Abstract

We propose and demonstrate experimentally the generation of chaos with suppressed time-delay signature (TDS) and physical random bits in two mutually coupled semiconductor lasers (MCSL) by introducing an auxiliary fiber Bragg grating (FBG) filtered injection path. The measurements show that, even by simply adding a single FBG path, the TDS of chaotic signals generated by both lasers in our proposed scheme can be better concealed compared to the conventional MCSL system. Moreover, better TDS concealment can be achieved in the laser with smaller wavelength. Additionally, two random bit streams extracted from the two chaotic lasers in the proposed scheme are achieved with minimal post-processing. The total generation rate reaches 640-Gbps.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
  3. J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
    [Crossref]
  4. C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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2018 (5)

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

2017 (9)

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7(4), 041050 (2017).
[Crossref]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[Crossref] [PubMed]

M. Naruse, Y. Terashima, A. Uchida, and S. J. Kim, “Ultrafast photonic reinforcement learning based on laser chaos,” Sci. Rep. 7(1), 8772 (2017).
[Crossref] [PubMed]

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photon. Res. 5(1), 6–10 (2017).
[Crossref]

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor lasers system,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

2016 (4)

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

A. Argyris, E. Pikasis, and D. Syvridis, “Gb/s one-time-pad data encryption with synchronized chaos-based true random bit generators,” J. Lightwave Technol. 34(22), 5325–5331 (2016).
[Crossref]

2015 (4)

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

S. S. Li and S. C. Chan, “Chaotic time-delay signature suppression in a semiconductor laser with frequency-detuned grating feedback,” IEEE J. Sel. Top. Quantum Electron. 21(6), 541–552 (2015).
[Crossref]

J. Song, Z. Q. Zhong, L. X. Wei, Z. M. Wu, and G. Q. Xia, “Experimental investigations on nonlinear dynamics of a semiconductor laser subject to optical injection and fiber Bragg grating feedback,” Opt. Commun. 354, 213–217 (2015).
[Crossref]

2014 (2)

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

H. Lin, Y. H. Hong, and K. A. Shore, “Experimental study of time-delay signatures in vertical-cavity surface-emitting lasers subject to double-cavity polarization-rotated optical feedback,” J. Lightwave Technol. 32(9), 1829–1836 (2014).
[Crossref]

2013 (2)

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

2012 (4)

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

J. G. Wu, X. Tang, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Parallel generation of 10 Gbits/s physical random number streams using chaotic semiconductor lasers,” Laser Phys. 22(10), 1476–1480 (2012).
[Crossref]

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photonics J. 4(5), 1930–1935 (2012).
[Crossref]

J. G. Wu, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express 20(2), 1741–1753 (2012).
[Crossref] [PubMed]

2011 (1)

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

2010 (4)

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[Crossref] [PubMed]

2009 (3)

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[Crossref] [PubMed]

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronization,” IET Optoelectron. 3(6), 326–330 (2009).
[Crossref]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

2008 (1)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

2007 (1)

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).
[Crossref] [PubMed]

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

2004 (1)

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40(6), 815–820 (2004).
[Crossref]

Akizawa, Y.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Alan Shore, K.

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Arai, K.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Argyris, A.

A. Argyris, E. Pikasis, and D. Syvridis, “Gb/s one-time-pad data encryption with synchronized chaos-based true random bit generators,” J. Lightwave Technol. 34(22), 5325–5331 (2016).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Chan, S. C.

S. S. Li and S. C. Chan, “Chaotic time-delay signature suppression in a semiconductor laser with frequency-detuned grating feedback,” IEEE J. Sel. Top. Quantum Electron. 21(6), 541–552 (2015).
[Crossref]

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photonics J. 4(5), 1930–1935 (2012).
[Crossref]

Chen, X.

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

Citrin, D. S.

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).
[Crossref] [PubMed]

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Davis, P.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Deng, T.

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

Fan, L.

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

Fan, Y. L.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

Feng, C.

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

Feng, G. Y.

J. G. Wu, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express 20(2), 1741–1753 (2012).
[Crossref] [PubMed]

J. G. Wu, X. Tang, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Parallel generation of 10 Gbits/s physical random number streams using chaotic semiconductor lasers,” Laser Phys. 22(10), 1476–1480 (2012).
[Crossref]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Gao, H.

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

García-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Gerhardt, I.

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7(4), 041050 (2017).
[Crossref]

Giessen, H.

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7(4), 041050 (2017).
[Crossref]

Greiner, J. N.

