Abstract

A wideband complexity-enhanced chaos generation scheme is proposed by using a semiconductor laser subject to delay-interfered self-phase-modulated optical feedback. The influences of feedback strength, phase modulation index, and interference delay on the effective bandwidth and time-delay-signature (TDS) characteristics of the proposed scheme-generated chaos are extensively investigated both experimentally and numerically. The results demonstrate that with the joint effects of phase modulation-induced spectrum expansion and nonlinear filtering of delayed interference, wideband chaos with flat spectrum and excellent TDS suppression characteristics can be generated over a wide dynamic operation range. In comparisons with the relevant chaos generation schemes under conventional optical feedback, individual self-phase modulated optical feedback, and delay-interfered optical feedback, the proposed scheme cannot only significantly enhance the effective bandwidth of chaos but also considerably enhance the complexity of chaos by suppressing the TDS toward an indistinguishable level close to 0.

© 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]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  35. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically-injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1–3), 173–180 (2003).
    [Crossref]
  36. D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
    [Crossref]
  37. C. Li, J. Mao, R. Dai, X. Zhou, and J. Jiang, “Frequency-sextupling optoelectronic oscillator using a Mach–Zehnder interferometer and an FBG,” IEEE Photonics Technol. Lett. 28(12), 1356–1359 (2016).
    [Crossref]
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    [Crossref]
  39. A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic application,” IEEE J. Quantum Electron. 44(2), 119–124 (2008).
    [Crossref]
  40. D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24(1), 335–341 (2006).
    [Crossref]

2018 (5)

J. Ke, L. Yi, G. Xia, and W. Hu, “Chaotic optical communications over 100-km fiber transmission at 30-Gb/s bit rate,” Opt. Lett. 43(6), 1323–1326 (2018).
[Crossref]

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

N. Jiang, A. Zhao, S. Liu, C. Xue, and K. Qiu, “Chaos synchronization and communication in closed-loop semiconductor lasers subject to common chaotic phase-modulated feedback,” Opt. Express 26(25), 32404–32416 (2018).
[Crossref]

N. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (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]

2017 (4)

2016 (6)

C. Cheng, Y. Chen, and F. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).
[Crossref]

N. Jiang, C. Xue, Y. Lv, and K. Qiu, “Physically enhanced secure wavelength division multiplexing chaos communication using multimode semiconductor lasers,” Nonlinear Dyn. 86(3), 1937–1949 (2016).
[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]

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]

D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
[Crossref]

C. Li, J. Mao, R. Dai, X. Zhou, and J. Jiang, “Frequency-sextupling optoelectronic oscillator using a Mach–Zehnder interferometer and an FBG,” IEEE Photonics Technol. Lett. 28(12), 1356–1359 (2016).
[Crossref]

2015 (8)

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]

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Chaos time delay signature suppression and bandwidth enhancement by electrical heterodyning,” Opt. Express 23(3), 2308–2319 (2015).
[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]

Y. Hong, X. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, J. J. Chen, L. Fan, Z. Q. Zhong, and G. Q. Xia, “Tbits/s physical random bit generation based on mutually coupled semiconductor laser chaotic entropy source,” Opt. Express 23(26), 33130–33141 (2015).
[Crossref]

X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
[Crossref]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

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]

2014 (4)

M. Zhang, Y. Ji, Y. Zhang, Y. Wu, H. Xu, and W. Xu, “Remote radar based on chaos generation and radio over fiber,” IEEE Photonics J. 6(5), 1–12 (2014).
[Crossref]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref]

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref]

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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]

2013 (1)

2012 (1)

S. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

2011 (1)

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[Crossref]

2010 (1)

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]

2009 (2)

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (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]

2008 (3)

A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
[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]

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic application,” IEEE J. Quantum Electron. 44(2), 119–124 (2008).
[Crossref]

2006 (1)

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]

2003 (1)

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically-injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1–3), 173–180 (2003).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Alan Shore, K.

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]

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. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic application,” IEEE J. Quantum Electron. 44(2), 119–124 (2008).
[Crossref]

D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24(1), 335–341 (2006).
[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]

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]

Bloch, M.

