摘要
垂直腔面发射激光器(VCSEL)是一种新型的半导体激光器,较传统的边发射激光器来说具有低阈值、单纵模工作、发散角小、动态调制频率高、易实现二维集成等优点,在光通信,光互联,图像信号处理等方面有着重要的应用前景。
近年来混沌保密通信得到了广泛的应用。由于光混沌的动力学行为复杂,对参数相当敏感,因此成为保密通信的一个热点。在混沌通信中,传输速率是最重要的指标之一,由混沌载波基频决定。混沌载波频率与激光器的弛豫振荡频率密切相关,弛豫振荡频率限制了半导体激光器的最大调制频率,最近,通过强光注入到VCSEL,实验上已获得50GHz的调制带宽,因此可以预计,外部光注入可以使外光反馈VCSEL输出的混沌载波基频得到很大的提高。
基于此本文研究了外部光注入对VCSEL带光反馈的VCSEL输出混沌载波基频的影响。研究结果表明,在注入锁定区域内,当外部注入光频率与VCSEL自由运行的振荡频率失谐一定时,随着外部光注入强度的增加,混沌载波基频总体呈现上升的趋势,在增加的过程中伴随着波动;同时失谐频率对混沌载波基频也有重大影响,在正失谐时,混沌载波基频随着失谐频率的增加而增大,通过调整失谐频率和注入强度大小,外部光注入可以使混沌载波基频得到大幅度的提高;当归一化的注入系数K=330,失谐频率为42GHz,可得到基频位于47.3GHz的混沌信号输出。众所周知,混沌载波基频决定着最大的混沌传输速率,所以本文的研究对提高混沌传输速率具有很高的价值。
As a new kind of semiconductor laser, vertical-cavity surface-emitting lasers(VCSEL) have such merits as low threshold, single longitudinal mode operation, small angle of divergence, high dynamic modulating frequency, easily implemented two-dimension integration which makes VCSEL have significant implication prospects in optical communication, optical interconnection, image signal processing, etc. As a result, the researches on VCSEL have been paid special attention
Recently, Chaos private communication has get an extensive application, optical chaos become a hot topic of private communication for a fundamental phenomenon of nonlinear dynamics and highly sensitivity to the parameters, the rate of transmission is one of the most important Index sign in chaotic communication which is determined by the chaotic carrier fundamental frequency. Carrier frequency is closely related to the relaxation oscillation frequency, and the relaxation oscillation frequency is considered to be the characteristic frequency that defines the maximum modulation frequency of a semiconductor. At present, the experiments focused on the VCSELs, where a relaxation oscillation frequency 50GHZ was achieved, therefore we can anticipate, the chaotic carrier fundamental frequency of VCSEL's output with optical feedback can be enhanced by using the external optical injection technique.
In this paper, the influences of the external light injection on the chaotic carrier fundamental frequency of VCSEL with optical feedback have been investigated. The results show that in the injection locking area, for the fixed frequency offset between the master laser diode and the slave VCSEL, the chaotic carrier fundamental frequency will be increased generally with the increase of injected strength, accompany with motion in the process of increase; Simultaneously, the frequency offset have the important influence to the chaotic carrier fundamental frequency, when the frequency offset is positive, the chaotic carrier fundamental frequency also increased generally with the increase of the frequency offset, chaotic carrier fundamental frequency can be improved significantly by adjusting frequency offset and injected strength. For the normalized injected strength K is 330 and frequency offset is 42GHz, chaotic output with 47.3GHz fundamental frequency can be obtained. Therefore, the investigation in this paper has the high research value for improving the transmission rates.
