Time delay signature and bandwidth of chaotic laser output from semiconductor laser

Zhang Yi-Ning; Feng Yu-Ling; Wang Xiao-Qian; Zhao Zhen-Ming; Gao Chao; Yao Zhi-Hai

doi:10.7498/aps.69.20191881

Abstract

Semiconductor laser (SL) can output chaotic lasers under external disturbances such as optical injection or optical feedback, and the bandwidth can reach up to GHz magnitude. External-cavity feedback semiconductor lasers can output high-dimensional chaotic lasers and are considered to be better sources of chaotic entropy. However, due to external cavity feedback and other effects, it will give rise to obvious external cavity time delay signature (TDS) in the output chaotic laser, which restricts the application of chaotic lasers. On the other hand, the bandwidth of chaotic laser determines the transmission rate of confidential communication, and therefore TDS and bandwidth are two important parameters that will affect chaotic laser’s applications. Therefore, it is significant to take appropriate measures to suppress the TDS and increase the bandwidth of chaotic laser output by semiconductor laser. In this paper the output laser from a semiconductor laser with single optical feedback is partially injected to another semiconductor laser with double filtered optical feedback. Thus they form a semiconductor laser system with external optical injection and double filtered optical feedback, i.e. a master-slave laser system which is used to suppress the TDS of chaotic laser and investigate its bandwidth. We numerically investigate the influences of external light injection coefficient, feedback intensity, pumping factor, and filter bandwidth on TDS. Then the suppression effects of this system on TDS are analyzed and compared with those of semiconductor laser system with external optical injection and single optical feedback, those of semiconductor laser system with external optical injection and double optical feedback, those of semiconductor laser system with external optical injection and single filtered optical feedback, and those of semiconductor laser system with double filtered optical feedback. The results show that the proposed scheme in this paper has the best suppression effect on TDS. Then the bandwidth of the chaotic laser output from the system is investigated under the condition of parameters of effectively suppressing TDS. The results show that the system proposed in this paper can increase the bandwidth of the system output chaotic laser by properly selecting the parametric values, and the maximum bandwidth value of the obtained chaotic laser is about 8.8 GHz. The above investigations indicate the effectiveness of the proposed scheme. The results of this investigation are significant for the application of chaotic lasers.

Keywords:

Authors and contacts

Department of Physics, Changchun University of Science and Technology, Changchun 130022, China

Corresponding author: Feng Yu-Ling, FYLCUST@163.com

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References

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图 1 SL-EOI-DFOF系统示意图

Figure 1. Schematic diagram of the SL-EOI-DFOF system.

DownLoad: Full-Size Img PowerPoint

图 2 SL-EOI-DFOF在不同的延迟时间${\tau _1}$下输出混沌激光的(a1)−(a3)时间序列、(b1)−(b3)自相关曲线以及(c1)−(c3)互信息曲线　(a1)−(c1)${\tau _1} = 2.7\;{\rm{ns}}$; (a2)−(c2)${\tau _1} = 2.8\;{\rm{ns}}$; (a3)−(c3)${\tau _1} = 2.9\;{\rm{ns}}$

Figure 2. Time series (a1)−(a3), ACF curves (b1)−(b3) and MI curves (c1)−(c3) of chaotic laser from the SL-EOI-DFOF at different delay times ${\tau _1}$: (a1)−(c1)${\tau _1} = 2.7\;{\rm{ns}}$; (a2) −(c2)${\tau _1} = 2.8\;{\rm{ns}}$; (a3)−(c3)${\tau _1} = 2.9\;{\rm{ns}}$.

DownLoad: Full-Size Img PowerPoint

图 3 SL-EOI-DFOF输出混沌激光延时特征值$\beta $随参数${k_{{\rm{in}}}}$和${k_{{\rm{f1}}}}$变化的二维图

Figure 3. Two-dimensional maps of the time-delay characteristic $\beta $ in the parameter space of ${k_{{\rm{in}}}}$ and ${k_{{\rm{f1}}}}$ of chaotic laser from the SL-EOI-DFOF.

DownLoad: Full-Size Img PowerPoint

图 4 SL-EOI-SOF, SL-EOI-DOF, SL-EOI-SFOF, SL-EOI-DFOF和SL-DFOF输出混沌激光的延时特征值$\beta $随${P_{\rm{m}}}$的变化

Figure 4. Variations of the time delay characteristic values $\beta $ with ${P_{\rm{m}}}$ of chaotic laser from the SL-EOI-SOF, SL-EOI-DOF, SL-EOI-SFOF, SL-EOI-DFOF and SL-DFOF, respectively.