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7(4), 041050 (2017).
[Crossref]

Guo, X.

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Guo, X. M.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

Guo, X. X.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

Guo, Y.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Guo, Y. Q.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

Harayama, T.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Hong, Y. H.

H. Lin, Y. H. Hong, and K. A. Shore, “Experimental study of time-delay signatures in vertical-cavity surface-emitting lasers subject to double-cavity polarization-rotated optical feedback,” J. Lightwave Technol. 32(9), 1829–1836 (2014).
[Crossref]

Hou, Y. S.

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor lasers system,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Inubushi, M.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

Iwakawa, K.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

Ji, Y.

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

Jiang, N.

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Kanno, K.

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Kim, S. J.

M. Naruse, Y. Terashima, A. Uchida, and S. J. Kim, “Ultrafast photonic reinforcement learning based on laser chaos,” Sci. Rep. 7(1), 8772 (2017).
[Crossref] [PubMed]

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Li, G.

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

Li, J. F.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

Li, K. Y.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

Li, M.

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

Li, N.

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

Li, N. Q.

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Li, P.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[Crossref] [PubMed]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[Crossref] [PubMed]

Li, S. S.

S. S. Li and S. C. Chan, “Chaotic time-delay signature suppression in a semiconductor laser with frequency-detuned grating feedback,” IEEE J. Sel. Top. Quantum Electron. 21(6), 541–552 (2015).
[Crossref]

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photonics J. 4(5), 1930–1935 (2012).
[Crossref]

Li, Z.

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

Lin, F. Y.

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40(6), 815–820 (2004).
[Crossref]

Lin, H.

H. Lin, Y. H. Hong, and K. A. Shore, “Experimental study of time-delay signatures in vertical-cavity surface-emitting lasers subject to double-cavity polarization-rotated optical feedback,” J. Lightwave Technol. 32(9), 1829–1836 (2014).
[Crossref]

Lin, L.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

Lin, S.

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

Lin, X. D.

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

Liu, J.

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[Crossref] [PubMed]

Liu, J. M.

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40(6), 815–820 (2004).
[Crossref]

Liu, Q.

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photonics J. 4(5), 1930–1935 (2012).
[Crossref]

Liu, S.

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

Liu, X.

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Liu, X. L.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

Liu, X. Y.

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Liu, Y.

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

Liu, Y. R.

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

Locquet, A.

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).
[Crossref] [PubMed]

Luo, B.

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Lv, Y.

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Naruse, M.

M. Naruse, Y. Terashima, A. Uchida, and S. J. Kim, “Ultrafast photonic reinforcement learning based on laser chaos,” Sci. Rep. 7(1), 8772 (2017).
[Crossref] [PubMed]

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Pan, W.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Pikasis, E.

A. Argyris, E. Pikasis, and D. Syvridis, “Gb/s one-time-pad data encryption with synchronized chaos-based true random bit generators,” J. Lightwave Technol. 34(22), 5325–5331 (2016).
[Crossref]

Qiu, K.

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Rontani, D.

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).
[Crossref] [PubMed]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Sakuraba, R.

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

Sang, L.

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

Sciamanna, M.

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).
[Crossref] [PubMed]

Shahverdiev, E. M.

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronization,” IET Optoelectron. 3(6), 326–330 (2009).
[Crossref]

Shang, L.

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Shore, K. A.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

H. Lin, Y. H. Hong, and K. A. Shore, “Experimental study of time-delay signatures in vertical-cavity surface-emitting lasers subject to double-cavity polarization-rotated optical feedback,” J. Lightwave Technol. 32(9), 1829–1836 (2014).
[Crossref]

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronization,” IET Optoelectron. 3(6), 326–330 (2009).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Song, J.

J. Song, Z. Q. Zhong, L. X. Wei, Z. M. Wu, and G. Q. Xia, “Experimental investigations on nonlinear dynamics of a semiconductor laser subject to optical injection and fiber Bragg grating feedback,” Opt. Commun. 354, 213–217 (2015).
[Crossref]

Steinle, T.

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7(4), 041050 (2017).
[Crossref]

Sun, Y.

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Sunada, S.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Syvridis, D.

A. Argyris, E. Pikasis, and D. Syvridis, “Gb/s one-time-pad data encryption with synchronized chaos-based true random bit generators,” J. Lightwave Technol. 34(22), 5325–5331 (2016).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Tang, X.

