Influence of the linewidth enhancement factor on the characteristics of the random number extracted from the optical feedback semiconductor laser

Han Tao; Liu Xiang-Lian; Li Pu; Guo Xiao-Min; Guo Yan-Qiang; Wang Yun-Cai

doi:10.7498/aps.66.124203

Abstract

Random numbers play an important role in many fields, including information security, testing and engineering practice. Especially in information security, generation of secure and reliable random numbers, they have a significant influence on national security, financial stability, trade secrets and personal privacy. Generally, random number generators can be classified as two main types: pseudo random number generators and physical random number generators. Pseudo random numbers with high speed are generated by software algorithms, but the inherent periodicity will cause serious hidden dangers when they are used in information security. Random numbers based on physical entropy sources (such as electronic thermal noise, frequency jitter of oscillator, quantum randomness) can produce reliable random numbers. However, due to the limitation of traditional physical source bandwidth, their generation speeds are at a level of Mbit/s typically, which cannot meet the needs of the current high-speed and largecapacity communication. In 2008, Uchida et al. (2008 Nat. Photon. 2 728) realized the physical random number of 1.7 Gbit/s by using a wideband chaotic laser for the first time. The emergence of wideband physical entropy sources such as chaotic laser greatly promote the rapid development of the physical random number generators. As far as we know, a semiconductor laser can generate wideband chaotic signals under external disturbances such as optical feedback, optical injection or photoelectric feedback. However, compared with the structures of other two lasers, the structure of the optical feedback semiconductor laser is simple and easy to integrate. Therefore, chaotic signals have received great attention to produce high-speed physical random number extracted from the optical feedback semiconductor laser. In the reported schemes, a variety of post-processing methods are used to improve the speed and randomness of random numbers. Besides, optimizing the chaotic entropy source can also improve the performance of random number. So far, the influence of internal parameters on the dynamic characteristics of semiconductor lasers has attracted wide attention. The linewidth enhancement factor is one of the key parameters for a semiconductor laser. The values of linewidth enhancement factor are different, depending on the type of semiconductor laser. The existence of linewidth enhancement factor results in a large number of unstable dynamic characteristics of semiconductor lasers. Therefore, it is of great significance for studying the influence of the linewidth enhancement factor on performance of random numbers. In this paper, we focus on the influence of the linewidth enhancement factor on the randomness of the obtained random numbers. The time delay characteristics and complexity are two important parameters to measure the quality of chaotic signals. The simulation results show that with the increase of the linewidth enhancement factor, the time delay characteristic peak of the chaotic signal from an optical feedback semiconductor laser decreases gradually, meanwhile, the maximum Lyapunov exponent of chaotic signal increases gradually. The randomness of random numbers, generated by the chaotic signal from the optical feedback semiconductor laser under different linewidth enhancement factors, is tested by NIST SP 800-22. The test results show that semiconductor laser with larger linewidth enhancement factor is chosen as a physical entropy source to generate random numbers with high quality.

Keywords:

Authors and contacts

1.
Key Laboratory of Advanced Transducers and Intelligent Control System of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China;
2.
Institute of Optoelectronic Engineering, College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China

Corresponding author: Liu Xiang-Lian, liuxianglian@tyut.edu.cn

Funds: Project supported by the Natural Science Foundation of Shanxi Province, China (Grant No. 201601D021021), the National Natural Science Foundation of China (Grant Nos. 61671316, 61505137, 61405138, 61505136), the Special Fund For Basic Research on Scientific Instruments of the National Natural Science Foundation of China (Grant No. 61227016), the Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (Grant No. 2014DFA50870), and the Qualified Personnel Foundation of Taiyuan University of Technology (Grant No. tyutrc201387a).