Bogris, A.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic application,” IEEE J. Quantum Electron. 44(2), 119–124 (2008).
[Crossref]

D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24(1), 335–341 (2006).
[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]

X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
[Crossref]

Chen, J. J.

Chen, X.

Y. Hong, X. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

Chen, Y.

C. Cheng, Y. Chen, and F. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).
[Crossref]

Chen, Y. C.

Cheng, C.

C. Cheng, Y. Chen, and F. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).
[Crossref]

Cheng, C. H.

Cheng, M.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

Chizhevsky, V. N.

Chlouverakis, K. E.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic application,” IEEE J. Quantum Electron. 44(2), 119–124 (2008).
[Crossref]

Citrin, D. S.

N. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
[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]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

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]

Dai, R.

C. Li, J. Mao, R. Dai, X. Zhou, and J. Jiang, “Frequency-sextupling optoelectronic oscillator using a Mach–Zehnder interferometer and an FBG,” IEEE Photonics Technol. Lett. 28(12), 1356–1359 (2016).
[Crossref]

Davis, P.

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, L.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

Deng, T.

Fan, L.

Fischer, I.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[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]

Fu, S.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

Fu, Y.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

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]

Guo, X.

Guo, Y.

He, H.

A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonics Technol. Lett. 20(19), 1633–1635 (2008).
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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.

Y. Hong, X. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[Crossref]

Hu, W.

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]

Iwakawa, K.

Ji, Y.

M. Zhang, Y. Ji, Y. Zhang, Y. Wu, H. Xu, and W. Xu, “Remote radar based on chaos generation and radio over fiber,” IEEE Photonics J. 6(5), 1–12 (2014).
[Crossref]

Jiang, J.

C. Li, J. Mao, R. Dai, X. Zhou, and J. Jiang, “Frequency-sextupling optoelectronic oscillator using a Mach–Zehnder interferometer and an FBG,” IEEE Photonics Technol. Lett. 28(12), 1356–1359 (2016).
[Crossref]

Jiang, N.

Jiang, X.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
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Kanakidis, D.

Kanno, K.

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).
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Ke, C.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
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Ke, J.

Kim, B.

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
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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).
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Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
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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]

Li, C.

C. Li, J. Mao, R. Dai, X. Zhou, and J. Jiang, “Frequency-sextupling optoelectronic oscillator using a Mach–Zehnder interferometer and an FBG,” IEEE Photonics Technol. Lett. 28(12), 1356–1359 (2016).
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Li, G.

Li, L.

Li, N.

N. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
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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]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref]

S. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Li, P.

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).
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X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
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Li, X. Z.

Lin, F.

C. Cheng, Y. Chen, and F. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).
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Lin, F. Y.

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Chaos time delay signature suppression and bandwidth enhancement by electrical heterodyning,” Opt. Express 23(3), 2308–2319 (2015).
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F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically-injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1–3), 173–180 (2003).
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Lin, L.

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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.

Liu, D.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

Liu, J. M.

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically-injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1–3), 173–180 (2003).
[Crossref]

Liu, S.

Liu, X.

Locquet, A.

N. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
[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]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

Luo, B.

S. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Lv, Y.

N. Jiang, C. Xue, Y. Lv, and K. Qiu, “Physically enhanced secure wavelength division multiplexing chaos communication using multimode semiconductor lasers,” Nonlinear Dyn. 86(3), 1937–1949 (2016).
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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]

Mao, J.

C. Li, J. Mao, R. Dai, X. Zhou, and J. Jiang, “Frequency-sextupling optoelectronic oscillator using a Mach–Zehnder interferometer and an FBG,” IEEE Photonics Technol. Lett. 28(12), 1356–1359 (2016).
[Crossref]

Mercier, E.

Mirasso, C. R.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[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]

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]

Nguimdo, R. M.

N. Li, R. M. Nguimdo, A. Locquet, and D. S. Citrin, “Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection,” Nonlinear Dyn. 92(2), 315–324 (2018).
[Crossref]

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]

Ortin, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

Pan, W.

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]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref]

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Panajotov, K.