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

J. G. Wu, X. Tang, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Parallel generation of 10 Gbits/s physical random number streams using chaotic semiconductor lasers,” Laser Phys. 22(10), 1476–1480 (2012).
[Crossref]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

Terashima, Y.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

M. Naruse, Y. Terashima, A. Uchida, and S. J. Kim, “Ultrafast photonic reinforcement learning based on laser chaos,” Sci. Rep. 7(1), 8772 (2017).
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Uchida, A.

M. Naruse, Y. Terashima, A. Uchida, and S. J. Kim, “Ultrafast photonic reinforcement learning based on laser chaos,” Sci. Rep. 7(1), 8772 (2017).
[Crossref] [PubMed]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Ugajin, K.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

Wang, A.

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[Crossref] [PubMed]

Wang, A. B.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Wang, B.

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

Wang, C.

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

Wang, D.

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

Wang, D. M.

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Wang, L.

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[Crossref] [PubMed]

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

Wang, L. S.

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Wang, Y.

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[Crossref] [PubMed]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Wang, Y. C.

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[Crossref] [PubMed]

Wei, L. X.

J. Song, Z. Q. Zhong, L. X. Wei, Z. M. Wu, and G. Q. Xia, “Experimental investigations on nonlinear dynamics of a semiconductor laser subject to optical injection and fiber Bragg grating feedback,” Opt. Commun. 354, 213–217 (2015).
[Crossref]

Wen, A. J.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Wrachtrup, J.

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7(4), 041050 (2017).
[Crossref]

Wu, C.

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

Wu, D. Y.

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Wu, J.

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Wu, J. G.

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

J. G. Wu, X. Tang, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Parallel generation of 10 Gbits/s physical random number streams using chaotic semiconductor lasers,” Laser Phys. 22(10), 1476–1480 (2012).
[Crossref]

J. G. Wu, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express 20(2), 1741–1753 (2012).
[Crossref] [PubMed]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

Wu, Y.

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

Wu, Z. M.

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photon. Res. 5(1), 6–10 (2017).
[Crossref]

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor lasers system,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

J. Song, Z. Q. Zhong, L. X. Wei, Z. M. Wu, and G. Q. Xia, “Experimental investigations on nonlinear dynamics of a semiconductor laser subject to optical injection and fiber Bragg grating feedback,” Opt. Commun. 354, 213–217 (2015).
[Crossref]

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

J. G. Wu, X. Tang, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Parallel generation of 10 Gbits/s physical random number streams using chaotic semiconductor lasers,” Laser Phys. 22(10), 1476–1480 (2012).
[Crossref]

J. G. Wu, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express 20(2), 1741–1753 (2012).
[Crossref] [PubMed]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[Crossref] [PubMed]

Xia, G. Q.

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photon. Res. 5(1), 6–10 (2017).
[Crossref]

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor lasers system,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

J. Song, Z. Q. Zhong, L. X. Wei, Z. M. Wu, and G. Q. Xia, “Experimental investigations on nonlinear dynamics of a semiconductor laser subject to optical injection and fiber Bragg grating feedback,” Opt. Commun. 354, 213–217 (2015).
[Crossref]

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

J. G. Wu, X. Tang, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Parallel generation of 10 Gbits/s physical random number streams using chaotic semiconductor lasers,” Laser Phys. 22(10), 1476–1480 (2012).
[Crossref]

J. G. Wu, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express 20(2), 1741–1753 (2012).
[Crossref] [PubMed]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[Crossref] [PubMed]

Xiang, S. Y.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Xue, C.

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

Yamazaki, T.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Yan, L. S.

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Yang, L.

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Yi, L. L.

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor lasers system,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

Yi, X.

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Yoshimura, K.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Zhang, H.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

Zhang, H. X.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Zhang, J.

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Zhang, J. Z.

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[Crossref] [PubMed]

Zhang, L. Y.

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

Zhang, M.

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

Zhang, W. L.

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Zhao, A.

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

Zhao, T.

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Zheng, D.

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

Zhong, Z. Q.

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photon. Res. 5(1), 6–10 (2017).
[Crossref]

J. Song, Z. Q. Zhong, L. X. Wei, Z. M. Wu, and G. Q. Xia, “Experimental investigations on nonlinear dynamics of a semiconductor laser subject to optical injection and fiber Bragg grating feedback,” Opt. Commun. 354, 213–217 (2015).
[Crossref]

Zhou, L.

