Multiplexing synchronization implementation of micro-nano laser chaotic system based on active-passive decomposition method

MU Penghua; WANG Yiqiao; HE Pengfei; XU Yuan

doi:10.7498/aps.74.20241659

Abstract

Nanolaser (NL), as an important optical source device, has a significant influence on photonic integrated circuits and has become a research hotspot in recent years. In this work, the synchronization performance of a dual-channel laser chaotic multiplexing system is investigated based on NLs and an active-passive decomposition is used to enhance signal processing and multiplexing efficiency. By establishing a rate equation model, the synchronization characteristics of the system are analyzed, with a focus on two key parameters— Purcell factor (F ) and spontaneous emission coupling factor (β )—as well as the effects of system parameters, single-parameter mismatch, and multi-parameter mismatch. Numerical simulations show that with appropriate parameter configurations, the two master NLs can maintain low correlation, ensuring the "pseudo-orthogonality" of chaotic signals while achieving high-quality chaotic synchronization with their paired slave NLs. In this work it is found that both the Purcell factor (F ) and the spontaneous emission coupling factor (β ) significantly affect the synchronization performance of the system, and the optimal parameter ranges for achieving high-quality synchronization are identified. Additionally, the effects of feedback strength and frequency detuning are explored, revealing that frequency detuning plays a more critical role in the synchronization between the master NLs. The influence of parameter mismatches on system synchronization performance is also emphasized. The system exhibits robustness against single-parameter mismatch and has minimum influence on master-slave synchronization quality. However, multi-parameter mismatch gives rise to more complex effects. Compared with the traditional semiconductor laser systems, this system can maintain “pseudo-orthogonality” over a wider range of parameters, thus achieving higher security and lower channel interference. This research lays a theoretical foundation for chaos synchronization based on NLs and provides new insights for designing secure, stable, and efficient optical communication systems.

Keywords:

Authors and contacts

School of Physics and Electronic Information, Yantai University, Yantai 264005, China

Corresponding author: MU Penghua, ph_mu@ytu.edu.cn ; XU Yuan, xuyuan@ytu.edu.cn

Funds: Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2020QF090) and the Yantai City 2023 School-Land Integration Development Project Fund, China (Grant No. 2323013-2023XDRH001).