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]

Pikasis, E.

Qiu, K.

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]

Rizomiliotis, P.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic application,” IEEE J. Quantum Electron. 44(2), 119–124 (2008).
[Crossref]

Rontani, D.

D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
[Crossref]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

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]

Rosso, O. A.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[Crossref]

Sakuraba, R.

Sang, L.

Sciamanna, M.

D. Rontani, E. Mercier, D. Wolfersberger, and M. Sciamanna, “Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback,” Opt. Lett. 41(20), 4637–4640 (2016).
[Crossref]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

Shang, L.

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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]

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.

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

Y. Hong, X. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[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]

Shum, P.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

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]

Soriano, M. C.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[Crossref]

Spencer, P. S.

Y. Hong, X. Chen, P. S. Spencer, and K. A. Shore, “Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator,” IEEE J. Quantum Electron. 51(3), 1–6 (2015).
[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. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a secret key for cryptographic application,” IEEE J. Quantum Electron. 44(2), 119–124 (2008).
[Crossref]

D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24(1), 335–341 (2006).
[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]

Tang, M.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

Tang, X.

Thienpont, H.

Uchida, A.

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]

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]

Virte, M.

Wang, A.

Wang, B.

Wang, C.

Wang, L.

Wang, Y.

Wen, A.

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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]

Wolfersberger, D.

Wu, J. G.

Wu, Y.

M. Zhang, Y. Ji, Y. Zhang, Y. Wu, H. Xu, and W. Xu, “Remote radar based on chaos generation and radio over fiber,” IEEE Photonics J. 6(5), 1–12 (2014).
[Crossref]

Wu, Z.

Wu, Z. M.

Xia, G.

Xia, G. Q.

Xiang, S.

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Xu, H.

M. Zhang, Y. Ji, Y. Zhang, Y. Wu, H. Xu, and W. Xu, “Remote radar based on chaos generation and radio over fiber,” IEEE Photonics J. 6(5), 1–12 (2014).
[Crossref]

Xu, W.

M. Zhang, Y. Ji, Y. Zhang, Y. Wu, H. Xu, and W. Xu, “Remote radar based on chaos generation and radio over fiber,” IEEE Photonics J. 6(5), 1–12 (2014).
[Crossref]

Xue, C.

Yan, L.

S. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Yang, Y.

Yi, L.

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.

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, B.

Zhang, H.

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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]

Zhang, J.

Zhang, L.

S. Xiang, W. Pan, L. Zhang, A. Wen, L. Shang, H. 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]

Zhang, M.

Y. Fu, M. Cheng, X. Jiang, L. Deng, C. Ke, S. Fu, M. Tang, M. Zhang, P. Shum, and D. Liu, “Wavelength division multiplexing secure communication scheme based on an optically coupled phase chaos system and PM-to-IM conversion mechanism,” Nonlinear Dyn. 94(3), 1949–1959 (2018).
[Crossref]

M. Zhang, Y. Ji, Y. Zhang, Y. Wu, H. Xu, and W. Xu, “Remote radar based on chaos generation and radio over fiber,” IEEE Photonics J. 6(5), 1–12 (2014).
[Crossref]

Zhang, Y.

M. Zhang, Y. Ji, Y. Zhang, Y. Wu, H. Xu, and W. Xu, “Remote radar based on chaos generation and radio over fiber,” IEEE Photonics J. 6(5), 1–12 (2014).
[Crossref]

Zhao, A.

Zhong, Z.

Zhong, Z. Q.

Zhou, X.

C. Li, J. Mao, R. Dai, X. Zhou, and J. Jiang, “Frequency-sextupling optoelectronic oscillator using a Mach–Zehnder interferometer and an FBG,” IEEE Photonics Technol. Lett. 28(12), 1356–1359 (2016).
[Crossref]

Zhu, H.

S. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Zhuang, J. P.

Zou, X.