引文
[1]赵路民,980nm高功率垂直腔ICI发射激光器的研制及测试分析[硕士论文].长春:吉林大学,2004年5月
[2]H.Soda,K.Iga,C.Kitahara et al."GslnAsP/Inp surface emitting injection lasers,"Japan.J.Appl.Phys.,1979,18(12):2329-2330
[3]Burnham R D,Scifres D R,Streifer W,et al."Transverse light emitting electroluminescent devices,"[P]U.S.Patent.1982,4309670
[4]Jayaraman V,Mehta M,Jackson A W,et al."High-power 1320nm wafer-bonded VCSELs with tunnel junctions,"[J].IEEE Photon.Technol.Lett.2003,15(11):1495-1497
[5]Karim A,Abraham P,Lofgreen D,et al."Wafer bonded 1.55 μm vertical-cavity lasers with continuous-wave operation up to 105℃," Appl Phys Lett,2001,78(18):2632-2633
[6]Boucart J,Starck C,Gaborit F,et al."Metamorphic DBR and tunnel junction injection:ACWRT monolithic long-wavelength VCSEL,"[J].IEEE J.Select.Topics Quantum Electron.,1999,5:520-529
[7]江剑平,半导体激光器,2000年2月第一版
[8]Huang D,Sze T,Landin A,et al."Optical interconnects:Out of the box forever?"[J].IEEE J.Select.Topics Quantum Electron Mar./Apr.2003,9(2):614-623
[9]Shinji Nishimura,Hiroaki moue,Takashi Yokota,"Opticalinterconnections for the massively parallel computer,"[J].IEEE Photon.Technol.Lett.,July.1997,9:1029-1031
[10]??n D,Fan W,Kner P,et al."Long wavelength tunable VCSELs with optimized MEMS bridge tuning structure,"[J].IEEE Photon.Technol.Lett.,Mar.2004,16:714-716
[11]Macdougal M H,Dapkus P D,Jun.Bond A E,et al."Design and fabrication of VCSEL's with AlxOy-GaAs DBR's,"[J].IEEE J.Select.Topics Quantum Electron.1997,3(3):905-915
[12]Chang-Hasnain C J,Berkeley V C."Progress and prospects of long-wavelength VCSELs,"[J].IEEE Communications Magazine,2003,2:30-34.
[13]Shimizu H,"First CW operation of 1.3,um range GalnNAsSb VCSELs and VCSEL Array,"[A].Int'l Semiconductor Lasers conf.2002[C].Germany.
[14]Lin C K."High temperature continuous-wave operation of 1.3-1.55,um VCSELs with InP/air-gap DBRs,"[A].Int'l Semiconductor Lasers Conf.2002[C].Germany.
[15]Chang-Hasnain C J."Tunable VCSEL,"[J].IEEE J.Select.Topics in Quantum Electron.,2002(6):978-987.
[16]赵路民、王青、晏长岭等,980nm高功率垂直腔而发射激光器,中国激光,2004,31(2):142-144
[17]赵路民、王青、宁永强等,垂直腔而发射微腔激光器,激光与光电子学进展,2003,40(8):39-43
[18]Mark Kuznetsov,Farhad Hakimi,Robert Sprague,etc."Design and Characteristics of High-Power(0.5W-CW)Diode-Pumped Vertical External Cavity Surface-Emitting Semiconductor Lasers with Circular TEM00 Beams," IEEE J.Sel Topics in Quantum Electronics.1999,5(3):561-573
[19]H.J.Unold,S.W.Z.Mahmoud,R.Jager,etc."Improving Single-Mode VCSEL Performance by Introducing a Long Monolithic Cavity," IEEE Photon.Technol Lett.2000,12(8):939-941
[20]Michael Miller,Martin Grabherr,Roger King,etc."Improved Output Performance of High-Power VCSELs," IEEE J.Sel Topics in QuantumElectronics.2001,7(2):210-216
[21]D.B.Bour,R.S.Geels,D.W.treat,T.L.Paoli,F.Ponce,R.L.Thomton,B.S.Krusor,R.D.Bringans and D.F.Welch,"Strained Ga_xIn_(-x)P/(A1Ga)0.5In0.5P heterostructure and quantum well laser diodes," IEEE J.Quantum Electron.,vol.1994,30:593-607
[22]伊贺键一、小由二三夫、而发射激光器基础与应用,第一版,科学出版社,共立出版,2002,32-33,114-115
