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In this paper, various nonlinear dynamic behaviors of distributed feedback semiconductor laser (DFB-SL) subjected to self-delayed optical and electrical feedback are studied numerically. The results show that the DFB-SL output presents a variety of nonlinear dynamic states such as single-period, quasi-period, and multi-period under different optical feedback intensities. When the external light feedback reaches a certain intensity, the laser output enters a chaotic regime. When the optical feedback intensity is small, a variety of nonlinear dynamic states will appear in the DFB-SL output under different electrical feedback intensities. When the optical feedback intensity is large, the single-period dynamic state cannot be obtained by changing the electrical feedback intensity. The optical feedback and electrical feedback delay time also have a significant influence on the nonlinearity of DFB-SL. When their time delays match, the relaxation oscillation of the laser is enhanced and exhibits a single-period state. And time mismatch may lead to chaos or instability. The bias current also affects the dynamic state, however, the direction of evolution of the dynamic states is not unidirectional as the current changes unidirectionally. When the DFB-SL is in a single-period state, changing the bias current will result in the change of the single-cycle oscillation frequency. These findings provide an important theoretical basis for applying the self-delayed feedback DFB-SL to microwave photonic signal processing and secure optical communication, as well as experimental means for conducting various nonlinear scientific researches.
[1] Olesen H, Osmundsen J, Tromborg B 1986 IEEE J. Quantum Electron. 22 762
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[2] 操良平, 邓涛, 林晓东, 吴加贵, 夏光琼, 吴正茂 2010 中国激光 37 939
Google Scholar
Cao L P, Deng T, Lin X D, Wu J G, Xia G Q, Wu Z M 2010 Chin. Lasers 37 939
Google Scholar
[3] 刘凌锋, 妙锁霞 2015 光电子·激光 26 86
Google Scholar
Liu L F, Miao S X 2015 J. Optoelectron. Laser 26 86
Google Scholar
[4] Lang R, Kobayashi K 1980 IEEE J. Quantum Electron. 16 347
Google Scholar
[5] Soriano M C, Garcíaojalvo J, Mirasso C R, Fischer I, Soriano M C 2013 Rev. Mod. Phys. 85 421
Google Scholar
[6] Saboureau P, Foing J P, Schanne P 1997 IEEE J. Quantum Electron. 33 1582
Google Scholar
[7] Tang S, Liu J M 2001 IEEE J. Quantum Electron. 37 329
Google Scholar
[8] Hizanidis J, Deligiannidis S, Bogris A, Syvridis D 2010 IEEE J. Quantum Electron. 46 1642
Google Scholar
[9] Chen G C, Lu D, Guo L, Zhao W, Huang Y G, Zhao L J 2019 Optik 180 313
Google Scholar
[10] 包琪 2020 硕士学位论文 (杭州: 杭州电子科技大学)
Bao Q 2020 M. S. Thesis (Hangzhou: Hangzhou Dianzi University
[11] 张梦雨 2022 硕士学位论文 (郑州: 郑州大学)
Zhang M Y 2022 M.S. Thesis (Zhengzhou: Zhengzhou University
[12] Argyris A, Syvridis D, Larger L 2005 Nature 438 343
Google Scholar
[13] 孔慧君, 吴正茂, 吴加贵, 林晓东, 谢瑛珂, 夏光琼 2006 中国激光 17 1490
Google Scholar
Kong H J, Wu Z M, Wu J G, Lin X D, Xie Y K, Xia G Q 2006 Chin. Lasers 17 1490
Google Scholar
[14] Argyris A, Hamacher M, Chlouverakis K E 2008 Phys. Rev. Lett. 100 194101
Google Scholar
[15] Vicente R, Dauden J, Colet P, Toral R 2005 IEEE J. Quantum Electron. 41 541
Google Scholar
[16] 蔺玉雪, 高慧, 王龙生, 李腾龙, 赵彤, 常朋发, 王安帮, 王云才 2024 中国激光 51 0606002
Google Scholar
Lin Y X, Gao H, Wang L S, Li T L, Zhao T, Chang P F, Wang A B, Wang Y C 2024 Chin. Lasers 51 0606002
Google Scholar
[17] Heil T, Fischer I, Elsasser W, Gavrielides A 2001 Phys. Rev. Lett. 87 243901
Google Scholar
[18] Lin F Y, Liu J M 2004 IEEE J. Quantum Electron. 40 815
Google Scholar
[19] Lin F Y, Liu J M 2003 IEEE J. Quantum Electron. 39 562
Google Scholar
[20] 韩韬, 刘香莲, 李璞, 郭晓敏, 郭龑强, 王云才 2017 66 124203
Google Scholar
Han T, Liu X L, Li P, Guo X M, Guo Y Q, Wang Y C 2017 Acta Phys. Sin. 66 124203
Google Scholar
[21] Mork J, Tromborg B, Mark J 1992 IEEE J. Quantum Electron. 28 93
Google Scholar
[22] 李增, 冯玉玲, 王晓茜, 姚治海 2018 67 140501
Google Scholar
Li Z, Feng Y L, Wang X Q, Yao Z H 2018 Acta Phys. Sin. 67 140501
Google Scholar
[23] 戈杉杉, 王腾午, 戈静怡, 周沛, 李念强 2023 72 164201
Google Scholar
Ge S S, Wang T W, Ge J Y, Zhou P, Li N Q 2023 Acta Phys. Sin. 72 164201
Google Scholar
[24] 张依宁, 徐艾诗, 冯玉玲, 赵振明, 姚治海 2020 光学学报 40 125
Zhang Y N, Xu A S, Feng Y L, Zhao Z M, Yao Z H 2020 Acta Opt. Sin. 40 125
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图 1 DFB-SL自延迟光电反馈结构图
Figure 1. Diagram of the DFB-SL self-delay photoelectric feedback structure.