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References

[1]	Jiang N, Zhao A K, Liu S Q, Xue C P, Qiu K 2018 Opt. Express 26 32404 Google Scholar
[2]	Tang Y W, Li Q L, Dong W L, Hu M, Zeng R 2021 Opt. Commun. 498 127232 Google Scholar
[3]	Wang L S, Du X Y, Mao X X, Guo Y Y, Wang A B, Wang Y C 2024 Opt. Lett. 49 5901 Google Scholar
[4]	Wang Y M, Huang Y, Zhou P, Li N Q 2023 Electronics 12 509 Google Scholar
[5]	Wang L S, Guo Y Y, Wang D M, Wang Y C, Wang A B 2019 Opt. Commun. 453 124350 Google Scholar
[6]	Rontani D, Choi D, Chang C Y, Locquet A, Citrin D S 2016 Sci. Rep. 6 35206 Google Scholar
[7]	Lin F Y, Liu J M 2004 IEEE J. Sel. Top. Quant. 10 991 Google Scholar
[8]	Cai D Y, Mu P H, Huang Y, Zhou P, Li N Q 2024 Chaos Soliton. Fract. 189 115652 Google Scholar
[9]	Li X Y, Jiang N, Zhang Q, Tang C J, Zhang Y Q, Hu G, Cao Y S, Qiu K 2023 Opt. Express 31 28764 Google Scholar
[10]	Liu Y, Wu Z M, Tan S L, Xia G Q 2023 Opt. Laser Technol. 161 109200 Google Scholar
[11]	Jin J Y, Jiang N, Zhang Y Q, Feng W Z, Zhao A K, Liu S Q, Peng J F, Qiu K, Zhang Q W 2022 Opt. Express 30 13647 Google Scholar
[12]	Wang Q P, Xia G Q, Tan S L, Liu Y, Liu Y T, Zhao M R, Wu Z M 2022 Appl. Opt. 61 10086 Google Scholar
[13]	Zhou C D, Huang Y, Yang Y G, Cai D Y, Zhou P, Lau K, Li N Q, Li X F 2024 Opto-Electron Adv. 8 240135
[14]	Robertson J, Wade E, Kopp Y, Bueno J, Hurtado A 2019 IEEE J. Sel. Top. Quant. 26 1
[15]	Xiang S Y, Wen A J, Pan W 2016 IEEE Photonics J. 8 1
[16]	Fan X Q, Mao X X, Wang L S, Fu S N, Wang A B, Wang Y C 2024 Opt. Lett. 49 4445 Google Scholar
[17]	Xiang S Y, Song Z W, Gao S, Han Y N, Zhang Y H, Guo X X, Hao Y 2021 Acta Photonica Sin. 50 1020001 Google Scholar
[18]	Xiang S Y, Ren Z X, Song Z W, Zhang Y H, Guo X X, Han G Q, Hao Y 2021 IEEE T. Neur. Net. Lear. 32 2494
[19]	Xiang S Y, Wang B, Wang Y, Han Y N, Wen A J, Hao Y 2019 J. Lightwave Technol. JLT 37 3987 Google Scholar
[20]	Zhang S Y, Tang X, Xia G Q, Wu Z M 2020 Semiconductor Lasers and Applications X 11545 70
[21]	Huang Y, Zhou P, Lau K Y, Li N Q 2024 ACS Photonics 11 5012 Google Scholar
[22]	Kinzel W, Kanter I 2007 Handbook of Chaos Control pp301–324
[23]	Li A R, Jiang N, Geng Y, Zhang Q, Xiao Y L, Zhang Y Q, Xu B, Qiu K 2024 J. Lightw. Technol. 42 8730 Google Scholar
[24]	Zhang W L, Pan W, Luo B, Li X F, Zou X H, Wang M Y 2007 Chin. Phys. 16 1996 Google Scholar
[25]	Wang Z R, Li P, Jia Z W, Wang W J, Xu B J, Shore K A, Wang Y C 2021 Opt. Express 29 17940 Google Scholar
[26]	Li N Q, Pan W, Yan L S, Luo B, Zou X H 2014 Commun. Nonlinear Sci. 19 1874 Google Scholar
[27]	Saldutti M, Yu Y, Mørk J 2024 Laser Photonics Rev. 18 2300840 Google Scholar
[28]	Fan Y L, Shi T, Zhang J, Shore K A 2024 Opt. Express 32 19361 Google Scholar
[29]	Fan Y L, Shore K A, Shao X P 2023 Photonics 10 1249 Google Scholar
[30]	Rontani D, Locquet A, Sciamanna M, Citrin D S 2010 Opt. Lett. 35 2016 Google Scholar
[31]	Flunkert V, Schöll E 2012 New J. Phys. 14 033039 Google Scholar
[32]	El-Azab J, El-Khodary A, Hassab-Elnaby S 2013 High Capacity Optical Networks and Emerging/Enabling Technologies, Magosa, Cyprus, 2013, pp199–203
[33]	Liu H J, Feng J C 2011 J. Electron. (China) 28 126 Google Scholar
[34]	赵跃鹏, 张明, 江安义, 王云才 2008 光学学报 28 1236 Zhao Y P, Zhang M, Jiang A Y, Wang Y C 2008 Acta Opt. Sin. 28 1236
[35]	Jiang N, Zhao A K, Xue C P, et al. 2019 Opt. Lett. 44 1536 Google Scholar
[36]	Zhao Q C, Yin H X 2013 Opt. Laser Technol. 47 208 Google Scholar
[37]	穆鹏华, 潘炜, 李念强, 闫连山, 罗斌, 邹喜华, 徐明峰 2015 物理学报 64 124206 Google Scholar Mu P H, Pan W, Li N Q, Yan L S, Lou B, Zou X H, Xu M F 2015 Acta Phys Sin. 64 124206 Google Scholar
[38]	Zhang X T, Guo G, Liu X T, Hu G S, Wang K, Mu P H 2023 Photonics 10 1196 Google Scholar
[39]	Wu S F, Buckley S, Schaibley J R, Feng L F, Yan J Q, Mandrus D G, Hatami F, Yao W, Vučković J, Majumdar A, Xu X D 2015 Nature 520 69 Google Scholar
[40]	Qu Y, Xiang S Y, Wang Y, Lin L, Wen A J, Hao Y 2019 IEEE J. Quant. 55 1
[41]	Jiang P, Zhou P, Li N Q, et al. 2020 Opt. Express 28 26421 Google Scholar
[42]	Li N Q, Pan W, Yan L S, Luo B, Xu M F, Tang Y L, Jiang N, Xiang S Y, Zhang Q 2012 J. Opt. Soc. Am. B 29 101 Google Scholar
[43]	Sattar Z A, Shore K A 2015 IEEE J. Sel. Topi. Quant. 21 500 Google Scholar
[44]	Sattar Z A, Shore K A 2016 IEEE J. Quant. 52 1
[45]	蒋培, 周沛, 李念强, 穆鹏华, 李孝峰 2021 物理学报 70 114201 Google Scholar Jiang P, Zhou P, Li N Q, Mu P H, Li X F 2021 Acta Phys. Sin. 70 114201 Google Scholar