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Appl. Opt. (1)

J. Zhang, M. Li, A. Wang, M. Zhang, Y. Ji, and Y. Wang, “Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection,” Appl. Opt. 57(22), 6314–6317 (2018).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40(6), 815–820 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

S. S. Li and S. C. Chan, “Chaotic time-delay signature suppression in a semiconductor laser with frequency-detuned grating feedback,” IEEE J. Sel. Top. Quantum Electron. 21(6), 541–552 (2015).
[Crossref]

IEEE Photonics J. (3)

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photonics J. 4(5), 1930–1935 (2012).
[Crossref]

L. S. Wang, T. Zhao, D. M. Wang, D. Y. Wu, L. Zhou, J. Wu, X. Y. Liu, Y. C. Wang, and A. B. Wang, “Real-time 14-Gbps physical random bit generator based on time-interleaved sampling of broadband white chaos,” IEEE Photonics J. 9(2), 1–13 (2017).
[Crossref]

Y. S. Hou, L. L. Yi, G. Q. Xia, and Z. M. Wu, “Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor lasers system,” IEEE Photonics J. 9(5), 1–10 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (3)

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photonics Technol. Lett. 23(12), 759–761 (2011).
[Crossref]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

S. Y. Xiang, W. Pan, A. J. Wen, N. Q. Li, L. Y. Zhang, L. Shang, and H. X. Zhang, “Conceal time delay signature of chaos in semiconductor lasers with dual-path injection,” IEEE Photonics Technol. Lett. 25(14), 1398–1401 (2013).
[Crossref]

IET Optoelectron. (1)

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronization,” IET Optoelectron. 3(6), 326–330 (2009).
[Crossref]

J. Lightwave Technol. (6)

H. Lin, Y. H. Hong, and K. A. Shore, “Experimental study of time-delay signatures in vertical-cavity surface-emitting lasers subject to double-cavity polarization-rotated optical feedback,” J. Lightwave Technol. 32(9), 1829–1836 (2014).
[Crossref]

P. Li, Y. Guo, Y. Q. Guo, Y. L. Fan, X. M. Guo, X. L. Liu, K. Y. Li, K. A. Shore, Y. C. Wang, and A. B. Wang, “Ultrafast fully photonic random bit generator,” J. Lightwave Technol. 36(12), 2531–2540 (2018).
[Crossref]

J. G. Wu, Z. M. Wu, Y. R. Liu, L. Fan, X. Tang, and G. Q. Xia, “Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system,” J. Lightwave Technol. 31(3), 461–467 (2013).
[Crossref]

A. Argyris, E. Pikasis, and D. Syvridis, “Gb/s one-time-pad data encryption with synchronized chaos-based true random bit generators,” J. Lightwave Technol. 34(22), 5325–5331 (2016).
[Crossref]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[Crossref]

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. X. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of chaos time delay signature in a ring network consisting of three semiconductor lasers coupled with heterogeneous delays,” J. Lightwave Technol. 34(18), 4221–4227 (2016).
[Crossref]

Laser Phys. (1)

J. G. Wu, X. Tang, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Parallel generation of 10 Gbits/s physical random number streams using chaotic semiconductor lasers,” Laser Phys. 22(10), 1476–1480 (2012).
[Crossref]

Nat. Photonics (2)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Opt. Commun. (2)

S. Y. Xiang, W. Pan, L. Y. Zhang, A. J. Wen, L. Shang, H. X. Zhang, and L. Lin, “Phase-modulated dual-path feedback for time delay signature suppression from intensity and phase chaos in semiconductor laser,” Opt. Commun. 324, 38–46 (2014).
[Crossref]

J. Song, Z. Q. Zhong, L. X. Wei, Z. M. Wu, and G. Q. Xia, “Experimental investigations on nonlinear dynamics of a semiconductor laser subject to optical injection and fiber Bragg grating feedback,” Opt. Commun. 354, 213–217 (2015).
[Crossref]

Opt. Express (10)

D. Wang, L. Wang, T. Zhao, H. Gao, Y. Wang, X. Chen, and A. Wang, “Time delay signature elimination of chaos in a semiconductor laser by dispersive feedback from a chirped FBG,” Opt. Express 25(10), 10911–10924 (2017).
[Crossref] [PubMed]

J. G. Wu, Z. M. Wu, G. Q. Xia, and G. Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express 20(2), 1741–1753 (2012).
[Crossref] [PubMed]

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[Crossref] [PubMed]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25(6), 6511–6523 (2017).
[Crossref] [PubMed]

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[Crossref] [PubMed]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[Crossref] [PubMed]

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[Crossref] [PubMed]