[23]Takashi Yoshikawa,Takeshi Kawakami,Hideaki Saito,etc."Polarization Controlled Single Mode VCSEL," IEEE J.Sel Topics in Quantum Electronics.1998,34(6):1009-1015
[24]刘立新、赵洪东、曹萌,垂直腔而发射激光器热场特性分析,微纳电子技术,2003.4:8-11
[25]高洪海、林世鸣、康学军等,垂直腔而发射激光器热特性的实验研究,光子学报,1997 26(6):522-526
[26]J.A.Lehman,et al.Electron.Lett.,1997,33:298-300
[27]T.B.Simpson,J.M.Liu,A.Gavrielides,"Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor," IEEE Photo.Technol.Lett.,1995,7:709-711,
[28]X.J.Meng,T.Chau,M.C.Wu,"Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection,"Electron.Lett.,1998,34:2031-2032
[29]Y.Okajima,S.K.Hwang,J.M.Liu,"Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection," Opt.Commun.,2003,219:357-364
[30]L.Chrostowski,C.H.Chang,C.J.Chang-Hasnain,"Injection-locked1.55μm VCSEL's with enhanced spur-free dynamic range," Electron.lett.,2002,38:965-967
[31]A.Murakami,K.Kawashima,K.Atsuki,"Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection," IEEE J.Quantum Electron.,2003,39:1196-1204
[32]L.Chrostoski,X.Zhao,C.J.Chang-Hasnain,R.Shau,M.Ortsiefer,M.-C.Amann,"50 GHZ optically injection-locked 1.55 μm VCSELs," IEEE Photo.Technol.Lett,2006,16:367-369
[33]S.Wieczorek,W.W.Chow,L.Chrostowski,C.J.Chang-Hasnain,"Improved semiconductor-laser dynamics from induced population pulsation," IEEE J.Quantum Electron.Lett.,2006,42:552-562
[34]Hui R,Dapos,Ottavi A,Mecozzi A,Spano P,"Injection locking in distributed feedback semiconductor lasers," IEEE J.Quantum Electron.,1991,27:1688-1695,
[35]B.Tromborg,H.Olesen,X.Pan,and S.Saito,"Transmission line description of optical feedback and injection locking for Fabry-Perot and DFB lasers," IEEE J.Quantum Electron.1987,23:1875-1889
[36]Chan L Y,Chung W H,Wai P K A,et al."Simultaneous re-polarization of two 10Gbit/s polarization-scrambled wavelength channels using a mutual-injection-locked laser diode," IEEE Photon Technol Lett,2002,14(12):1740-1742
[37]Y.Liu,H.F.Chen,J.M.Liu,P.Davis,and T.Aida,"Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys.Rev.A,2001,63:1-4
[38]S.Kobayashi,J.Yamada,S.Machida,and T.Kimura,"Single mode operation of 500Mbit/s modulated AIGaAs semiconduc-tor laser by injection locking," Electron.Lett.1980,14:746-748
[39]J.M.Liu,H.F.Chen,X.J.Meng,and T.B.Simpson,"Modulation bandwidth,noise,and stability of a semiconduc-tor laser subject to strong injection locking" IEEE Photon.Technol.Lett.1997,9:1325-1327
[40]Apostolos Argyris,Dimitris Syvridis,"Performance of open-loop all-optical chaotic communication systems under strong injection condition,"[J].J.Lightwave Technol.,2004,22(5):1272-1279
[41]Yun Liu,Peter Davis,Yoshiro Takiguchi et al."Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers,"[J].IEEE J.Quantum Electron.,2003,39(2):269-278
[42]H.F.Chen and J.M.Liu,"Complete chaos synchronization in semiconductor lasers subject to optical Injection," Phys.Rev.E 71,2005,046216
[1]Zorn M,Knigge A,Zeimer U et al."MOVPE growth of visible vertical cavity surface emitting lasers(VCSELs),"[J].J.Crystal Growth,2003,248:186-193.