DownLoad: Full-Size Img PowerPoint

图 5 SL-EOI-DFOF和SL-EOI-SFOF输出混沌激光的延时特征值$\beta $随${\varLambda _1}$的变化

Figure 5. Variations of the time delay characteristic values $\beta $ with ${\varLambda _1}$ of chaotic laser from the SL-EOI-DFOF and SL-EOI-SFOF, respectively.

DownLoad: Full-Size Img PowerPoint

图 6 SL-EOI-DFOF在不同的外光注入系数${k_{{\rm{in}}}}$下输出混沌激光的(a1)−(a3)时间序列以及(b1)−(b3)对应的功率谱　(a1), (b1)${k_{{\rm{in}}}} = 0$; (a2), (b2)${k_{{\rm{in}}}} = 0.1$; (a3), (b3)${k_{{\rm{in}}}} = 0.2$, 其中(b1)—(b3)中的虚线标示了混沌激光3 dB带宽的值

Figure 6. Time series (a1)−(a3) and the corresponding power spectra (b1)−(b3) of chaotic laser from SL-EOI-DFOF at different external light injection coefficient ${k_{{\rm{in}}}}$: (a1), (b1) ${k_{{\rm{in}}}} = 0$; (a2), (b2) ${k_{{\rm{in}}}} = 0.1$; (a3), (b3)${k_{{\rm{in}}}} = 0.2$, the dashed lines in (b1)−(b3) indicate the value of the 3 dB bandwidth of the chaotic laser.

DownLoad: Full-Size Img PowerPoint

图 7 SL-EOI-DFOF输出混沌激光的带宽随${k_{{\rm{in}}}}$的变化

Figure 7. Bandwidth versus ${k_{{\rm{in}}}}$ of chaotic laser from the SL-EOI-DFOF.

DownLoad: Full-Size Img PowerPoint

图 8 SL-EOI-DFOF输出混沌激光的带宽随${\varLambda _1}$的变化

Figure 8. Bandwidth versus ${\varLambda _1}$ of chaotic laser from the SL-EOI-DFOF.

DownLoad: Full-Size Img PowerPoint

图 9 SL-EOI-DFOF输出混沌激光的带宽随${k_{{\rm{f1}}}}$的变化

Figure 9. Bandwidth versus ${k_{{\rm{f1}}}}$ of chaotic laser from the SL-EOI-DFOF.

DownLoad: Full-Size Img PowerPoint

图 10 SL-EOI-DFOF输出混沌激光的带宽随${P_{\rm{m}}}$的变化

Figure 10. Bandwidth versus ${P_{\rm{m}}}$ of chaotic laser from the SL-EOI-DFOF.

