本篇論文是利用數值模擬光注入半導體雷射系統，產生之非線性動態行為中的週期二動態，作為OTDM系統中的時脈除頻之應用，再加上光回饋半導體雷射系統，使輸出除頻時脈品質提升。同時介紹光注入、光回饋系統與兩者結合系統之原理，與各系統產生的動態變化及其動態應用。在光注入結合光回饋系統產生的週期二動態之靜態分析中，光注入條件與主共振頻率呈正相關；而光回饋條件則使動態隨回饋時間變化，並在迴圈頻率約等於半導體雷射鬆弛震盪頻率或其子諧波時，有更大的主共振頻率可調性。在動態分析中，光注入系統中的主雷射載入33%RZ訊號，在20GHz除頻至10GHz分析中，可得峰對峰週期擾動為2016fs，加入光回饋系統可降至1587fs；在40GHz除頻至20GHz的分析中，光注入系統可得峰對峰週期擾動為840fs，加入光回饋系統可降低至511fs。

An all-optical microwave frequency division by synchronized semiconductor lasers is numerically investigated in this study. Nonlinear period-two (P2) dynamic of optically-injected semiconductor lasers is applied for microwave frequency division. A fundamental frequency and its subharmonic are generated in power spectrum. By injecting a data-modulated optical signal, its additive clock signal will be frequency-locked toward the fundamental frequency simultaneously with a synchronized P2 dynamics. With optical feedback and effects of laser parameters on period-two oscillation, precise clock division is demonstrated by modulating the master laser at 20GHz and 40GHz.A locked subharmonic at 10GHz and 20GHz with period jitter of 2016fs and 840fs. Appropriate optical feedback can lower the period jitter to 1587fs and 511fs.

