在本論文中，主要探討半導體雷射遭光脈衝注入所產生的非線性動態和鎖頻 (frequency locking) 的現象。在非線性動態方面，可藉由改變光脈衝注入的強度和脈衝重複的頻率產生不同的非線性狀態，其中主要可區分為脈衝 (pulsing) 和波動 (oscillation) 兩種不同的狀態。吾發現在不同的光脈衝注入強度時，其個別會依循不同之倍數週期路徑 (period-doubling route) 進入渾沌脈衝 (chaotic pulsing) 或渾沌波動 (chaotic oscillation) 的狀態。相較於鬆弛震盪 (relaxation oscillation) 之頻率，此渾沌態之頻寬有二至四倍之頻寬增益 (bandwidth enhancement)。另一方面，藉由改變不同光脈衝注入的頻率，被注入之雷射將產生具有不同旋轉數 (winding number) 的鎖頻狀態。
在應用層面上，利用半導體雷射遭光脈衝注入所產生的非線性動態現象，吾亦探討其於渾沌通訊方面上之可行性。此光脈衝注入渾沌通訊系統相較於傳統的光注入通訊系統有許多優點，如高頻寬、抗雜訊，以及高保密性。其基本原理是利用非線性動態所產生的渾沌態作為渾沌載波 (chaotic carrier)，將所需要傳輸的訊號利用ACM (Additive Chaos Modulation) 的加密方式傳送至接收端，再利用同步化的效應可以解密出所傳輸的訊息，以達到保密通訊的效果。於此系統中，當訊噪比 (SNR) 大於30 dB 時此系統的誤碼率 (bit-error-rate) 可以達到低於傳統通訊上所要求的標準值10-9。

The nonlinear dynamics and frequency locking of semiconductor lasers under repetitive optical pulse injection are studied numerically. Different dynamical states, including pulsation and oscillation states, are found by varying the intensity and the repetition frequency of the injection pulses. Through individual period-doubling routes, the laser enters into chaotic pulsation (CP) states and chaotic oscillation (CO) states, respectively.
Moreover, the bandwidths of the chaos states are also investigated. The time series and power spectra of frequency-locked states with di®erent winding numbers, which is the ratio of the oscillation frequency and the repetition frequency of the injection pulses, are
shown.
Chaotic communication of semiconductor lasers under repetitive optical pulse injection is demonstrated and investigated numerically. The advantages of this chaotic
communication system include large bandwidth, robust, and high security compared to the chaotic communication system based on constant optical injection. In this system, the chaotic carrier is generated by injecting repetitive pulses to a semiconductor laser. The message is encoded to the chaotic carrier with additive chaotic modulation (ACM)
method, while decoding is realized by synchronizing a receiver laser with a transmitter laser. For a signal-to-noise ratio (SNR) above 30 dB, a bit-error-rate (BER) below the benchmark of 10-9 set by the conventional communication is achieved.

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A, vol. 51, pp. 4181-4185, 1995.
J. Mork, B. Tromborg, and J. Mark, "Chaos in semiconductor lasers with optical feedback: theory and experiment," IEEE J. Quantum Electron., vol. 28, pp. 93-108, 1992.
F. Y. Lin and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum Electron., vol. 39, pp. 562-568, 2003.
T. B. Simpson and J. M. Liu, "Enhanced modulation bandwidth in injection-locked semiconductor lasers," IEEE Photonics Technol. Lett., vol. 9, pp. 1322-1324, 1997.
J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, "Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking," IEEE Photonics Technol. Lett., vol. 9, pp. 1325-1327, 1997.
J. Sahcer, D. Baums, P. Panknin, W. Elsasser, and E. O. Gobel, "Intensity instabilities of semiconductor lasers under current modulation, external light injection, and delayed feedback," Phys. Rev. A, vol. 45, pp. 1893-1905, 1992.
T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling route to chaos in a semiconductor laser subject to optical injection," Appl. Phys. Lett., vol. 64, pp. 3539-3541, 1994.
V. Kovanis, A. Gavrielides, T. B. Simpson, and J. M. Lin, "Instabilities and chaos in optically injected semiconductor lasers," Appl. Phys. Lett., vol. 67, pp. 2780-2782, 1995.
A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, \High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection," IEEE J. Quantum Electron., vol. 39, pp. 1462, 2003.
Y. J. Wen, H. F. Liu, and D. Novak, "Optical signal generation at millimeter-wave repetition rates using semiconductor lasers with pulsed subharmonic optical injection," IEEE J. Quantum Electron., vol. 37, pp. 1183-1193, 2001.
M. H. Jensen, P. Bak, and T. Bohr, "Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps," Phys. Rev. A, vol. 30, pp. 1960-1969, 1984.
L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett., vol. 64, pp. 821-824, 1990.
J. M. Liu, H. F. Chen, and S. Tang, "Synchronized chaotic optical communications at high bit rates," IEEE J. Quantum Electron., vol. 38, pp. 1184-1196, 2002.
F. Y. Lin and J. M. Liu, "Chaotic radar using nonlinear laser dynamics," IEEE J. Quantum Electron., vol. 40, pp. 15-820, 2004.
