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In this paper, a randomness-enhanced chaotic system model of mutually coupled vertical-cavity surface-emitting lasers (VCSELs) is established by adding anothor injected VCSEL with variable polarizer optical feedback (VPOF). The randomness of chaotic signals is evaluated quantitatively by an information-theory-based quantifier, the permutation entropy (PE). The influences of VPOF-VCSEL rotating polarizer degree, feedback strength, injection strength, mutual coupling strength, path time delay and frequency detuning about injected VCSEL and coupled VCSELs on chaotic signal permutation entropy are numerically studied. It is shown that the chaotic signal permutation entropy of mutually coupled VCSEL system driven by the third VCSEL is much higher than the mutual system with no-driving VCSEL. That is to say, the randomness of coupled system chaotic signal can be enhanced by optical injection. When the rotating polarizer degree is approximately 45 degrees and the injection strength is saturated at a constant level, the system PE can be increased by coupled strength, which is set to be higher than feedback strength. In addition, unequal delay time between both coupled time and feedback time, and higher detuning frequency between driving VCSEL and coupled VCSELs can contribute to randomness-enhanced chaotic signals.
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Keywords:
- vertical-cavity surface-emitting laser /
- a driven mutually coupled /
- permutation entropy /
- variable-polarization optical feedback
[1] Vicente R, Mirasso R, Fischer I 2007 Opt. Lett. 32 403
[2] Zhao Q C, Wang Y C 2010 Lasers Optoelectron. Prog. 47 030602 (in Chinese) [赵清春, 王云才 2010 激光与光电子学进展 47 030602]
[3] Sukow D W, Gavrielides A, Erneux T, Mooneyham B, Lee K 2010 Phys. Rev. A 81 025206
[4] Yan S L 2011 Acta Phys. Sin. 60 050509 (in Chinese) [颜森林 2011 60 050509]
[5] Zhang J, Yu J L, Cheng S Y, Lai Y F, Chen Y H 2014 Chin. Phys. B 23 027304
[6] Someya H, Oowada I, Okumura H, Kida T, Uchida A 2009 Opt. Express 17 19536
[7] Oliver N, Soriano M C, Sukow D W, Fischer I 2011 Opt. Lett. 36 4632
[8] Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 110509 (in Chinese) [唐曦, 吴加贵, 夏光琼, 吴正茂 2011 60 110509]
[9] Tlidi M, Averlant E, Vladimirov A, Panajotov K 2012 Phys. Rev. A 86 033822
[10] Zhang W L 2008 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [张伟利 2008 博士学位论文(成都: 西南交通大学)]
[11] Wu J, Cui H Y, Huang M, Ma M L 2013 Chin. Phys. B 22 124203
[12] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 4102
[13] Bandt C, Keller G, Pompe B 2002 Nonlinearity 15 1595
[14] Zunino L, Pérez D G, Martín M T, Garavaglia M, Plastino A, Rosso O A 2008 Phys. Lett. A 372 4768
[15] Tiana-Alsina J, Torrent M C, Rosso O A, Masoller C, Garcia-Ojalvo J 2010 Phys. Rev. A 82 013819
[16] Soriano M C, Zunino L, Rosso O A, Fischer I, Mirasso C R 2011 IEEE J. Quantum Electron. 47 252
[17] Xiang S Y, Pan W, Li N Q, Yan L S, Zhang L 2013 IEEE J. Quantum Electron. 49 274
[18] Cao T, Xu C, Xie Y Y, Kan Q, Wei S M, Mao M M, Chen H D 2013 Chin. Phys. B 22 024205
[19] Zheng A J, Wu Z M, Deng T, Li X J, Xia G Q 2012 Acta Phys. Sin. 61 234203 (in Chinese) [郑安杰, 吴正茂, 邓涛, 李小坚, 夏光琼 2012 61 234203]
[20] Wang X F, Li J 2013 Acta Phys. Sin. 62 014203 (in Chinese) [王小发, 李骏 2013 62 014203]
[21] Miguel M S, Feng Q, Moloney J V 1995 Phys. Rev. A 52 1728
[22] Jiang N, Pan W, Yan L S, Luo B, Zhang W L 2010 IEEE/OSA J. Lightw. Technol. 28 1978
[23] Martin-Regalado J, Prati F, Miguel M S, Abraham N B 1997 IEEE J. Quantum Electron. 33 765
[24] Sciamanna M, Gatare I, Locquet A, Panajotov K 2007 Phys. Rev. E 75 056213
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[1] Vicente R, Mirasso R, Fischer I 2007 Opt. Lett. 32 403
[2] Zhao Q C, Wang Y C 2010 Lasers Optoelectron. Prog. 47 030602 (in Chinese) [赵清春, 王云才 2010 激光与光电子学进展 47 030602]
[3] Sukow D W, Gavrielides A, Erneux T, Mooneyham B, Lee K 2010 Phys. Rev. A 81 025206
[4] Yan S L 2011 Acta Phys. Sin. 60 050509 (in Chinese) [颜森林 2011 60 050509]
[5] Zhang J, Yu J L, Cheng S Y, Lai Y F, Chen Y H 2014 Chin. Phys. B 23 027304
[6] Someya H, Oowada I, Okumura H, Kida T, Uchida A 2009 Opt. Express 17 19536
[7] Oliver N, Soriano M C, Sukow D W, Fischer I 2011 Opt. Lett. 36 4632
[8] Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 110509 (in Chinese) [唐曦, 吴加贵, 夏光琼, 吴正茂 2011 60 110509]
[9] Tlidi M, Averlant E, Vladimirov A, Panajotov K 2012 Phys. Rev. A 86 033822
[10] Zhang W L 2008 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [张伟利 2008 博士学位论文(成都: 西南交通大学)]
[11] Wu J, Cui H Y, Huang M, Ma M L 2013 Chin. Phys. B 22 124203
[12] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 4102
[13] Bandt C, Keller G, Pompe B 2002 Nonlinearity 15 1595
[14] Zunino L, Pérez D G, Martín M T, Garavaglia M, Plastino A, Rosso O A 2008 Phys. Lett. A 372 4768
[15] Tiana-Alsina J, Torrent M C, Rosso O A, Masoller C, Garcia-Ojalvo J 2010 Phys. Rev. A 82 013819
[16] Soriano M C, Zunino L, Rosso O A, Fischer I, Mirasso C R 2011 IEEE J. Quantum Electron. 47 252
[17] Xiang S Y, Pan W, Li N Q, Yan L S, Zhang L 2013 IEEE J. Quantum Electron. 49 274
[18] Cao T, Xu C, Xie Y Y, Kan Q, Wei S M, Mao M M, Chen H D 2013 Chin. Phys. B 22 024205
[19] Zheng A J, Wu Z M, Deng T, Li X J, Xia G Q 2012 Acta Phys. Sin. 61 234203 (in Chinese) [郑安杰, 吴正茂, 邓涛, 李小坚, 夏光琼 2012 61 234203]
[20] Wang X F, Li J 2013 Acta Phys. Sin. 62 014203 (in Chinese) [王小发, 李骏 2013 62 014203]
[21] Miguel M S, Feng Q, Moloney J V 1995 Phys. Rev. A 52 1728
[22] Jiang N, Pan W, Yan L S, Luo B, Zhang W L 2010 IEEE/OSA J. Lightw. Technol. 28 1978
[23] Martin-Regalado J, Prati F, Miguel M S, Abraham N B 1997 IEEE J. Quantum Electron. 33 765
[24] Sciamanna M, Gatare I, Locquet A, Panajotov K 2007 Phys. Rev. E 75 056213
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