本篇論文研究以雙光回饋半導體雷射系統來產生高頻且低線寬的微波訊號，即半導體雷射接收自身的第一道回饋光後，所產生的非線性週期一動態，藉此作為高頻微波訊號源，再受第二道回饋光使微波訊號之3-dB線寬進一步下降，以優化微波訊號質量。接著，我們將以模擬證明雙光回饋系統產生之微波訊號，具備頻率可調範圍廣的優點，只需調整至適當回饋條件，微波頻率就能從10GHz改變到60GHz，且微波線寬約可從10MHz降至176kHz。最後，討論回饋光之延遲相位對微波訊號之頻率及相位雜訊的影響，挑選合適延遲相位將能進一步降低相位雜訊，使微波訊號穩定。

The generation of a high-frequency and low-noise microwave signal by using semiconductor laser subject to dual optical feedbacks is investigated. The period-one nonlinear dynamic is induced by adding the first feedback to the semiconductor laser, and it is also the source of the microwave signal. To improve the quality of the microwave signal, adding the second feedback to the laser can compress the 3-dB linewidth of the microwave signal. And then, we numerically prove the microwave signal, which is generated by dual feedback laser system, has the advantage of widely tunable frequency. Under suitable feedback parameters, the microwave frequency tunable from 10 to 60 GHz and the linewidth reduced from 10 MHz to 176 kHz is demonstrated. Moreover, the effect of the delay phase on the frequency and phase noise of the microwave signal is analyzed. Choosing a proper delay phase can further reduce the phase noise and stabilize the microwave signal.

[1] S. Kumar and S. Shukla, Concepts and Application of MICROWAVE ENGINEERING.PHI Learning, 2014.
[2] C. Liu, J. Wang, L. Cheng, M. Zhu, and G. K. Chang, "Key Microwave Photonics Technologies for Next-Generation Cloud-Based Radio access Networks," Journal of Lightwave Technology, vol. 32, no. 20, pp. 3452-3460, 2014.
[3] J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat Photon, vol. 1, no. 6, pp. 319–330, 2007.
[4] J. Yao, "Microwave Photonics," Journal of Lightwave Technology, vol. 27, pp. 314 - 335, 2009.
[5] X. Q. Qi, J. M. Liu, "Photonic Microwave Applications of the Dynamics of Semiconductor Lasers," IEEE Journal of Selected Topics in Quantum Electronics, vol. 17, pp. 1198 - 1211, 2011.
[6] J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat Photon, vol. 1, no. 6, pp. 319–330, 2007.
[7] J. Yao, "Microwave photonics," Journal of Lightwave Technology, vol. 27, pp. 314–335, 2009.
[8] L. F. Lester, N. A. Naderi, F. Grillot, R. Raghunathan, and V. Kovanis, "Strong optical injection and the differential gain in a quantum dash laser," Optics Express, vol. 22, pp. 7222–7228, 2014.
[9] F. Grillot, C. Wang, N. A. Naderi, and J. Even, "Modulation properties of self-injected quantum-dot semiconductor diode lasers," IEEE Journal of Selected Topics in Quantum Electronics, vol. 19, pp. 1900812, 2013.
[10] S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, "Improved semiconductor-laser dynamics from induced population pulsation," IEEE Journal of Quantum Electronics, vol. 42, pp. 552–562, 2006.
[11] B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. Luo, A. K. Y. Jen, W. H. Steier, and H. R. Fetterman, " Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE Journal of Selected Topics in Quantum Electronics, vol. 13, pp. 104–110, 2007.
[12] J.L. Zhou, L. Xia , X.P. Cheng, X.P. Dong, P. Shum, "Photonic generation of tunable microwave signals by beating a dual-wavelength single longitudinal mode fiber ring laser," Applied Physics B, vol. 91, pp. 99-103, 2008.
[13] D. Chen, H. Fu, W.Liu, Y. Wei, S. He "Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre bragg grating pair and its application in microwave signal generation," Electronics Letters, vol. 44, pp. 459 - 461, 2008.
[14] M. Haji, L. P. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, "High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes," Optics Express, vol. 20, pp. 3268–3274, 2012.
[15] C. Y. Lin, F. Grillot, Y. Li, R. Raghunathan, and L. F. Lester, "Microwave characterization and stabilization of timing jitter in a quantum-dot passively mode-locked laser via external optical feedback," IEEE Journal of Selected Topics in Quantum Electronics, vol. 17, pp. 1311–1317, 2011.
[16] S. L. Pan and J. P. Yao, "Wideband and frequency-tunable microwave generation using an optoelectronic oscillator incorporating a Fabry-Perot laser diode with external optical injection," Optics Letters, vol. 35, pp. 1911–1913, 2010.