[2]D.B.Bour,R.S.Geels,D.W.treat,T.L.Paoli,F.Ponce,R.L.Thomton,B.S.Krusor,R.D.Bringans and D.F.Welch,"Strained Ga_xIn_(1-x)P/(AlGa)0.5In0.5P heterostructure and quantum well laser diodes," IEEE J.Quantum Electron.,1994,30:593-607
[3]A.Knigge,M.Zorn,M.Weyers,and G.Trankle,"High-performance vertical-cavity surface-emitting lasers with emission wavelength between 650 and 670 nm," Electron.Lett.,2002,38:882-883
[4]Scott J W,Young D B,Thibbeault B J,et al."Design of index-guided verticahcavity lasers for low temperatum-sensitivity,sulr-milliamp threshold,and single-mode operation," IEEE J.Sel Topics quantum Electron,1995,1(2):638-645
[5]Kuo H C,Shi G Q,Trieu M,et al."Highlv uniform and highly reliable 850 nm V CSEL plat-form for high-speed optical communications,"[J].Proceedings of SP1 E,2002,4905:304-309
[6]Thiheault B J,Bertilsson K,Heghlom E B,et al."High speed characteristics of low optical loss oxide-apertured vertical cavity lasers," IEEE Photonics Technol Lett,1997,9:11-13
[7]Hatori N,Mizutani A,Nishiyama N,et al."An over 10Gbit/s transmission experimentusing a P-type delta-doped InGaAs-GaAs quantum-well vertical-cavity surfacf-emitting laser," IEEE Photonics Technol Lett,1997,4:409-414
[8]J.W.Jang,C.L.Chien,W.M.Chyi,et al."A new process to improve the performance of 850nm wavelength GaAs VCSELs,"[J].J.Solid state Electron.,2002,46:2287-2289
[9]张劲松、曹明翠、陈涛、谭伟,VCSEL技术与并行光互联,光通信研究,2002114(6):54-58
[10]毛容伟、左玉华、成步文、于金中,王启明1.3-1.55μm光通信VCSEL的研究进展,光子技术2005,1:1-5
[11]YueA,Shen K,Wang R F,et al."Low threshold cun'ent 1.3μm GalnNAs VCSELs grown by MOVPE,"[J].IEEE Photon.Technol.Lett,2004,16(3):717-719
[12]Louderback D A,Fish M A,Klem J F,et al."Development of bottom-emitting 1300-nm vertical-cavity surface-emitting lasers,"[J].IEEE Photon.Technol.Lett.,2004,16(4):963-965
[13]Nakagawa S,Hall E,Almuneau G;et al."1.55μm InP-lattice-matched VCSELs with AI-GaAsSb-AIAsSb DBRs,"[J].IEEE J.Select.Topics Quantum Electron.,2001,7(2):224-230
[14]Blum O,Hafich M J,Klem J F,et al."Electrical and optical characteristics of AIAsSb/GaAsSb distributed Bragg reflectors for surfaceetting lasers,"[J].Appl.Phys.L.ett.,1995,67(22):3233-3235
[15]Nakagawa S,Hall E,Almuneau G,et al."88℃ continuous-wave operation of apertured intracavity contacted 1.55μm vertical-cavity surface-emitting lasers,"[J].Appl.Phys.L.ett.,2001,78(10):1337-1339
[16]Hawthorne.R.A,et al."Reliability Study of 850nm VCSELs for Data Communications," 1996 IEEE International Reliability Physics Proceedings,1996,34:203-210
[17]Shau R,Ortsiefer M,Rosskopf J,et al."Vertical-cavity surface-emitting laser diodes at 1.55μm with large output power and high operation temperature,"[J].Electron.Lett.,2001,37(21):1295-1296
[18]Ortsiefer M,Electron.Lett Shau R,Mederer F,et al."High-speed modulation up to 10Gbit/s with 1.55μm wavelength InGaAIAs VCSELs,"[J].2002,38(20):1180-1181
[19]Boucart J,Starck C,Gaborit F,et al."Metamorphic DBR and tunnel junction injection:ACWRT monolithie long-wavelength VCSEL,"[J].IEEE J.Select.Topics Quantum Electron.,1999,2:520-529
[20]Karim A,Abraham P,Lfgreen D,et al."Wafer bonded 1.55 μm vertical-cavity lasers with continuous-wave operation up to 105℃,"[J].Appl.Phys.Lett.,2001,78(18):2632-2633
[21]Gerhard Boehm,Markus Ortsiefer,Robert Shau,et al."InP-based VCSEL technology covering the wavelength range from 1.3 to 2.0μm,"[J].J.Crystal Growth,2003,251:748-753
[22]Vail E C,Li G S,Yuen W,et al."High performance micromechanical tunable vertical cavity surface emitting lasers,"[J].Electron.Lett.,1996,32:1888-1889.
[23]Li M Y,Yuen W,Li G S,et al."High performance continuously tunable top-emitting vertical cavity laser with 20nm wavelength range,"[J].Electron.Lett.,1997,33:1051-1052.
[24]Chang-Hasnain C J."Tunable VCSEL,"[J].IEEE.J.Quantum Electron.,2000,6:978-987.
[25]Li M Y,Yuen W,Li G S,et al."Top-emitting micromechanical VCSEL with a 31.6nm tuning range,"[J].IEEE.Photon.Technol.Lett.,1998,10:18-20.
