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Under proper feedback strength, an external-cavity feedback semiconductor laser can operate at a chaos state, and its chaotic output can be used as a physical entropy source to generate a physical random number sequence. In this paper, we focus on the influence of feedback strength on the randomness of the obtained binary code sequence. The simulation results show that with the increase of feedback strength, the time delay characteristic peak of the chaotic signal from an external-cavity feedback semiconductor laser first decreases and then increases gradually, meanwhile, the permutation entropy characteristic value of chaotic signal first increases and then decreases gradually, namely, there exists an optimized feedback strength for obtaining the chaotic signal with the weakest time delay signature and high complexity. The randomness of binary code sequences, generated by the chaotic signal from the external-cavity feedback semiconductor laser under different feedback strengths, is tested by NIST Special Publication 800-22, and the influence of feedback strength on the test results is also discussed.
[1] Gallager R G 2008 Principles of Digital Communication (New York: Cambridge University Press) pp199-244
[2] Metropolis N, Ulam S 1949 J. Am. Stat. Assoc. 44 335
[3] Asmussen S, Glynn P W 2007 Stochastic Simulation: Algorithms and Analysis (New York: Springer-Verlag) pp30-65
[4] Stinson D R 2005 Cryptography: Theory and Practice (Ontario: CRC Press) pp423-452
[5] Aaldert C 1991 J. Stat. Phys. 63 883
[6] Holman W T, Connelly J A, Dowlatabadi A B 1997 IEEE Trans. Circuits Syst. Regul. Pap. 44 521
[7] Fairfield R C, Mortenson R L, Coulthart K B 1985 An LSI Random Number Generator (RNG) (Berlin: Springer-Verlag) p203
[8] Kuusela T 1993 J. Nonlinear Sci. 3 445
[9] Qi B, Chi Y M, Lo H K, Qian L 2010 Opt. Lett. 35 312
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[14] Ren X L, Wu Z M, Fan L, Xia G Q 2014 Chin. Sci. Bull. 59 259 (in Chinese) [任小丽, 吴正茂, 樊利, 夏光琼 2014 科学通报 59 259]
[15] Xiang S Y, Pan W, Luo B, Yan L S, Zou X H, Li N Q, Zhang L Y 2012 Opt. Commun. 285 5293
[16] Yan S L 2010 Opt. Commun. 283 3305
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[18] Zhong D Z, Wu Z M 2009 Opt. Commun. 282 1631
[19] Xie Y Y, Wu Z M, Deng T, Tang X, Fan L, Xia G Q 2013 IEEE Photon. Technol. Lett. 25 1605
[20] Argyris A, Hamacher M, Chlouverakis K E, Bogris A, Syvridis D 2008 Phys. Rev. Lett. 100 194101
[21] Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimiri S, Davis P 2008 Nat. Photon. 2 728
[22] Reidler I, Aviad Y, Rosenbluh M, Kanter I 2009 Phys. Rev. Lett. 103 024102
[23] Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58
[24] Li P, Wang Y C, Zhang J Z 2010 Opt. Express 18 20360
[25] Wu J G, Tang X, Wu Z M, Xia G Q, Feng G Y 2012 Laser Phys. 22 1476
[26] Hirano K, Amano K, Uchida A, Naito S, Inoue M, Yoshimiri S, Yoshinura K, Davis P 2009 IEEE J. Quantum Electron. 45 1367
[27] 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 59 7679]
[28] 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 61 150502]
[29] 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
[30] Rukhin A, Rukhin J, Nechvatal J, Smid M, Barker E, Leigh S, Levenson M 2008 NIST Special Publication 800-22 (rev. 1) (Gaithersburg: National Institute of Standards and Technology)
[31] Lang R, Kobayashi K 1980 IEEE J. Quantum Electron. 16 347
[32] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[33] Zunino L, Rosso O A, Soriano M C 2011 IEEE J. Sel. Top. Quantum Electron. 17 1250
[34] Soriano M C, Zunino L, Rosso O A 2011 IEEE J. Lightwave Technol. 29 2173