[1] K. C. Kao and G. A. Hochham, "Dielectric-fibre surface waveguides for optical frequency, "Proc. IEEE., vol. 113,pp.1151, 1966.
[2] S. Kawanishi, "Ultra-speed optical time-division-multiplexed transmission technology based on optical signal processing," IEEE J. Quantum Electron., vol. 34, pp. 2064–2079, 1998.
[3] S. A. Hamilton, B. S. Robinson, T. E. Murphy, S. J. Savage, and E. P. Ippen, “100 Gb/s optical time-division multiplexed networks," J. Lightw. Technol., vol. 20, no. 12, pp. 2086–2100, 2002.
[4] A. Takada, T. Sugie, and M. Saruwatari, "High-speed picosecond optical compression from gain-switched 1.3μm distributed feedback (DFB) LD through highly dispersive single-mode fiber," J. Lightwave Technol., vol. LT-5, pp. 1525–1533, 1987.
[5] A. Takada, K. Sato, M. Saruwatari, and M. Yamamoto, “Pulse width tunable subpicosecond pulse generation from an actively mode-locked monolithic MQW laser/MQW electroabsorption modulator," Electron. Lett., vol. 30, pp. 898–899, 1994.
[6] R. J. Manning, A. J. Poustie, and K. J. Blow, "All-optical clock division using a semiconductor optical amplifier loop mirror with feedback," Electron. Lett., vol. 32, pp. 1504–1506, 1996.
[7] A. E. Kelly, R. J. Manning, A. J. Poustie, and K. J. Blow, "All-optical clock division at 10 and 20 GHz in a semiconductor optical amplifier based nonlinear loop mirror," Electron. Lett., vol. 34, pp. 1337–1339, 1998.
[8] H. J. Lee and H. G. Kim, "Polarization-independent all-optical clock division using a semiconductor optical amplifier/grating filter switch," IEEE Photon. Technol. Lett., vol. 11, no. 4, pp. 469–471, 1999.
[9] A. Mecozzi and J. Mørk, "Saturation induced by picosecond pulses in semiconductor optical amplifiers," J. Opt. Soc. Amer. B, vol. 14, pp. 761–770, 1997.
[10] C. Y. Lou, L. Huo, G. Q. Chang, and Y. Z. Gao, "Experimental study of clock division using the optoelectronic oscillator," IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1178–1180, 2002.
[11] H. Tsuchida and M. Suzuki, "40-Gb/s optical clock recovery using an injection-locked optoelectronic oscillator," IEEE Photon. Technol. Lett., vol. 17, no. 1, pp. 211–213, 2005.
[12] M. Zhang, T. Liu, A. Wang, J. Zhang, and Y. Wang, "All-optical clock frequency divider using Fabry-Perot laser diode based on the dynamical period-one oscillation," Opt. Commun.,284, 1289–1294, 2010.
[13] S. C. Chan and J.M. Liu, "Microwave frequency division and multiplication using an optically injected semiconductor laser," IEEE J. Quantum Electron., vol. 41, no. 9, pp. 1142–1147, 2005.
[14] S. K. Hwang and J. M. Liu, "Dynamical characteristics of an optically injected semiconductor lasers," Optics Commun., vol. 183, no. 1/4, pp. 195–205, 2000.
[15] T. B. Simpson, J.-M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, "Tunable photonic microwave oscillator self-locked by polarization-rotated optical feedback," Proc. IEEE Int. Freq. Control Symp., pp. 1–5, May 2012.
[16] T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, "Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor laser oscillators," IEEE J. Sel. Topics Quantum Electron., vol. 19, no. 4, p. 1500807, 2013.
[17] K. H. Lo , S. K. Hwang , and S. Donati , "Optical feedback stabilization of photonic microwave period-one nonlinear dynamics of semiconductor lasers," Optics Express , 22 , pp.18648 - 18661, 2014.
[18] 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.
[19] J. M. Liu, H. F. Chen, and S. Tang, "Dynamics and Synchronization of Semiconductor Lasers for Chaotic Optical," Digital Communications Using Chaos and Nonlinear Dynamics Institute for Nonlinear Science, Chap. 10, pp. 285–340, 2006.
[20] J. M. Liu et al., "Modulation bandwidth, noise and stability of a semiconductor laser subject to strong injection locking," IEEE Photon. Technol. Lett., vol. 9, pp. 1325–1327, 1997.
[21] S. C. Chan, S. K. Hwang, and J. M. Liu, "Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser," Opt. Lett., vol. 31, pp. 2254–2256, 2006.
[22] 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.
[23] H. Someya, I. Oowada, H. Okumura, T. Kida, and A. Uchida, "Synchronization of bandwidth-enhanced chaos in semiconductor lasers with optical feedback and injection, " Opt. Exp., vol. 17, no. 22, pp. 19536–19543, 2009.
[24] C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, "Synchronization of chaotic semiconductor lasers: Application to encoded communications," IEEE Photon. Technol. Lett., vol. 8, pp. 299–301, 1996.
[25] J. M. Liu and T. B. Simpson, "Four-wave mixing and optical modulation in a semiconductor laser," IEEE J. Quantum Electron., vol. 30, pp. 957−965, 1994.
[26] J. M. Liu, C. Chang, and T. B. Simpson, "Amplitude noise enhancement caused by nonlinear interaction of spontaneous emission field in laser diodes," Opt. Commun., vol. 120, pp. 282−286, 1995.
[27] J. P. van der Ziel, J. L. Merz, and T. L. Paoli, "Study of intensity pulsations in proton-bombarded stripe geometry double-heterostructure AlxGa1xAs lasers," J. Appl. Phys., vol. 50, pp. 4620–4637, 1979.
[28] G. P. Agrawal and N. K. Dutta, "Semiconductor Lasers, 1st ed.," New York: Van Nostrand Reinhold, pp. 35-40, pp. 232-258, 1993.
[29] T. B. Simpson, J. M. Liu, and A. Gavrielides, "Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection," IEEE J. Quantum Electron., vol. 32, pp. 1456–1468, 1996.
[30] S. Chan, S. Hwang, and J.-M. Liu, "Period-one oscillation for photonic microwave transmission using an optically-injected semiconductor laser," Opt. Exp., vol. 15, pp. 14921–14935, 2007.
[31] J. Mork, B. Tromborg and J. Mark, "Chaos in semiconductor lasers with optical feedback: theory and experiment," IEEE J. Quant. Electron., Vol. 28, pp. 93-108, 1992.
[32] X. Li, C. Kim, and G. Li, "All-optical passive clock extraction of 40 Gbit/s NRZ data using narrow-band filtering," Opt. Expr., vol. 12, no. 14, pp. 3196–3203, 2004.
[33] S. C. Chan and J. M. Liu, "Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics," IEEE J. Sel. Topics Quantum Electron., vol. 10, pp. 1025–1032, 2004.
[34] F. Y. Lin and J. M. Liu, "Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback," Opt. Commun., vol. 221, no. 1–3, pp. 173–180, 2003.

[35] Q. Wang, L. Huo, Y. Xing, C. Lou, and B. Zhou, "Low-phase-noise clock recovery from NRZ signal and simultaneous NRZ-to-RZ format conversion," Photon. Technol. Lett., 2339–2341, 2013.
[36] X. Tang, J. C. Cartledge, A. Shen, F. van Dijk, A. Akrout, and G.-H Duan, "Characterization of all-optical clock recovery for 40 Gb/s RZ-OOK and RZ-DPSK data using mode-locked semiconductor lasers," J. Lightw. Technol., vol. 27, pp. 4603–4609, 2009.
[37] S. K. Hwang, J. M. Liu, and J. K. White, "35-GHz intrinsic bandwidth for direct modulation in 1.3-µm semiconductor lasers subject to strong injection locking," IEEE Photon. Technol. Lett. 16, 972–974, 2004.