[26]M.C.Y.Huang,Kan Bun Cheng,Ye Zhou,B.Pesala,C.J.Chang-Hasnain,A.P.Pisano,"Demonstration of Piezoelectric Actuated GaAs-Based MEMS Tunable VCSEL,"[J],IEEE.Photon.Technol.Lett.,2006,18:1041-1135.
[27]F Sugihwo,M C Larson,J S Harris."Low threshold continuously tunable vertical-cavity surface-emitting lasers with 19.1 nm wavelength range,"[J].Appl.Phys.Lett.,1997,70(5):547-549.
[28]F Sugihwo,M C Larson,J S Harris."Simultaneous optimization of membrane reflectance and tuning voltage for tunable vertical cavity lasers,"[J].Appl.Phys.Lett.,1998,72(1):10-12.
[29]Michael Miller,Martin Grabherr,Roger King,etc."Improved Output Performance of High-Power VCSELs," IEEE J.Sel Topics in QuantumElectronics.2001,7(2):210-216
[30]D.Vakhshoori,P.Tayebati,Chih-Cheng Lu,et al."2mW CW singlemode operation of a tunable 1550nm vertical cavity surface emitting laser with 50nm tuning range,"[J].Electron.Lett.,1999,35(11):900-901.
[31]Y.Matsui,D.Vakhshoori,P.Wang,P.Chen,C.-C.Lu,M.Jiang,K.Knopp,S.Burroughs,P.Tayebati,"Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers Over 65nm tuning up to 14mW output power," J.Quantum Electron.,2003,39(9):1037-1048
[32]Boucart Julien,Pathak Rajiv,Zhang Dongxu,et al."Long wavelength MEMS tunable VCSEL with InP-InAIGaAs bottom DBR,"[J].IEEE.Photon,Technol.Lett.,2003,15(9):1186-1188.
[33]M.Ortsiefer,R.Shau,G.Bohm,et al."Low-threshold index-guided 1.5μm long-wavelength vertical-cavity surface-emitting laser with high efficiency,"[J].Appl.Phys.Lett.,2000,76(16):2179-2181.
[34]E Riemenschneider,M.Maute,H.Halbritter,G.Boehm,M.-C.Amann,P.Meissner,"Continuously tunable long wavelength MEMS-VCSEL with over 40nm tuning range,"[J].IEEE.Photon.Technol.Lett.,2004,16(10):2212-2214.
[35]Decai Sun,Kner P,Boucart J,et al."Electrically pumped directly modulated 1550nm tunable VCSELs,"[J].Proc.SPIE,2002,4905:198-202
[36]J.K.Guenter,R.A.Hawthorne Ⅲ,D.N.Granville,M.K.Hibbs-Brenner,and R.A.Morgan,"Reliability of proton-implanted VCSELs for data communications,"Proceedings of the SPIE,1996,2683:102-113
[37]Wagner A,Ellmers C,Hohnsdorf F,"(Gain)(NAs)/GaAs vertical-cavity surface-emitting laser with ultra broad temperature operation range,"[J]Appl.Phys.Lett.,2000,76(3):271-272
[38]J.A.Taturn,J.K.Guenter,and R.H.Johnson,"Manufacturability of VCSEL components and VCSEL products," Proceedings of the 1 lth Annual Meeting of the IEE Lasers and Electro-Optics Society,1998,2:409-410
[39]R.A.Hawthorne Ⅲ,J.K.Guenter,D.N.Granville,M.K.Hibbs-Brenner,and R.A.Morgan,"Reliability Study of 850nm VCSELs for Data Communications," IEEE international Reliability Physics Proceedings,1996,34:203-210
[40]Kosaka H,"Smartintegration and packaging of 2-DVCSELs for high-speed parallellinks," IEEE J.of Selected Topics in QuantumElectron,1999,5(2):184-192
[41]J.Tatum,D.L.MacFarlane,and H.B.Serreze,"Sustained oscillations in GalnP/A1GalnP visible diode lasers," Optical and Quantum Electronics,1995,27:101-116
[1]Z.G.Shi,L.X.Ran,"Microwave chaotic colpitts oscillator:design implementation and applications," Electronmagn.Waves and Appl.,2006,20:1335-1349