[35] Mikami T, Kanno K, Aoyama K, Uchida A, Ikeguchi T, Harayama T, Sunada S, Arai K, Yoshimura K, Davis P 2012 Phys. Rev. Lett. 85 016211
[36] Rontani D, Locquet A, Sciamanna M, Citrin D S 2007 Opt. Lett. 32 2960
[37] Wu J G, Xia G Q, Tang X, Lin X D, Deng T, Fan L, Wu Z M 2010 Opt. Express 18 6661
[38] Argyris A, Pikasis E, Deligiannidis S, Syvridis D 2012 J. Lightwave Technol. 30 1329
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[1] Gallager R G 2008 Principles of Digital Communication (New York: Cambridge University Press) pp199-244
[2] Metropolis N, Ulam S 1949 J. Am. Stat. Assoc. 44 335
[3] Asmussen S, Glynn P W 2007 Stochastic Simulation: Algorithms and Analysis (New York: Springer-Verlag) pp30-65
[4] Stinson D R 2005 Cryptography: Theory and Practice (Ontario: CRC Press) pp423-452
[5] Aaldert C 1991 J. Stat. Phys. 63 883
[6] Holman W T, Connelly J A, Dowlatabadi A B 1997 IEEE Trans. Circuits Syst. Regul. Pap. 44 521
[7] Fairfield R C, Mortenson R L, Coulthart K B 1985 An LSI Random Number Generator (RNG) (Berlin: Springer-Verlag) p203
[8] Kuusela T 1993 J. Nonlinear Sci. 3 445
[9] Qi B, Chi Y M, Lo H K, Qian L 2010 Opt. Lett. 35 312
[10] 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]
[11] Ren M, Wu E, Liang Y, Jian Y, Wu G, Zeng H 2011 Phys. Rev. A 83 023820
[12] Zhou Q, Hu Y, Liao X F 2008 Acta Phys. Sin. 57 5413 (in Chinese) [周庆, 胡月, 廖晓峰 2008 57 5413]
[13] Wu J G, Wu Z M, Tang X, Lin X D, Deng T, Xia G Q, Feng G Y 2011 IEEE Photon. Technol. Lett. 23 759
[14] Ren X L, Wu Z M, Fan L, Xia G Q 2014 Chin. Sci. Bull. 59 259 (in Chinese) [任小丽, 吴正茂, 樊利, 夏光琼 2014 科学通报 59 259]
[15] Xiang S Y, Pan W, Luo B, Yan L S, Zou X H, Li N Q, Zhang L Y 2012 Opt. Commun. 285 5293
[16] Yan S L 2010 Opt. Commun. 283 3305
[17] Zhang M J, Liu T G, Li P, Wang A B, Zhang J Z, Wang Y C 2011 IEEE Photon. Technol. Lett. 23 1872
[18] Zhong D Z, Wu Z M 2009 Opt. Commun. 282 1631
[19] Xie Y Y, Wu Z M, Deng T, Tang X, Fan L, Xia G Q 2013 IEEE Photon. Technol. Lett. 25 1605
[20] Argyris A, Hamacher M, Chlouverakis K E, Bogris A, Syvridis D 2008 Phys. Rev. Lett. 100 194101
[21] Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimiri S, Davis P 2008 Nat. Photon. 2 728
[22] Reidler I, Aviad Y, Rosenbluh M, Kanter I 2009 Phys. Rev. Lett. 103 024102
[23] Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58
[24] Li P, Wang Y C, Zhang J Z 2010 Opt. Express 18 20360
[25] Wu J G, Tang X, Wu Z M, Xia G Q, Feng G Y 2012 Laser Phys. 22 1476
[26] Hirano K, Amano K, Uchida A, Naito S, Inoue M, Yoshimiri S, Yoshinura K, Davis P 2009 IEEE J. Quantum Electron. 45 1367
[27] 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 59 7679]
[28] 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 61 150502]
[29] 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
[30] Rukhin A, Rukhin J, Nechvatal J, Smid M, Barker E, Leigh S, Levenson M 2008 NIST Special Publication 800-22 (rev. 1) (Gaithersburg: National Institute of Standards and Technology)
[31] Lang R, Kobayashi K 1980 IEEE J. Quantum Electron. 16 347
[32] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[33] Zunino L, Rosso O A, Soriano M C 2011 IEEE J. Sel. Top. Quantum Electron. 17 1250
[34] Soriano M C, Zunino L, Rosso O A 2011 IEEE J. Lightwave Technol. 29 2173
[35] Mikami T, Kanno K, Aoyama K, Uchida A, Ikeguchi T, Harayama T, Sunada S, Arai K, Yoshimura K, Davis P 2012 Phys. Rev. Lett. 85 016211
[36] Rontani D, Locquet A, Sciamanna M, Citrin D S 2007 Opt. Lett. 32 2960
[37] Wu J G, Xia G Q, Tang X, Lin X D, Deng T, Fan L, Wu Z M 2010 Opt. Express 18 6661
[38] Argyris A, Pikasis E, Deligiannidis S, Syvridis D 2012 J. Lightwave Technol. 30 1329
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