[17] X. S. Yao and L. Maleki, "Optoelectronic microwave oscillator," Journal of the Optical Society of America B, vol. 13, pp. 1725–1735, 1996.
[18] T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, "Nonlinear dynamics induced by external optical injection in semiconductor lasers," Quantum Semiclassical Optics: Journal of the European Optical Society Part B, vol. 9, pp. 765–784, 1997.
[19] S. C. Chan, "Analysis of an optically injected semiconductor laser for microwave generation," IEEE Journal of Quantum Electronics, vol. 46, no. 3, pp. 421–428, 2010.
[20] S. C. Chen, S. K. Hwang, and J. M. Liu, "Period-one oscillation for photonic microwave transmission using an optically injected semiconductor laser," Optics Express, vol. 15, no. 22, pp. 14921–14935, 2007.
[21] S. K. Hwang, J. M. Liu, and J. K. White, "Characteristics of period-one oscillations in semiconductor lasers subject to optical injection," IEEE Journal of Selected Topics in Quantum Electronics, vol. 10, no. 5, pp. 974–981, 2004.
[22] M. Pochet, N. A. Naderi, V. Kovanis, and L. F. Lester, "Modeling the dynamic response of an optically-injected nanostructure diode laser," IEEE Journal of Selected Topics in Quantum Electronics, vol. 47, pp. 827–833, 2011.
[23] A. Hurtado, I. D. Henning, M. J. Adams, and L. F. Lester, "Generation of tunable millimeter-wave and THz signals with an optically injected quantum dot distributed feedback laser," IEEE Photonics Journal, vol. 5, pp.5900107, 2013.
[24] Y. H. Hung and S. K. Hwang, "Photonic microwave amplification for radio-over-fiber links using period-one nonlinear dynamics of semiconductor lasers," Optics Letters, vol. 38, pp. 3355–3358, 2013.
[25] Y. H. Hung, C. H. Chu, and S. K. Hwang, "Optical double-sideband modulation to single-sideband modulation conversion using period-one nonlinear dynamics of semiconductor lasers for radio-over-fiber links," Optics Letters, vol. 38, pp. 1482–1484, 2013.
[26] S. C. Chan, S. K. Hwang, and J. M. Liu, "Period-one oscillation for photonic microwave transmission using an optically injected semiconductor laser," Optics Express, vol. 15, pp. 14921–14935, 2007.
[27] M. Pochet, T. Locke, and N. G. Usechak, "Generation and modulation of a millimeter-wave subcarrier on an optical frequency generated via optical injection," IEEE Photonics Journal, vol. 4, pp. 1881–1891, 2012.
[28] C. Cui, X. Fu, and S. C. Chan, “Double-locked semiconductor laser for radio-over-fiber uplink transmission,” Optics Letters, vol. 34, pp. 3821–3823, 2009.
[29] J.M. Saucedo Solorio, D.W. Sukow, D.R. Hicks, A. Gavrielides, "Bifurcations in a semiconductor laser subject to delayed incoherent feedback," Optics Communications, vol. 214, pp. 327–334, 2002.
[30] A. Karsaklian Dal Bosco, K. Kanno, A.Uchida, M. sciamanna, T. Harayama, and K. Yoshimura, "Cycles of Self-Pulsations in a Photonic Integrated Circuit," Physical Review E, vol. 92, no. 6, p. 062905, 2015.
[31] Y. A. Leem, D. S. Yee, E. Sim, S. B. Kim, D. C. Kim, and K. H. Park, Self-Pulsation in Multisection Laser Diodes With a DFB Reflector," IEEE Photonics Technology Letters, vol. 18, no.4, pp. 622-624, 2006.
[32] S. C. Chan and J. M. Liu, "Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics," IEEE Journal of Selected Topics in Quantum Electronics, vol. 10, pp. 1025–1032, 2004.
[33] 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 Journal of Selected Topics in Quantum Electronics, vol. 19, pp. 1500807, 2013.
[34] J. P. Zhuang and S. C. Chan, "Phase noise characteristics of microwave signals generated by semiconductor laser dynamics," Optics Express, vol. 23, no. 3, pp. 2777–2797, 2015.
[35] Arecchi, F.T., Lippi, G.L., Puccioni, G.P, Tredicce, J.R. "Deterministic chaos in laser with injected signal," Optics Communications, vol. 51, no. 5, pp. 308-314, 1984.
[36] J. M. Liu, H. F. Chen and S. Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 48, no.12, pp.1475-1483, 2001.
[37] L. E. Larson, J.-M. Liu, L. S. Tsimring, Digital Communications Using Chaos and Nonlinear Dynamics, Springer, United States of America, pp. 285-294, 2006.