F. Y. Lin and J. M. Liu, "Chaotic lidar," IEEE J. of Selected Topics in Quantum Electron., vol. 10, pp. 991-997, 2004.
F. Y. Lin and M. C. Tsai, "Chaotic communication in radio-over-fiber transmission based on optoelectronic feedback semiconductor lasers," Optics Express, vol. 15, pp. 302-311, 2007.
T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, "Nonlinear dynamics induced by external optical injection in semiconductor lasers," Quantum Semiclass. Opt., vol. 9, pp. 765-784, 1997.
T. B. Simpson and J. M. Liu, "Phase and amplitude characteristics of nearly degenerate four-wave mixing in Fabry-Perot semiconductor lasers," J. Appl. Phys., vol.
73, pp. 2587-2589, 1993.
F. Y. Lin and J.M. Liu, "Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback," Opt. Commun., vol. 221, pp. 173-180, 2003.
M. H. Jensen, P. Bak, and T. Bohr, "Transition to chaos by interaction of resonances in dissipative. I. Circle maps," Phys. Rev. A, vol. 30, pp. 1960-1069, 1984.
H. G. Winful, Y. C. Chen, and J. M. Liu, "Frequency locking, quasiperiodicity, and chaos in modulated self-pulsing semiconductor lasers," Appl. Phys. Lett., vol. 48, pp. 616-618, 1986.
D. Baums, W. ElsÄasser, and E. O. Gobel, "Farey tree and devil's staircase of a modulated external-cavity semiconductor laser," Phys. Rev. Lett., vol. 63, pp. 155-
158, 1989.
F. Y. Lin and J. M. Liu, "Harmonic frequency locking in a semiconductor laser with delayed negative optoelectronic feedback," Appl. Phys. Lett., vol. 81, pp. 3128-3120, 2002.
N. Gastaud, S. Poinsot, L. Larger, J. -M. Merolla, M. Hanna, J. -P. Goedgebuer and F. Malassenet, "Electro-optical chaos for multi-10 Gbit/s optical transmissions,"
Electronics Letters, vol. 40, pp. 898-899, 2004.
L. Kocarev and U. Parlitz, "General approach for chaotic synchronization with applications to communication," Phys. Rev. Lett., vol. 74, pp. 5028-5031, 1995.
H. F. Chen and J. M. Liu, "Complete phase and amplitude synchronization of broadband chaotic optical fields generated by semiconductor lasers subject to optical injection," Phys Rev. E, vol. 71, no. 046216, 2005.
H. F. Chen and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron.,
vol. 36, pp. 27-34, 2000.
H. F. Chen and J. M. Liu, "Unidirectionally coupled synchronization of optically injected semiconductor lasers," IEEE J. of Selected Topics in Quantum Electron.,
vol. 10, pp. 918-926, 2004.
K. S. Halle, C. W. Wu, M. Itoh, and L. O. Chua, "Spread spectrum communication through modulation of chaos," Int. J. of Bifurcation and Chaos, vol. 3, pp. 469-477, 1993.
L. Kocarev, K. S. Halle, K. Eckert, L. O. Chua, and U. Parlitz, "Experimental demonstration of secure communication via chaotic synchronization," Int. J. of Bifurcation and Chaos, vol. 2, pp. 709-713, 1992.
U. Parlitz, L. O. Chua, L. Kocarev, K. S. Halle, and A. Shang, "Transmission of digital signals by chaotic synchronization," Int. J. of Bifurcation and Chaos, vol. 2,
pp. 973-977, 1992.
M. Sushchik, Jr., N. Rulkov, L. Larson, L. Tsimring, H. Abarbanel, K. Yao, and A. Volkovskii, "Chaotic pulse position modulation: A robust method of communicating with chaos," IEEE Commun. Lett., vol. 4, pp. 128-130, 2000.
C. W. Wu and L. O. Chua, "A simply way to synchronize chaotic systems with applications to secure communiation systems," Int. J. of Bifurcation and Chaos, vol. 3, pp. 1619-1627, 1993.
S. Tang, H. F. Chen, S. K. Hwang, and J. M. Lin, "Message encoding and decoding through chaos modulation in chaotic optical communications," IEEE Trans. Circuits Syst. I, vol. 49, pp. 163-169, 2002.
F. Zang and P. L. Chu, "Effect of transmission ‾ber on chaos communication system based on erbium-doped fiber ring laser," J. Lightwave Technol., vol. 21, pp. 3334-3343, 2003.
J. M. Liu, H. F. Chen, and S, Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Trans. Circuits Syst. I, vol. 48, pp. 1475-1483, 2001.
N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and A. R. Volkovskii, "Digital communication using chaotic-pulse-position modulation," IEEE Trans. Circuits Syst. I, vol. 48, pp. 1436-1444, 2001.
A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature, vol. 438, pp. 343-346, 2005.
D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, "Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation
schemes," J. of Lightwave Technol., vol. 22, pp. 2256-2263, 2004.
V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-‾ber communication systems," J. Lightwave
Technol., vol. 21, pp.61-68, 2003.
S. Sivaprakasam and K. A. Shore, "Message Encoding and Decoding Using Chaotic External-Cavity Diode Lasers," IEEE J. Quantum Electron., vol. 36, pp. 35-39, 2000.
S. Sivaprakasam and K. A. Shore, "Critical signal strength for effective decoding in diode laser chaotic optical communications," Phys Rev. E, vol. 61, pp. 5997-5999, 2000.