References

[1]	Li P 2014 Ph. D. Dissertation (Taiyuan: Taiyuan University of Technology) (in Chinese) [李璞 2014 博士学位论文(太原: 太原理工大学)]
[2]	Xu P, Wong Y L, Hoduchi T K, Abshire P A 2006 Electron. Lett. 42 1346
[3]	Petrie C S, Connelly J A 2000 IEEE Trans. Circuits I 47 615
[4]	Bucci M, Germani L, Luzzi R, Trifiletti A, Varanonuovo M 2003 IEEE Trans. Comput. 52 403
[5]	Schmidt H 1970 J. Appl. Phys. 41 462
[6]	Stipčević M, Rogina B M 2007 Rev. Sci. Instrum. 78 045104
[7]	Martino A J, Morris G M 1991 Appl. Opt. 30 981
[8]	Jennewein T, Achleitner U, Weihs G, Weinfurter H, Zeilinger A 2000 Rev. Sci. Instrum. 71 1675
[9]	Guo H, Liu Y, Dang A H, Wei W 2009 Chin. Sci. Bull. 54 3651 (in Chinese) [郭弘, 刘钰, 党安红, 韦韦 2009 科学通报 54 3651]
[10]	Ren M, Wu E, Liang Y, Jian Y, Wu G, Zeng H 2011 Phys. Rev. A 83 023820
[11]	Zhou Q, Hu Y, Liao X F 2008 Acta Phys. Sin. 57 5413 (in Chinese) [周庆, 胡月, 廖晓峰 2008 物理学报 57 5413]
[12]	Zhang M J, Liu T G, Wang A B, Zheng J Y, Meng L N, Zhang Z X, Wang Y C 2011 Opt. Lett. 36 1008
[13]	Zhao Q C, Yin H X 2013 Laser Optoelectron. Prog. 50 030003 (in Chinese) [赵清春, 殷洪玺 2013 激光与光电子学进展 50 030003]
[14]	Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimiri S, Yoshimura K, Davis P 2008 Nat. Photon. 2 728
[15]	Reidler I, Aviad Y, Rosenbluh M, Kanter I 2009 Phys. Rev. Lett. 103 024102
[16]	Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58
[17]	Li X, Chan S 2012 Opt. Lett. 37 2163
[18]	Li X, Chan S 2013 IEEE J. Quantum Electron. 49 829
[19]	Argyris A, Deligiannidis S, Pikasis E, Bogris A, Syvridis D 2010 Opt. Express 18 18763
[20]	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 物理学报 60 110509]
[21]	Wu J G, Tang X, Wu Z M, Xia G Q, Feng G Y 2012 Laser Phys. 22 1476
[22]	Li N Q, Kim B, Chizhevsky V N, Locquet A, Bloch M, Citrin D S, Pan W 2014 Opt. Express 22 6634
[23]	Wang A, Li P, Zhang J, Zhang J, Zhang J, Li L, Wang Y 2013 Opt. Express 21 20452
[24]	Yang H B, Wu Z M, Tang X, Wu J G, Xia G Q 2015 Acta Phys. Sin. 64 084204 (in Chinese) [杨海波, 吴正茂, 唐曦, 吴加贵, 夏光琼 2015 物理学报 64 084204]
[25]	Hirano K, Amano K, Uchida A, Naito S, Inoue M, Yoshimiri S, Yoshinura K, Davis P 2009 IEEE J. Quantum Electron. 45 1367
[26]	Zhang J B, Zhang J Z, Yang Y B, Liang J S, Wang Y C 2010 Acta Phys. Sin. 59 7679 (in Chinese) [张继兵, 张建忠, 杨毅彪, 梁君生, 王云才 2010 物理学报 59 7679]
[27]	Xiao B J, Hou J Y, Zhang J Z, Xue L G, Wang Y C 2012 Acta Phys. Sin. 61 150502 (in Chinese) [萧宝瑾, 侯佳音, 张建忠, 薛路刚, 王云才 2012 物理学报 61 150502]
[28]	Zhang J Z, Wang Y C, Xue L G, Hou J Y, Zhang B B, Wang A B, Zhang M J 2012 Appl. Opt. 51 1709
[29]	Hwang S K, Liu J M 2000 Opt. Commun. 183 195
[30]	Hwang S K, Liang D H 2006 Appl. Phys. Lett. 89 061120
[31]	Zhang M J, Liu T G, Li J X, Wang Y C 2011 Acta Phot. Sin. 40 542 (in Chinese) [张明江, 刘铁根, 李静霞, 王云才 2011 光子学报 40 542]
[32]	Wieczorek S, Chow W W 2005 Opt. Commun. 246 471
[33]	Wieczorek S, Krauskopf B, Simpson T B, Lenstra D 2005 Phys. Report 416 1
[34]	Pochet M, Naderi N A, Terry N, Kovanis V, Lester L F 2009 Opt. Express 17 20623
[35]	Liu G, Jin X, Chuang S L 2001 IEEE Photon. Technol. Lett. 13 430
[36]	Yang S Q, Zhang X H, Zhao C A 2000 Acta Phys. Sin. 49 636 (in Chinese) [杨绍清, 章新华, 赵长安 2000 物理学报 49 636]