图 2 DFB-SL自延迟光反馈结构图
Figure 2. Diagram of the DFB-SL self-delay optical feedback structure.
图 3 不同光反馈强度下DFB激光器的S-N图及其输出的时序图和频谱图 (a1)—(a3) $\kappa = 0.018$; (b1)—(b3) $\kappa = 0.044$; (c1)—(c3) $\kappa = 0.059$
Figure 3. Under different optical feedback intensities, S-N plots of DFB lasers and their output timing plots and spectrograms: (a1)–(a3) $\kappa = 0.018$; (b1)–(b3) $\kappa = 0.044$; (c1)–(c3) $\kappa = 0.059$.
图 4 不同光反馈时间下DFB激光器的S-N图及其输出的时序图和频谱图 (a1)—(a3) $\tau = 2.18 {\text{ ns}}$; (b1)—(b3) $\tau = 2.21 {\text{ ns}}$
Figure 4. Under different optical feedback time, S-N plots of DFB lasers and their output timing plots and spectrograms: (a1)–(a3) $\tau = 2.18 {\text{ ns}}$; (b1)–(b3) $\tau = 2.21 {\text{ ns}}$.
图 5 DFB-SL自延迟电反馈结构图
Figure 5. Diagram of the DFB-SL self-delay electricity feedback structure.
图 6 不同光电反馈强度下DFB激光器的S-N图及其输出的时序图和频谱图 (a1)—(a3) $\zeta = 0.045$; (b1)—(b3) $\zeta = 0.0555$; (c1)—(c3) $\zeta = 0.0973$; (d1)—(d3) $\zeta = 0.19$
Figure 6. Under different feedback intensity, S-N plots of DFB lasers and their output timing plots and spectrograms: (a1)–(a3) $\zeta = 0.045$; (b1)–(b3) $\zeta = 0.0555$; (c1)–(c3) $\zeta = 0.0973$; (d1)–(d3) $\zeta = 0.19$.
图 7 不同光-电反馈强度下的动力学态相图
Figure 7. Effect of photo-electrical feedback intensity on laser dynamics.
图 8 不同光-电反馈延迟时间条件下的动力学态相图
Figure 8. Effect of optical-electrical feedback delay time on laser dynamics.
图 9 不同偏置电流下DFB激光器的S-N图及激光器输出的时序图和频谱图 (a1)—(a3) $I = 40 {\text{ mA}}$; (b1)—(b3) $I = 36 {\text{ mA}}$; (c1)—(c3) $I = 20 {\text{ mA}}$
Figure 9. Under different bias current, S-N plots of DFB lasers and their output timing plots and spectrograms: (a1)–(a3) $I = 40 {\text{ mA}}$; (b1)–(b3) $I = 36 {\text{ mA}}$; (c1)–(c3) $I = 20 {\text{ mA}}$.
图 10 偏置电流对单周期信号频率的影响
Figure 10. Effect of the bias current on P1 signal frequency.
表 1 参数符号及取值
Table 1. Parameter symbols and their values.