[2]A.S.Dmitrive,A.I.Panas,K.V.Zakharchenko,"Nonlinear Phenomena in Complex Systems," 2003,6:488-501
[3]吴加贵、吴正茂、林晓东、张毅、钟东洲、夏光琼,“双信道光混沌通信系统的理论模型及系统性能的研究,”物理学报,2006,54:4169-4175
[4]李孝峰、潘炜、马冬、罗斌、张伟利、熊悦,“激光器自发辐射噪声对混沌光通信系统的影响,”物理学报,2006,55:5094-5104
[5]颜森林、汪胜前“激光混沌串联同步以及混沌中继器系统理论研究,”物理学报,2006,55:1687-1695
[6]王云才、张耕玮、王安帮、王冰洁、李艳丽、郭萍,“光注入提高半导体激光器混沌载波发射机的带宽,”物理学报,2007,56:4372-4377
[7]Y.Liu,Y.Takiguchi,P.DAvis,T Aida,S.saito,J.M.Liu," Experimental observation of complete chaos synchronization in semiconductor Lasers," appl.phys.lett.,2002,80:4306-4308
[8]V.A 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
[9]Y.Takiguchi,K.Ohyagi,J.Ohtsubo,"bandwidth- enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback," Opt.Lett.,2003,28:319-321
[10]T.B.Simpson,J.M.Liu,A.Gavrielides,"Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor," IEEE Photo.Technol.Lett.,1995,7,709-711
[11]X.J.Meng,T.Chau,M.C.Wu,"Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection," Electron.Lett.,1998,34:2031-2032
[12]Y.Okajima,S.K.Hwang,J.M.Liu,"Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection," Opt.Commun.,2003,219:357-364
[13]L.Chrostowski,C.H.Chang,C.J.Chang-Hasnain,"Injection-locked 1.55μm VCSEL's with enhanced spur-free dynamic range," Electron.lett.,2002,38:965-967
[14]A.Murakami,K.Kawashima,K.Atsuki,"Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection," IEEE J.Quantum Electron.,2003,39:1196-1204
[15]L.Chrostoski,X.Zhao,C.J.Chang-Hasnain,R.Shau,M.Ortsiefer,M.-C.Amann,"50 GHZ optically injection-locked 1.55μm VCSELs," IEEE Photo.Technol.Lett.,2006,16:367-369
[16]S.Wieczorek,W.W.Chow,L.Chrostowski,C.J.Chang-Hasnain,"Improved semiconductor-laser dynamics from induced population pulsation," IEEE J.Quantum Electron.Lett.,2006,42:552-562
[17]J.Yang,G.Hu,J.Xiao,"Chaos synchronization in coupled chaotic oscillators with multiple positive Lyapunov exponents," Phys.Rev.Lett.,1998,80:496-499
[18]陈奉苏编著,《混沌学及其应用》,中国电力出版社,1998。
[19]卢侃等编译,《混沌动力学》,上海翻译出版公司,1990,6.
[20]苗东升、刘华杰,《混沌学纵横论》.中国人民大学出版社,北京,1994
[21]刘曾容,《混沌的微扰判据》,上海科技出版社,上海,1995。
[22]郝柏林,《分岔、混沌、奇异吸引子、湍流及其他-关于确定性混沌的随机性》。物理学进展,1983,3(11):329-515
[23]关新平、范正平等,“混沌控制及其在保密通信中的应用”,pp:168-169,(国防工业出版社,北京,2002)
[24]王东生、曹磊,《混沌、分形及其应用》,中国科学技术大学出版,1995.6
[25]C.W.Wu,L.O.Chua,"A simple way to synchronization chaotic systems with applications to secure communication," Int.J.Bifurcation and Chaos,1993,3(6):1619-1627
[26]谭伟贤等编,《计算机网络安全教程》,国防工业出版社,2001。
[27]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。
[28]郝柏林,《从抛物线谈起》,pp:1-107,上海科教出版社,上海,1993。
[29]利昂.格拉斯,《从摆钟到混沌—生命的节律》,上海远东出版社,1996。
[30]P.Colet,R.Roy,"Digital communication with synchronization chaotic laser," Opt.Lett.,1994,19(24):2056-2058
[31]Y.Mastsui,S.Kutsuzawa "Bifurcation in 20GHz gain-switched 1.55 MQW laser and its control by CW injection seeding," IEEE J.Quantum.Electronics.,1998,34(7):1213-1223
[32]Y Hong,K A Shore,"Locking characteristic of a side-mode injected semiconductor laser," IEEE J.Quantum Electronics,1999,35(11):32-38