Cited By

[1]	Li P 2014 Ph. D. Dissertation (Taiyuan: Taiyuan University of Technology) (in Chinese) [李璞 2014 博士学位论文(太原: 太原理工大学)]
[2]	Xu P, Wong Y L, Hoduchi T K, Abshire P A 2006 Electron. Lett. 42 1346
[3]	Petrie C S, Connelly J A 2000 IEEE Trans. Circuits I 47 615
[4]	Bucci M, Germani L, Luzzi R, Trifiletti A, Varanonuovo M 2003 IEEE Trans. Comput. 52 403
[5]	Schmidt H 1970 J. Appl. Phys. 41 462
[6]	Stipčević M, Rogina B M 2007 Rev. Sci. Instrum. 78 045104
[7]	Martino A J, Morris G M 1991 Appl. Opt. 30 981
[8]	Jennewein T, Achleitner U, Weihs G, Weinfurter H, Zeilinger A 2000 Rev. Sci. Instrum. 71 1675
[9]	Guo H, Liu Y, Dang A H, Wei W 2009 Chin. Sci. Bull. 54 3651 (in Chinese) [郭弘, 刘钰, 党安红, 韦韦 2009 科学通报 54 3651]
[10]	Ren M, Wu E, Liang Y, Jian Y, Wu G, Zeng H 2011 Phys. Rev. A 83 023820
[11]	Zhou Q, Hu Y, Liao X F 2008 Acta Phys. Sin. 57 5413 (in Chinese) [周庆, 胡月, 廖晓峰 2008 物理学报 57 5413]
[12]	Zhang M J, Liu T G, Wang A B, Zheng J Y, Meng L N, Zhang Z X, Wang Y C 2011 Opt. Lett. 36 1008
[13]	Zhao Q C, Yin H X 2013 Laser Optoelectron. Prog. 50 030003 (in Chinese) [赵清春, 殷洪玺 2013 激光与光电子学进展 50 030003]
[14]	Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimiri S, Yoshimura K, Davis P 2008 Nat. Photon. 2 728
[15]	Reidler I, Aviad Y, Rosenbluh M, Kanter I 2009 Phys. Rev. Lett. 103 024102
[16]	Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58
[17]	Li X, Chan S 2012 Opt. Lett. 37 2163
[18]	Li X, Chan S 2013 IEEE J. Quantum Electron. 49 829
[19]	Argyris A, Deligiannidis S, Pikasis E, Bogris A, Syvridis D 2010 Opt. Express 18 18763
[20]	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 物理学报 60 110509]
[21]	Wu J G, Tang X, Wu Z M, Xia G Q, Feng G Y 2012 Laser Phys. 22 1476
[22]	Li N Q, Kim B, Chizhevsky V N, Locquet A, Bloch M, Citrin D S, Pan W 2014 Opt. Express 22 6634
[23]	Wang A, Li P, Zhang J, Zhang J, Zhang J, Li L, Wang Y 2013 Opt. Express 21 20452
[24]	Yang H B, Wu Z M, Tang X, Wu J G, Xia G Q 2015 Acta Phys. Sin. 64 084204 (in Chinese) [杨海波, 吴正茂, 唐曦, 吴加贵, 夏光琼 2015 物理学报 64 084204]
[25]	Hirano K, Amano K, Uchida A, Naito S, Inoue M, Yoshimiri S, Yoshinura K, Davis P 2009 IEEE J. Quantum Electron. 45 1367
[26]	Zhang J B, Zhang J Z, Yang Y B, Liang J S, Wang Y C 2010 Acta Phys. Sin. 59 7679 (in Chinese) [张继兵, 张建忠, 杨毅彪, 梁君生, 王云才 2010 物理学报 59 7679]
[27]	Xiao B J, Hou J Y, Zhang J Z, Xue L G, Wang Y C 2012 Acta Phys. Sin. 61 150502 (in Chinese) [萧宝瑾, 侯佳音, 张建忠, 薛路刚, 王云才 2012 物理学报 61 150502]
[28]	Zhang J Z, Wang Y C, Xue L G, Hou J Y, Zhang B B, Wang A B, Zhang M J 2012 Appl. Opt. 51 1709
[29]	Hwang S K, Liu J M 2000 Opt. Commun. 183 195
[30]	Hwang S K, Liang D H 2006 Appl. Phys. Lett. 89 061120
[31]	Zhang M J, Liu T G, Li J X, Wang Y C 2011 Acta Phot. Sin. 40 542 (in Chinese) [张明江, 刘铁根, 李静霞, 王云才 2011 光子学报 40 542]
[32]	Wieczorek S, Chow W W 2005 Opt. Commun. 246 471
[33]	Wieczorek S, Krauskopf B, Simpson T B, Lenstra D 2005 Phys. Report 416 1
[34]	Pochet M, Naderi N A, Terry N, Kovanis V, Lester L F 2009 Opt. Express 17 20623
[35]	Liu G, Jin X, Chuang S L 2001 IEEE Photon. Technol. Lett. 13 430
[36]	Yang S Q, Zhang X H, Zhao C A 2000 Acta Phys. Sin. 49 636 (in Chinese) [杨绍清, 章新华, 赵长安 2000 物理学报 49 636]

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Vol. 66, Issue 12 - 2017-06-20

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