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图 1 基于纳米激光器的双路激光混沌复用系统结构图

Figure 1. Structure diagram of the dual-laser chaotic multiplexing system based on nanolasers.

DownLoad: Full-Size Img PowerPoint

图 2 M1/S1和M2/S2的混沌时间序列　(a) M1; (b) M2; (c) S1; (d) S2

Figure 2. The time series of M1/S1 and M2/S2: (a) M1; (b) M2; (c) S1; (d) S2.

DownLoad: Full-Size Img PowerPoint

图 3 (a) M1/S1和(b) M2/S2的互相关函数图

Figure 3. Cross-correlation function plots of (a) M1/S1 and (b) M2/S2.

DownLoad: Full-Size Img PowerPoint

图 4 M1/M2的同步图

Figure 4. Synchronization diagram of M1/M2.

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图 5 $F$和$\beta $不同时, NLs之间的CCF图　(a) M1/M2; (b) M1/S1; (c) M2/S2

Figure 5. CCF plots between NLs under different values of $F$ and $\beta $: (a) M1/M2; (b) M1/S1; (c) M2/S2.

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图 6 不同$I$值对M1/M2, M1/S1和M2/S2同步影响图　(a) M1/M2; (b) M1/S1; (c) M2/S2

Figure 6. Effect of different I values on the synchronization of M1/M2, M1/S1, and M2/S2: (a) M1/M2; (b) M1/S1; (c) M2/S2.

DownLoad: Full-Size Img PowerPoint

图 7 反馈强度和频率失谐对(a) M1/M2, (b) M1/S1和(c) M2/S2同步性影响的二维彩图

Figure 7. The two-dimensional colormap of feedback intensity and frequency detuning on the synchronization of (a) M1/M2, (b) M1/S1, and (c) M2/S2.

DownLoad: Full-Size Img PowerPoint

图 8 单个参数失配对(a) M1/M2, (b) M1/S1和(c) M2/S2同步影响图

Figure 8. Effect of single parameter mismatch on the synchronization of (a) M1/M2, (b) M1/S1, and (c) M2/S2.

DownLoad: Full-Size Img PowerPoint

图 9 参数失配对(a) M1/M2, (b) M1/S1和(c) M2/S2同步影响的二维图

Figure 9. The two-dimensional colormap of the effects of parameter mismatch on the synchronization of (a) M1/M2, (b) M1/S1, and (c) M2/S2.

DownLoad: Full-Size Img PowerPoint

表 1 仿真中使用的参数^[41]

Table 1. Parameters used in the simulation^[41].