S. Xiang, W. Pan, B. Luo, L. Yan, X. Zou, N. Li, and H. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Zunino, L.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
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IEEE J. Quantum Electron. (6)

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Figures (12)

Fig. 1
Fig. 1 (a) Experimental setup of the proposed scheme, (b) transmission spectrum of MZI. DFB, distributed-feedback laser; PM, electro-optic phase modulator; OC, optical circulator; PC, polarization controller; FC, fiber coupler; PD, photodetector; Amp: RF amplifier; DL, optical delay line; VOA, variable optical attenuator.
Fig. 2
Fig. 2 Experimental time series, RF spectra and ACF traces of chaos generated in the cases of COF (first column), SPMOF (second column), COF + MZI (third column) and the proposed SPMOF + MZI (fourth column). The feedback strength is fixed to −25dB.
Fig. 3
Fig. 3 Experimental time series, RF spectra and ACF traces of chaos generated in the proposed scheme with feedback strengths of −30dB, −20dB and −15dB.
Fig. 4
Fig. 4 Experimental (a) effective bandwidth and (b) TDS values in the ACF traces of chaos generated in the cases of COF (square), SPMOF (lower-triangle), COF + MZI (upper-triangle) and SPMOF + MZI (circle), as a function of the feedback strength.
Fig. 5
Fig. 5 Experimental time series (first row), RF spectra (second row) and ACF traces (third row) of chaos generated by the proposed SPMOF + MZI scheme, with different interference delays of (a) 0.1ns, (b) 0.2ns and (c) 1ns. The feedback strength is fixed to −30dB.
Fig. 6
Fig. 6 Bifurcation diagrams with peak-to-peak intensity of chaos generated under the scenarios of (a) COF, (b) SPMOF, (c) COF + MZI and (d) SPMOF + MZI, as a function of feedback strength.
Fig. 7
Fig. 7 Numerical time series (first row), RF spectra (second row) and ACF traces (third row) of chaos generated in the cases of (a) COF, (b) SPMOF, (c) COF + MZI and (d) SPMOF + MZI. The feedback strength is fixed to −25dB.
Fig. 8
Fig. 8 Numerical results for (a) effective bandwidth and (b) TDS value in ACF trace of chaos generated in the cases of COF (square), SPMOF (bottom-triangle), COF + MZI (upper-triangle) and SPMOF + MZI (circle), as a function of the feedback strength.
Fig. 9
Fig. 9 Numerical results of RF spectra (first row) and ACF traces (second row) of chaos generated in the proposed scheme with feedback strengths of −30 dB (first column), (b) −20 dB (second column) and (c) −10dB (third column). Insets: the details of ACF traces nearby 0ns lag.
Fig. 10
Fig. 10 Influences of PM index and feedback strength on (a) effective bandwidth (GHz) and (b) TDS in ACF in the proposed SPMOF + MZI scheme; (c1-c3) RF spectra of chaos generated in the proposed scheme with a PM index of 0.5. The interference delay is fixed at Δtd = 0.2ns.
Fig. 11
Fig. 11 Influences of interference delay of MZI and feedback strength on (a) effective bandwidth (GHz) and (b) TDS in ACF trace in the proposed SPMOF + MZI scheme, and the TDS value in ACF versus the interference delay in the vicinity of (c) Δtd = τf and (d) Δtd = 2τf. The PM index is fixed to 1.5.
Fig. 12
Fig. 12 Influences of feedback strength and SPM delay (Δt) on (a) effective bandwidth (GHz) and (b) TDS in ACF trace in the proposed SPMOF + MZI scheme. The PM index is fixed to 1.5.

Equations (3)

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d E ( t ) d t = 1 + i α 2 [ g ( N ( t ) N 0 ) 1 + ε | E ( t ) | 2 1 τ p ] E + k f 2 τ i n [ E ( t τ f ) exp ( i 2 π ω 0 τ f + i φ ( t τ f ) ) + E ( t τ f Δ t d ) exp ( i 2 π ω 0 ( τ f + Δ t d ) + i φ ( t τ f Δ t d ) ) ] + 2 β N ( t ) χ ( t ) ,
d N ( t ) d t = I q N ( t ) τ e g ( N ( t ) N 0 ) 1 + ε | E ( t ) | 2 | E ( t ) | 2 ,
φ ( t ) = K P M N ( | E ( t Δ t ) | 2 ) π ,

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