面发射激光器基础与应用.北京：科学出版社,2002.
[9]. J. Jewell, S. McCall, Y. Lee, A. Scherer, A. Scherer, A. Gossard, J. English, "Lasing characteristics of GaAs micro-resonators," Appl. Phys. Lett.,1988,54,1400-1402.
[10]. K. Iga, S. Kinoshita, F. Koyama, "Microcavity GaAIAs/GaAs surface-emitting laser with Ith=6mA," Electron. Lett.,1987,23(3):134-136.
[11]. R. S. Geels, L A. Coldren, "Sub-milliamp threshold vertical-cavity laser diodes," Appl. Phys. Lett.,1991,57,1605-1607.
[12]. T. Wipiejewski, K. Panzlaf, E. Zeeb, et al., "Submilliamp vertical cavity laser diode structure with 2.2 nm continuous tuning," 18# European Conf. on Opt. Commun., ECOC 92,1992, PDII-4.
[13]. B. Weigl, M. Grabherr, G Reiner, K. J. Ebeling, "High efficiency selectively oxidised MBE grown vertical-cavity surface-emitting lasers," Electron. Lett.,1996, 32,557-558.
[14]. C. C. Wu, K. Tai, T. C. Huang, K. F. Huang, "Reliability studies of gain-guided 0.85 μm GaAs/AlGaAs quantum well surface emitting lasers," IEEE Photon. Technol. Lett.,1994,6,37-39.
[15]. Y. Hong, R. Ju, P. S. Spencer, et al. "Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback," IEEE J. Quantum Electron.,2005,41(5):619-624.
[16]. M. Sciamanna, K. Panajotov, H. Thienpont. "Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers," Opt. Lett.,2003,28(17): 1543-1545.
[17]. K. Panajotov, M. Sciamanna, A. Tabaka et al. "Residence time distribution and coherence resonance of optical-feedback-induced polarization mode hopping in vertical-cavity surface-emitting lasers," Phys. Rev. A,2004,69(1):011801.
[18]. C. Masoller, M. S. Torre, P. Mandel. "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers," J. Appl. Phys.,2006,99(2):026108.
[19]. M. S. Miguel, Q. Feng, J. V Moloney. "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A,1995,52(2):1728-1739.
[20]. C. Masoller, M. S. Torre. "Influence of optical feedback on the polarization switching of vertical-cavity surface emitting lasers," IEEE J. Quantum Electron., 2005,41,483-489.
[21]. J. M. Regalado, F. Prati, M. S. Miguel, N. B. Abraham. "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron.,1997,33,
765-783.
[22]. M. Sciamanna, K. Panajotov. "Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers," Phys. Rev. A,2006,73(2): 023811.
[23]. L. Chrostowski, B. Faraji, W. Hofinann et al., "40 GHz Bandwidth and 64 GHz Resonance Frequency in Injection-Locked I.55μm VCSELs," IEEE J. Sel. Top. Quantum Electron.,2007,13(5):1200-1208.
[24]. I. Gatare, M. Sciamanna, A. Locquet, K. Panajotov, "Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers," Opt. Lett.2007,32,1629-1631,
[25]. R. Vicente, T. Perez, C. R. Mirasso, "Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J Quantum Electronics.2002,38(9):1197-1204.
[26]. S. Tang, J. M. Liu, "Effects of message encoding and decoding on synchronized chaotic optical communications," IEEE J. Quantum Electron.,2003, 39(11):1468-1475.
[27]. A. Sanchez-Diaz, C. R. Mirasso, P. Colet, P. Garcia-Fernandez, "Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers," IEEE J. Quantum Electron.1999,35,292-297.
[28]. D. Kanakidis, A.Argyris, A. Bogris, D. Syvridis, "Influence of the decoding process on the performance of chaos encrypted optical communication systems," IEEE/OSA J. Lightw. Technol.2006,24,335-341.
[1]. L. M. Pecora, T. L. Carroll. "Synchronization in chaotic systems," Phys. Rev. Lett., 1990,64(8):821-824.
[2].周炳琨,高以智,陈调嵘等.激光原理第四版.北京：国防工业出版社,2002.
[3]. C. Masoller, "Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett.2001,86,2782-2785.
[4]. A. Sanchez-Diaz, C. R. Mirasso, P. Colet, P. Garcia-Fernandez, "Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers," IEEE J. Quantum Electron.1999,35,292-297.
[5]. G. Q. Xia, Z. M. Wu, J. G Wu, "Theory and simulation of dual-channel optical chaotic communication system," Opt. Express,2005,13,3445-3453.
[6]. F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Megret, M. Blondel, "Secure communication scheme using chaotic laser diodes subject to incoherent optical feedback and incoherent optical injection," Opt. Lett.2001,26, 1486-1488.
[7]. J. M. Buldu, J. Garcia-Ojalvo, M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron.2004,40,640-650.
[8], M. S. Torre, C. Masoller, K. A. Shore, "Synchronization of unidirectionally coupled multi-transverse-mode vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 2004,21,1772-1780.
[9]. Gatare, M. Sciamanna, A. Locquet, K. Panajotov, "Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers," Opt. Lett.2007,32,1629-1631.
[10]. D. Z. Zhong, G Q. Xia, Z. M. Wu, X. H. Jia, "Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback," Opt. Commun.2008,281, 1698-1709.
[11]. Y. H. Hong, P. S. Spencer, K. A. Shore, "Enhanced chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers with polarization-preserved injection," Opt. Lett.2008,33,587-589.
[12]. Y. H. Hong, M. W. Lee, P. S. Spencer, K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett.2004,32,1215-1217.