参数	符号	参考值
约束因子	$\varGamma $	0.645
载流子寿命/ns	${\tau _{\text{n}}}$	1
光子寿命/ps	${\tau _{\text{p}}}$	0.36
反馈延迟/ns	${\tau _{\text{d}}}$	0.2
差分增益/(cm³·s^–1)	${g_n}$	1.64 × 10^–6
透明载流子密度/cm^–3	${N_0}$	1.1 × 10^–18
增益饱和因子/cm³	$\varepsilon $	2.3 × 10^–17
线宽增强因子	$\alpha $	5
活性区体积/cm³	${V_{\text{α }}}$	3.96 × 10^–13
纳米激光器的波长/nm	${\lambda _0}$	1591
激光面反射率	$R$	0.85
注入比	${R_{{\text{inj}}}}$	0—0.1
外镜的功率反射率	${R_{{\text{ext}}}}$	0.95
折射率	$n$	3.4
空腔长度/μm	$L$	1.39
反馈耦合分数	$f$	0—0.9

DownLoad: CSV

[1]	Jiang N, Zhao A K, Liu S Q, Xue C P, Qiu K 2018 Opt. Express 26 32404 Google Scholar
[2]	Tang Y W, Li Q L, Dong W L, Hu M, Zeng R 2021 Opt. Commun. 498 127232 Google Scholar
[3]	Wang L S, Du X Y, Mao X X, Guo Y Y, Wang A B, Wang Y C 2024 Opt. Lett. 49 5901 Google Scholar
[4]	Wang Y M, Huang Y, Zhou P, Li N Q 2023 Electronics 12 509 Google Scholar
[5]	Wang L S, Guo Y Y, Wang D M, Wang Y C, Wang A B 2019 Opt. Commun. 453 124350 Google Scholar
[6]	Rontani D, Choi D, Chang C Y, Locquet A, Citrin D S 2016 Sci. Rep. 6 35206 Google Scholar
[7]	Lin F Y, Liu J M 2004 IEEE J. Sel. Top. Quant. 10 991 Google Scholar
[8]	Cai D Y, Mu P H, Huang Y, Zhou P, Li N Q 2024 Chaos Soliton. Fract. 189 115652 Google Scholar
[9]	Li X Y, Jiang N, Zhang Q, Tang C J, Zhang Y Q, Hu G, Cao Y S, Qiu K 2023 Opt. Express 31 28764 Google Scholar
[10]	Liu Y, Wu Z M, Tan S L, Xia G Q 2023 Opt. Laser Technol. 161 109200 Google Scholar
[11]	Jin J Y, Jiang N, Zhang Y Q, Feng W Z, Zhao A K, Liu S Q, Peng J F, Qiu K, Zhang Q W 2022 Opt. Express 30 13647 Google Scholar
[12]	Wang Q P, Xia G Q, Tan S L, Liu Y, Liu Y T, Zhao M R, Wu Z M 2022 Appl. Opt. 61 10086 Google Scholar
[13]	Zhou C D, Huang Y, Yang Y G, Cai D Y, Zhou P, Lau K, Li N Q, Li X F 2024 Opto-Electron Adv. 8 240135
[14]	Robertson J, Wade E, Kopp Y, Bueno J, Hurtado A 2019 IEEE J. Sel. Top. Quant. 26 1
[15]	Xiang S Y, Wen A J, Pan W 2016 IEEE Photonics J. 8 1
[16]	Fan X Q, Mao X X, Wang L S, Fu S N, Wang A B, Wang Y C 2024 Opt. Lett. 49 4445 Google Scholar
[17]	Xiang S Y, Song Z W, Gao S, Han Y N, Zhang Y H, Guo X X, Hao Y 2021 Acta Photonica Sin. 50 1020001 Google Scholar
[18]	Xiang S Y, Ren Z X, Song Z W, Zhang Y H, Guo X X, Han G Q, Hao Y 2021 IEEE T. Neur. Net. Lear. 32 2494
[19]	Xiang S Y, Wang B, Wang Y, Han Y N, Wen A J, Hao Y 2019 J. Lightwave Technol. JLT 37 3987 Google Scholar
[20]	Zhang S Y, Tang X, Xia G Q, Wu Z M 2020 Semiconductor Lasers and Applications X 11545 70