参数 符号 取值 单位 光子数 $ S\left(t\right) $ — — 载流子数 $ N\left(t\right) $ — — 光功率 $ P\left(t\right) $ — — 微分增益 $ {G}_{{\mathrm{N}}} $ $ (3—4) \times {10}^{4}$ s–1 透明载流子数 $ {N}_{0} $ $ 1.36\times{10}^{8} $ — 阈值光子数 $ {S}_{0} $ $ 4.04\times{10}^{4} $ — 激光腔内反馈时间 $ {\tau }_{{\mathrm{i}}{\mathrm{n}}} $ 9 $ {\mathrm{p}}{\mathrm{s}} $ 光子寿命 $ {\tau }_{{\mathrm{p}}} $ 2 $ {\mathrm{p}}{\mathrm{s}} $ 载流子寿命 $ {\tau }_{{\mathrm{e}}} $ 2 $ {\mathrm{n}}{\mathrm{s}} $ 电子电荷 $ e $ $ 1.6\times{10}^{-19}$ C 限制因子 $ \varGamma $ 0.5 — 自发辐射因子 $ \beta $ $1\times {10}^{-5} $ — 饱和增益因子 $ \varepsilon $ $ (7—8)\times{10}^{-8} $ — 激光器的中心频率 $ {\omega }_{0} $ $ 1.938 \times {10}^{14}~{\mathrm{Hz}} $ — 线宽增强因子 $ a $ 4.5 — 
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[1] Olesen H, Osmundsen J, Tromborg B 1986 IEEE J. Quantum Electron. 22 762
Google Scholar
[2] 操良平, 邓涛, 林晓东, 吴加贵, 夏光琼, 吴正茂 2010 中国激光 37 939
Google Scholar
Cao L P, Deng T, Lin X D, Wu J G, Xia G Q, Wu Z M 2010 Chin. Lasers 37 939
Google Scholar
[3] 刘凌锋, 妙锁霞 2015 光电子·激光 26 86
Google Scholar
Liu L F, Miao S X 2015 J. Optoelectron. Laser 26 86
Google Scholar
[4] Lang R, Kobayashi K 1980 IEEE J. Quantum Electron. 16 347
Google Scholar
[5] Soriano M C, Garcíaojalvo J, Mirasso C R, Fischer I, Soriano M C 2013 Rev. Mod. Phys. 85 421
Google Scholar
[6] Saboureau P, Foing J P, Schanne P 1997 IEEE J. Quantum Electron. 33 1582
Google Scholar
[7] Tang S, Liu J M 2001 IEEE J. Quantum Electron. 37 329
Google Scholar
[8] Hizanidis J, Deligiannidis S, Bogris A, Syvridis D 2010 IEEE J. Quantum Electron. 46 1642
Google Scholar
[9] Chen G C, Lu D, Guo L, Zhao W, Huang Y G, Zhao L J 2019 Optik 180 313
Google Scholar
[10] 包琪 2020 硕士学位论文 (杭州: 杭州电子科技大学)
Bao Q 2020 M. S. Thesis (Hangzhou: Hangzhou Dianzi University
[11] 张梦雨 2022 硕士学位论文 (郑州: 郑州大学)
Zhang M Y 2022 M.S. Thesis (Zhengzhou: Zhengzhou University
[12] Argyris A, Syvridis D, Larger L 2005 Nature 438 343
Google Scholar
[13] 孔慧君, 吴正茂, 吴加贵, 林晓东, 谢瑛珂, 夏光琼 2006 中国激光 17 1490
Google Scholar
Kong H J, Wu Z M, Wu J G, Lin X D, Xie Y K, Xia G Q 2006 Chin. Lasers 17 1490
Google Scholar
[14] Argyris A, Hamacher M, Chlouverakis K E 2008 Phys. Rev. Lett. 100 194101
Google Scholar
[15] Vicente R, Dauden J, Colet P, Toral R 2005 IEEE J. Quantum Electron. 41 541
Google Scholar
[16] 蔺玉雪, 高慧, 王龙生, 李腾龙, 赵彤, 常朋发, 王安帮, 王云才 2024 中国激光 51 0606002
Google Scholar
Lin Y X, Gao H, Wang L S, Li T L, Zhao T, Chang P F, Wang A B, Wang Y C 2024 Chin. Lasers 51 0606002
Google Scholar
[17] Heil T, Fischer I, Elsasser W, Gavrielides A 2001 Phys. Rev. Lett. 87 243901
Google Scholar
[18] Lin F Y, Liu J M 2004 IEEE J. Quantum Electron. 40 815
Google Scholar
[19] Lin F Y, Liu J M 2003 IEEE J. Quantum Electron. 39 562
Google Scholar
[20] 韩韬, 刘香莲, 李璞, 郭晓敏, 郭龑强, 王云才 2017 66 124203
Google Scholar
Han T, Liu X L, Li P, Guo X M, Guo Y Q, Wang Y C 2017 Acta Phys. Sin. 66 124203
Google Scholar
[21] Mork J, Tromborg B, Mark J 1992 IEEE J. Quantum Electron. 28 93
Google Scholar
[22] 李增, 冯玉玲, 王晓茜, 姚治海 2018 67 140501
Google Scholar
Li Z, Feng Y L, Wang X Q, Yao Z H 2018 Acta Phys. Sin. 67 140501
Google Scholar
[23] 戈杉杉, 王腾午, 戈静怡, 周沛, 李念强 2023 72 164201
Google Scholar
Ge S S, Wang T W, Ge J Y, Zhou P, Li N Q 2023 Acta Phys. Sin. 72 164201
Google Scholar
[24] 张依宁, 徐艾诗, 冯玉玲, 赵振明, 姚治海 2020 光学学报 40 125
Zhang Y N, Xu A S, Feng Y L, Zhao Z M, Yao Z H 2020 Acta Opt. Sin. 40 125
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