DownLoad: Full-Size Img PowerPoint

[1]	Simpson T B, Liu J M, Gavrielides A, Kovanis V, Alsing P M 1995 Phys. Rev. A 51 4181 Google Scholar
[2]	Lin F Y, Liu J M 2003 Opt. Commun. 221 173 Google Scholar
[3]	Senlin Y 2009 J. Opt. Commun. 30 20 Google Scholar
[4]	Deng T, Xia G Q, Cao L P, Chen J G, Lin X D, Wu Z M 2009 Opt. Commun. 282 2243 Google Scholar
[5]	张明江, 刘铁根, 郑建宇, 王安帮, 王云才 2011 中国激光 4 136 Google Scholar Zhang M J, Liu T G, Zheng J Y, Wang A B, Wang Y C 2011 Chin. J. Lasers 4 136 Google Scholar
[6]	Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Yoshimura K 2008 Nat. Photonics 2 728 Google Scholar
[7]	Metropolis N, Ulam S 1949 J. Am. Stat. Assoc. 44 335 Google Scholar
[8]	Wang Y, Wang B, Wang A 2008 IEEE Photonics Technol. Lett. 20 1636 Google Scholar
[9]	Argyris A, Syvridis D, Larger L, Annovazzi V 2005 Nature 438 343 Google Scholar
[10]	Lin F Y, Liu J M 2004 IEEE J. Quantum Electron. 40 815 Google Scholar
[11]	张继兵, 张建忠, 杨毅彪, 梁君生, 王云才 2010 物理学报 59 7679 Google Scholar Zhang J B, Zhang J Z, Yang Y B, Liang J S, Wang Y C 2010 Acta Phys. Sin. 59 7679 Google Scholar
[12]	Wu J G, Xia G Q, Tang X, Lin X D, Wu Z M 2010 Opt. Express 18 6661 Google Scholar
[13]	Jafari A, Sedghi H, Mabhouti K, Behnia S 2011 Opt. Commun. 284 3018 Google Scholar
[14]	Udaltsov V S, Goedgebuer J P, Larger L, Vladimir S, Cuenot J, William T, Rhodes 2003 Phys. Lett. E 308 54 Google Scholar
[15]	Rontani D, Locquet A, Sciamanna M, Citrin D S 2007 Opt. Lett. 32 2960 Google Scholar
[16]	Vicente R, Daudén J, Colet P, Toral R 2005 IEEE J. Quantum Electron. 41 541 Google Scholar
[17]	Li S S, Chan S C 2015 IEEE J. Quantum Electron. 21 541 Google Scholar
[18]	孙巍阳, 张胜海, 吴天安, 张晓旭 2017 激光与光电子学进展 54 208 Google Scholar Sun W Y, Zhang S H, Wu T A, Zhang X X 2017 Las. Optoelect. Prog. 54 208 Google Scholar
[19]	Schires K, Gomez S, Gallet A, Duan G, Grillot F 2017 IEEE J. Quantum Electron. 99 1 Google Scholar
[20]	Xu Y P, Zhang L, Lu P, Mihailov S, Chen L, Bao X Y 2018 Opt. Laser Technol. 109 654 Google Scholar
[21]	Nguimdo R M, Soriano M C, Colet P 2011 Opt. Lett. 36 4322 Google Scholar
[22]	Zhao A, Jiang N, Liu S 2019 Opt. Express 27 12336 Google Scholar
[23]	Brunner D, Porte X, Soriano M C, Fischer I 2012 Sci. Rep. 2 732 Google Scholar
[24]	Uchida A, Heil T, Liu Y, Davis P, Aida T 2003 IEEE J. Quantum Electron. 39 0 Google Scholar
[25]	Wu J G, Xia G Q, Wu Z M 2009 Opt. Express 17 20124 Google Scholar
[26]	Lang R, Kobayashi K 1980 IEEE J. Quantum Electron. 16 347 Google Scholar
[27]	卢东, 钟祝强, 夏光琼, 吴正茂 2016 光子学报 45 1014003 Google Scholar Lu D, Zhong Z Q, Xia G Q, Wu Z M 2016 Acta Photon. Sin. 45 1014003 Google Scholar
[28]	Udaltsov V S, Larger L, Goedgebuer J P, Locquet A, Citrin D S 2005 J. Opt. Technol. 72 373 Google Scholar
[29]	高飞, 李念强, 张力月, 欧阳康 2016 量子光学学报 22 289 Gao F, Li N Q, Zhang L Y, Ouyang K 2016 J. Quantum Opt. 22 289
[30]	孙巍阳, 张胜海, 吴天安, 张晓旭 2016 激光与光电子学进展 53 121406 Google Scholar Sun W Y, Zhang S H, Wu T A, Zhang X X 2016 Las. Optoelect. Prog. 53 121406 Google Scholar
[31]	Wang A, Yang Y, Wang B, Zhang B, Li L, Wang Y C 2013 Opt. Express 21 8701 Google Scholar
[32]	蒋龙, 夏光琼, 吴加贵, 肖平, 吴正茂 2012 中国激光 39 1202003 Google Scholar Jiang L, Xia G Q, Wu J G, Xiao P, Wu Z M 2012 Chin. J. Lasers 39 1202003 Google Scholar
[33]	Wu Y, Wang B, Zhang J, Wang A, Wang Y 2013 Math. Probl. Eng. 2013 1 Google Scholar
[34]	张建忠, 王安帮, 张明江, 李晓春, 王云才 2011 物理学报 60 094207 Google Scholar Zhang J Z, Wang A B, Zhang M J, Li X C, Wang Y C 2011 Acta Phys. Sin. 60 094207 Google Scholar
[35]	王永胜, 赵彤, 王安帮, 张明江, 王云才 2017 激光与光电子进展 54 111404 Google Scholar Wang Y S, Zhao T, Wang A B, Zhang M J, Wang Y C 2017 Las. Optoelect. Prog. 54 111404 Google Scholar
[36]	Simpson T B, Liu J M, Huang K F, Tai K 1997 Quantum Semiclassical Opt. 9 765 Google Scholar
[37]	江宁, 刘丁, 薛琛鹏, 邱昆 2015 中国科技论文 10 1640 Google Scholar Jiang N, Liu D, Xue C P, Qiu K 2015 China Sciencepaper 10 1640 Google Scholar
[38]	王云才, 张耕玮, 王安帮, 王冰洁, 李艳丽, 郭萍 2007 物理学报 56 4372 Google Scholar Wang Y C, Zhang G W, Wang A B, Wang B J, Li Y L, Guo P 2007 Acta Phys. Sin. 56 4372 Google Scholar

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