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本文将交叉反馈半导体环形激光器（SRL）产生的两路混沌信号平行单向注入到从激光器对应的模式中，构成了宽带混沌激光生成方案.通过建立速率方程，数值分析了失谐频率和注入强度对系统带宽及安全性影响.利用强度时间序列的频域变化规律揭示了带宽增强的物理原因，并且对增强区域不对称进行了解释.仿真结果表明：两路混沌信号的带宽增强路径相似.在非注入锁定区域，选择较高失谐频率以及适当的注入强度可以实现两路信号的带宽以及不可预测度同时增强.通过分析混沌信号的光谱可知注入混沌光与从激光器激光之间的拍频作用产生的高频振荡是导致带宽增强的物理原因.主激光器发生红移现象导致带宽增强区域呈现不对称，并且负失谐频率下容易实现带宽增强.非对称注入强度使得注入锁定区域缩小，拓宽了高注入强度下带宽增强范围.Recently semiconductor ring laser (SRL) as a novel device has received much attention, for its special cavity allows the output light to propagate in two opposite directions, namely the clockwise mode and counterclockwise mode. SRL does not require gratings or cleaved facets for optical feedback and can be a candidate for small sized photonic integrated circuits which have been developed for secure data transmission, with chaotic carriers and high rate random bit generated. In this paper, we propose a method to obtain two broadband chaotic signals with high unpredictability degree by utilizing injected slave SRL and further explore the physical mechanism and injection conditions. Based on a conventional master-slave configuration, the proposed method obtains two modes of chaotic signals by master SRL with external cross feedback, which are injected in parallel to a slave SRL correspondingly. According to the well-known Lang-Kobayashi rate equations, we establish rate equations and numerically investigate the influences of frequency detuning and injection strength on bandwidth and unpredictability degree. We adapt the given definition of bandwidth and the normalized permutation entropy to respectively evaluate bandwidth and unpredictability degree of chaotic signals. Furthermore, we reveal the underlying physical mechanism of bandwidth enhancement and asymmetric bandwidth-enhancing region by analyzing the radiofrequency and optical spectra of intensity time series. The results show that two chaotic signals have similar routes to enhancing the bandwidth in frequency domain. In the unlocking injection area, two broadband and unpredictability-enhancing chaotic signals generated by slave SRL are simultaneously achieved by choosing appropriate control parameters. Analyses of optical spectra reveal that high-frequency periodic oscillation generated between injection chaotic signals and slave light via beating is the physical mechanism of bandwidth enhncment. The bandwidthenhancing domains of two chaotic signals are asymmetrical due to redshift of master SRL frequency, with external chaotic signals injected. Bandwidth-enhanced chaotic signals are easier to obtain in the domain of negative frequency detuning. The asymmetrical injections contribute to reducing the locking region and extending the bandwidthenhancing region under high injection strength. This conventional master-slave configuration composed of two SRLs can be easily implemented on chip and save other optical devices. The slave SRL subjected to parallel injection signals from master SRL can be used as a wideband unpredictability-enhancing chaotic source, which is extremely useful for the high capacity security-enhancing multiple chaotic communications, as well as for the potential applications of high speed random number generators.
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Keywords:
- semiconductor ring laser /
- bandwidth-enhanced /
- chaos /
- asymmetrical injection
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[1] Ermakov I V, Kingni S T, Tronciu V Z, Danckaert J 2013 Opt. Commun. 286 265
[2] Li N Q, Pan W, Yan L S, Luo B, Zou X H 2014 Commun. Nonlinear Sci. Numer. Simul. 19 1874
[3] Li N Q, Pan W, Xiang S Y, Luo B, Yan L S, Zou X H 2013 Appl. Opt. 52 1523
[4] Sunada S, Harayama T, Arai K, Yoshimura K, Tsuzuki K, Uchida A, Davis P 2011 Opt. Express 19 7439
[5] Hirano K, Yamazaki T, Morikatsu S, Okumura H, Aida H, Uchida A, Yoshimori S, Yoshimura K, Harayama T, Davis P 2010 Opt. Express 18 5512
[6] Wang A B, Wang B J, Li L, Wang Y C, Shore K A 2015 IEEE J. Sel. Top. Quantum Electron. 21 1800710
[7] Sakuraba R, Iwakawa K, Kanno K, Uchida A 2015 Opt. Express 23 1470
[8] Murakami A, Kawashima K, Atsuki K 2003 IEEE J. Quantum Electron. 39 1196
[9] Wang A B, Wang Y C, He H 2008 IEEE Photonics. Technol. Lett. 20 1633
[10] Wang A B, Wang Y C, Wang J F 2009 Opt. Lett. 34 1144
[11] Hong Y H, Spencer P S, Shore K A 2012 Opt. Soc. Am. 29 415
[12] Chen J J, Wu Z M, Tang X, Deng T, Fan L, Zhong Z Q, Xia G Q 2015 Opt. Express 23 7173
[13] Uchida A, Heil T, Liu Y, Davis P, Aida T 2003 IEEE J. Quantum Electron. 39 1462
[14] Xiang S Y, Pan W, Luo B, Yan L S, Zou X H, Li N Q, Zhu H N 2012 IEEE J. Quantum Electron. 48 1069
[15] Memon M I, Li B, Mezosi G, Wang Z R, Sorel M, Yu S Y 2009 IEEE Photonics Technol. Lett. 21 1792
[16] Yuan G H, Zhang X, Wang Z R 2013 Optik 124 5715
[17] Xiang S Y, Wen A J, Shang L, Zhang H X, Lin L 2013 International Conference on Optical Communications & Networks Bhopal, India July 26-28, 2013 p1
[18] Li N Q, Pan W, Xiang S Y, Yan L S, Luo B, Zou X H, Zhang L Y 2013 Optics & Laser Technology 53 45
[19] Nguimdo R M, Verschaffelt G, Danckaert J, van der Sande G 2012 Opt. Lett. 37 2541
[20] Wang Z R, Yuan G H, Verschaffelt G, Danckaert J, Yu S Y 2008 IEEE Photonics Technol. Lett. 20 1228
[21] Trita A, Mezosi G, Sorel M, Giuliani G 2014 IEEE Photonics Technol. Lett. 26 96
[22] Wang S T, Wu Z M, Wu J G, Zhou L, Xia G Q 2015 Acta Phys. Sin. 64 154205 (in Chinese)[王顺天, 吴正茂, 吴加贵, 周立, 夏光琼2015物理学报64 154205]
[23] Chrostowski L, Shi W 2008 IEEE J. Lightwave Technol. 26 3355
[24] Sorel M, Giuliani G, Scire A, Miglierina R, Donati S, Laybourn P J R 2003 IEEE J. Quantum Electron. 39 1187
[25] Xiang S Y 2012 Ph. D. Dissertation (Chengdu:Southwest jiaotong university) (in Chinese)[项水英2012博士学位论文(成都:西南交通大学)]
[26] Liu Q X, Pan W, Zhang L Y, Li N Q, Yan J 2015 Acta Phys. Sin. 64 242091 (in Chinese)[刘庆喜, 潘炜, 张力月, 李念强, 阎娟2015物理学报64 242091]
[27] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[28] Zunino L, Rosso O A, Soriano M C 2011 IEEE J. Sel. Top. Quantum Electron. 17 1250
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