Opt. Lett. (6)

P. Li, J. Zhang, L. Sang, X. Liu, Y. Guo, X. Guo, A. Wang, K. Alan Shore, and Y. Wang, “Real-time online photonic random number generation,” Opt. Lett. 42(14), 2699–2702 (2017).
[Crossref] [PubMed]

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

N. Li, W. Pan, A. Locquet, and D. S. Citrin, “Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection,” Opt. Lett. 40(19), 4416–4419 (2015).
[Crossref] [PubMed]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).
[Crossref] [PubMed]

N. Jiang, A. Zhao, S. Liu, C. Xue, B. Wang, and K. Qiu, “Generation of broadband chaos with perfect time delay signature suppression by using self-phase-modulated feedback and a microsphere resonator,” Opt. Lett. 43(21), 5359–5362 (2018).
[Crossref] [PubMed]

Photon. Res. (1)

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photon. Res. 5(1), 6–10 (2017).
[Crossref]

Phys. Rev. X (1)

T. Steinle, J. N. Greiner, J. Wrachtrup, H. Giessen, and I. Gerhardt, “Unbiased all-optical random-number generator,” Phys. Rev. X 7(4), 041050 (2017).
[Crossref]

Sci. Rep. (2)

M. Naruse, Y. Terashima, A. Uchida, and S. J. Kim, “Ultrafast photonic reinforcement learning based on laser chaos,” Sci. Rep. 7(1), 8772 (2017).
[Crossref] [PubMed]

J. Zhang, Z. Li, Y. Wu, M. Zhang, Y. Liu, and M. Li, “Optimized chaotic Brillouin dynamic grating with filtered optical feedback,” Sci. Rep. 8(1), 827 (2018).
[Crossref] [PubMed]

Other (1)

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, S. Vo, and L. E. Bassham, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” (NIST, 2010) paper 800–22.

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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of MCSL with an auxiliary FBG injection. DFB1, DFB2: distributed feedback semiconductor lasers; LDC: laser diode controller; FC: fiber coupler; OC: optical circulator; FBG: fiber Bragg grating; VOA1, VOA2: two variable optical attenuator; OSA: optical spectrum analyzer; PD: photodiode; OSC: oscilloscope.
Fig. 2
Fig. 2 (a) FBG reflection spectrum, (b) optical spectra of the DFB1 output (black line) and reflecting output of FBG (red line).
Fig. 3
Fig. 3 The outputs in the time domain (column a), the corresponding ACFs (column b), power spectra for two lasers (column c) and the details of parallel power spectra (column d). The row 1 and row 2 are the results of DFB1 and DFB2 in CMCSL system respectively. The coupling power, bias currents, wavelengths of two DFBs in two systems are k r1 =200μW, I 1 =24.5mA, I 2 =22.6mA, λ 1 =1552.875nm, λ 2 =1552.880nm. The row 3 and row 4 are the results of DFB1 and DFB2 in the FMCSL system respectively. k r2 =220μW in the FMCSL system.
Fig. 4
Fig. 4 ρ 1 (a), ρ 2 (b) as functions of k r1 in CMCSL system ( ρ C1 , ρ C2 ) and FMCSL system ( ρ F1 , ρ F2 ) with k r2 =220μW.
Fig. 5
Fig. 5 ρ m as functions of k r2 with k r1 =200μW, Δ f 12 =0.6GHz (a) and Δ f 12 =4GHz (b).
Fig. 6
Fig. 6 ρ m as functions of Δ f 12 with k r1 =200μW, k r2 =220μW.
Fig. 7
Fig. 7 ρ m as functions of bias currents I 1 (a), I 2 (b)and I m ( I 1 = I 2 ) (c)with k r1 =220μW, k r2 =200μW.
Fig. 8
Fig. 8 The procedure of post-processing. T is a delay value. MSB: the most significant bits; LSB: the least significant bits. All steps are performed offline via a computer. “Signal” represents the original chaotic waveforms collected by OSC.

Tables (1)

Tables Icon

Table 1 Results from the NIST randomness test suite, for the testing of 1G bits. In order to pass the tests, the composite P-value should be larger than 0.0001 and the corresponding proportion should be limited to the range of 0.99 ± 0.0094392 [10,11,36].

Equations (1)

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C m (Δt)= <[ I m (t+Δt)< I m (t+Δt)>][ I m (t)< I m (t)>]> < [ I m (t+Δt)< I m (t+Δt)>] 2 >< [ I m (t)< I m (t)>] 2 >

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