[13]. M. W. Lee, Y. Hong, K. A. Shore, "Experimental demonstration of VCSEL-based chaotic optical communications," IEEE Photon. Technol. Lett.2004,16,2392-2394.
[14]. R. Ju, P. S. Spencer, K. A. Shore, "Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron.2005,41,1461-1467.
[15]. M. Sciamanna, I. Gatare, A. Locquet, K. Panajotov, "Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection," Phys. Rev. E,2007,75,056213-1-10.
[16]. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, M. Y. Wang, "Separate polarization modes synchronization and synchronization switches between vertical-cavity surface-emitting lasers," Opt. Rev.2006,13,443-448.
[17]. D. Z. Zhong, Z. M. Wu, "Complete chaotic synchronization mechanism of polarization mode of VCSEL with anisotropic optical feedback," Opt. Commun. 2009,282,1631-1639.
[18]. D. Kanakidis, A.Argyris, A. Bogris, D. Syvridis, "Influence of the decoding process on the performance of chaos encrypted optical communication systems," IEEE/OSA J. Lightw. Technol.2006,24,335-341.
[19]. M. W. Lee, J. Paul, C. Masoller, K. A. Shore, "Observation of cascade complete chaos synchronisation with zero time lag in laser diodes," J. Opt. Soc. Am. B 2006, 23,846-851.
[20]. A. Locquet, C. Masoller, C. R. Mirasso, "Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers," Phys. Rev. E.2002,65,056205-1-12.
[21]. G Q. Xia, Z. M. Wu, J. F. Liao, "Theoretical investigations of cascaded chaotic synchronization and communication based on optoelectronic negative feedback semiconductor lasers," Opt. Commun.2009,282,1009-1015.
[22]. M. Liu, H. F. Chen, S. Tang, "Synchronized chaotic optical communications at high bit-rates," IEEE J. Quantum Electron.2002,38,1184-1195.
[23], C. Mirasso, J. Mulet, C. Masoller, "Chaos shift keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme," IEEE Photon. Technol. Lett.2002,14,456-458.
[24]. T. Deng, G Q. Xia, L. P. Cao, J. G Chen, X. D. Lin, Z. M. Wu, "Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback," Opt. Commun.2009,282,2243-2249.
[25]. S. Sivaprakasam, K. A. Shore, "Signal masking for chaotic optical communication using external-cavity diode lasers," Opt. Lett.1999,24,1200-1202.
[26]. J. M. Regalado, F. Prati, M. S. Miguel, N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron.1997,33, 765-783.
[1].方锦清,激光及其高阶级联系中的超混沌同步与控制[J]，强激光与粒子束,1996,8.138.
[2]. D. J. Deshazer, R. Breban, E. Ott, R. Roy, "Detecting phase chronization in a chaotic laserarray," Phys. Rey. Lett.2001,87,044101.
[3]. T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu, "Observation of synchronization inlaser chaos," Phys.Rev.Lett.1994,72,3502.
[4]. A. Murakami, "Synchronization of chaos due to linear response inoptically driven semiconductor lasers, Phys Rev.E,2002,65,056617.
[5]. S. Zhu, J. Fang, X. Luo, "Phase locking and chaotic synchronization in an array of threelasers," Eur.Phys.J.D,2002,18,123.
[6], N. F. Rulkov, M. M. Sushchik, L.S. Tsimring, "Generalizedsynchronization of chaos in directionally coupled chaotic systems," Phvs.Rev.E,1995,51,980.
[7]. L. Kocarev, U. Parlitz, "Generalized synchronization, predictability, and equivalence of unidirectionally coupled dyrtamical systems," Phys. Rev. Lett.1996, 76,1816.
[8]. A. N. Pisarchik, V. J. Pinto-Robledo, "Experimental observation of two-state on-off intermittency," Phys.Rev.E,2002,66,027203.
[9]. G D. Van Wiggeren, R. Roy, "Communication with chaotic lasers," Science,1998, 279,1198.
[10]. J. M. Liu, H. F. Chen, and S. Tang, "Synchronized chaotic optical communications at high bit rates, IEEE J. Quantum Electron.,2002,38,1184.
[11]. J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron.2002,38,1141.
[12]. J. Paul, S. Sivaprakasam, P.S. Spencer, P. Rees, K.A.Shore, "GHz bandwidth message transmission using chaotic diode lasers," Electron.2002,38,28.
[13]. J. Paul, S. Sivapralcasam, K. A. Shore, "Dual-channel chaotic optical communication using external-cavity semiconductor lasers," J. Opt. Soc. Am. B., 2004,21(3).
[14]. L. S. Tsimring, M. M. Sushchik, "Multiplexing chaotic signals using synchronization," Phys.Lett.A,1996,213,155.
[15]. Y. Liu, and P. Davis, "Dual synchronization of chaos," Phys. Rev. E 2000,61, 2176.
[16]. E. M. Shahverdiev, S. Sivaprakasam, K. A. Shore, "Dual and dual-cross synchronizations in chaotic systems," Opt.Commun.2003,216,179.
[17]. J. M. Buldu, J. Garcia-Ojalvo, M. C. Torrent, "Demultiplexing chaos from multimode semiconductor lasers," IEEE J Quantum Electronics.2005, 41(2):164-170.
[18]. L. Wu, S. Zhu, "Mufti-channel communication using chaotic synchronization of mufti-mode lasers," Phys. Rev. A,2003,157-161.
[19]. J. M. Buldu, J. G.arcia-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using un-directionally coupled semiconductor lasers," IEEE J. Quantum.,2004,40(6):640-650.