[21]	Huang Y, Zhou P, Lau K Y, Li N Q 2024 ACS Photonics 11 5012 Google Scholar
[22]	Kinzel W, Kanter I 2007 Handbook of Chaos Control pp301–324
[23]	Li A R, Jiang N, Geng Y, Zhang Q, Xiao Y L, Zhang Y Q, Xu B, Qiu K 2024 J. Lightw. Technol. 42 8730 Google Scholar
[24]	Zhang W L, Pan W, Luo B, Li X F, Zou X H, Wang M Y 2007 Chin. Phys. 16 1996 Google Scholar
[25]	Wang Z R, Li P, Jia Z W, Wang W J, Xu B J, Shore K A, Wang Y C 2021 Opt. Express 29 17940 Google Scholar
[26]	Li N Q, Pan W, Yan L S, Luo B, Zou X H 2014 Commun. Nonlinear Sci. 19 1874 Google Scholar
[27]	Saldutti M, Yu Y, Mørk J 2024 Laser Photonics Rev. 18 2300840 Google Scholar
[28]	Fan Y L, Shi T, Zhang J, Shore K A 2024 Opt. Express 32 19361 Google Scholar
[29]	Fan Y L, Shore K A, Shao X P 2023 Photonics 10 1249 Google Scholar
[30]	Rontani D, Locquet A, Sciamanna M, Citrin D S 2010 Opt. Lett. 35 2016 Google Scholar
[31]	Flunkert V, Schöll E 2012 New J. Phys. 14 033039 Google Scholar
[32]	El-Azab J, El-Khodary A, Hassab-Elnaby S 2013 High Capacity Optical Networks and Emerging/Enabling Technologies, Magosa, Cyprus, 2013, pp199–203
[33]	Liu H J, Feng J C 2011 J. Electron. (China) 28 126 Google Scholar
[34]	赵跃鹏, 张明, 江安义, 王云才 2008 光学学报 28 1236 Zhao Y P, Zhang M, Jiang A Y, Wang Y C 2008 Acta Opt. Sin. 28 1236
[35]	Jiang N, Zhao A K, Xue C P, et al. 2019 Opt. Lett. 44 1536 Google Scholar
[36]	Zhao Q C, Yin H X 2013 Opt. Laser Technol. 47 208 Google Scholar
[37]	穆鹏华, 潘炜, 李念强, 闫连山, 罗斌, 邹喜华, 徐明峰 2015 物理学报 64 124206 Google Scholar Mu P H, Pan W, Li N Q, Yan L S, Lou B, Zou X H, Xu M F 2015 Acta Phys Sin. 64 124206 Google Scholar
[38]	Zhang X T, Guo G, Liu X T, Hu G S, Wang K, Mu P H 2023 Photonics 10 1196 Google Scholar
[39]	Wu S F, Buckley S, Schaibley J R, Feng L F, Yan J Q, Mandrus D G, Hatami F, Yao W, Vučković J, Majumdar A, Xu X D 2015 Nature 520 69 Google Scholar
[40]	Qu Y, Xiang S Y, Wang Y, Lin L, Wen A J, Hao Y 2019 IEEE J. Quant. 55 1
[41]	Jiang P, Zhou P, Li N Q, et al. 2020 Opt. Express 28 26421 Google Scholar
[42]	Li N Q, Pan W, Yan L S, Luo B, Xu M F, Tang Y L, Jiang N, Xiang S Y, Zhang Q 2012 J. Opt. Soc. Am. B 29 101 Google Scholar
[43]	Sattar Z A, Shore K A 2015 IEEE J. Sel. Topi. Quant. 21 500 Google Scholar
[44]	Sattar Z A, Shore K A 2016 IEEE J. Quant. 52 1
[45]	蒋培, 周沛, 李念强, 穆鹏华, 李孝峰 2021 物理学报 70 114201 Google Scholar Jiang P, Zhou P, Li N Q, Mu P H, Li X F 2021 Acta Phys. Sin. 70 114201 Google Scholar

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