Abstract

We numerically investigated the chaos time delay signature (TDS) suppression and bandwidth enhancement by electrical heterodyning. Chaos signals generated with a semiconductor laser subject to optical feedback typically have distinct loop frequency peaks in their power spectra corresponding to the reciprocals of the time delays, which deteriorates the performance in applications including chaos radar/lidar and fast random bit generation. By electrically heterodyning the chaos signal with a single frequency local oscillator, we show that the power in the chaos spectrum can be redistributed and a smoother spectrum with a broader effective bandwidth can be obtained. Compared with the chaos directly generated from a semiconductor laser subject to optical feedback, the amplitudes of the TDS (ρTDS) measured under different feedback strengths can be suppressed up to 63% and the effective bandwidths can be enhanced up to 46% in average after the electrical heterodyning is applied.

© 2015 Optical Society of America

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  1. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438, 343–346 (2005).
    [Crossref] [PubMed]
  2. F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
    [Crossref]
  3. W. T. Wu, Y. H. Liao, and F. Y. Lin, “Noise suppressions in synchronized chaos lidars,” Opt. Express 18, 26155–26162 (2010).
    [Crossref] [PubMed]
  4. F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40, 815–820 (2004).
    [Crossref]
  5. 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, 728–732 (2008).
    [Crossref]
  6. Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
    [Crossref]
  7. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003).
    [Crossref]
  8. A. Murakami, J. Ohtsubo, and Y. Liu, “Stability analysis of semiconductor laser with phase-conjugate feedback,” IEEE J. Quantum Electron. 33, 1825–1831 (1997).
    [Crossref]
  9. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
    [Crossref]
  10. 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, 2960–2962 (2007).
    [Crossref] [PubMed]
  11. 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, 879–891 (2009).
    [Crossref]
  12. 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, 6661–6666 (2010).
    [Crossref] [PubMed]
  13. 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, 20124–20133 (2009).
    [Crossref] [PubMed]
  14. 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, 1930–1935 (2012).
    [Crossref]
  15. J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282, 3153–3156 (2009).
    [Crossref]
  16. F. Y. Lin and J. M. Liu, “Ambiguity functions of laser-based chaotic radar,” IEEE J. Quantum Electron. 40, 1732–1738 (2004).
    [Crossref]
  17. K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
    [Crossref]
  18. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2543 (2012).
    [Crossref] [PubMed]
  19. A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
    [Crossref]
  20. A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
    [Crossref]
  21. N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
    [Crossref]
  22. N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
    [Crossref]
  23. X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49, 829–838 (2013).
    [Crossref]
  24. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [Crossref]
  25. J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. 30, 957–965 (1994).
    [Crossref]
  26. S. K. Hwang, J. M. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3-μ m semiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
    [Crossref]
  27. V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72, 373–377 (2005).
    [Crossref]
  28. F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48, 1010–1014 (2012).
    [Crossref]
  29. A. Wang, Y. Yang, B. Wang, B. Zhang, L. Li, and Y. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express,  21, 8701–8710 (2013).
    [Crossref] [PubMed]

2013 (3)

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49, 829–838 (2013).
[Crossref]

A. Wang, Y. Yang, B. Wang, B. Zhang, L. Li, and Y. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express,  21, 8701–8710 (2013).
[Crossref] [PubMed]

2012 (5)

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48, 1010–1014 (2012).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2543 (2012).
[Crossref] [PubMed]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (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, 1930–1935 (2012).
[Crossref]

2010 (2)

2009 (4)

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, 20124–20133 (2009).
[Crossref] [PubMed]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282, 3153–3156 (2009).
[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, 879–891 (2009).
[Crossref]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[Crossref]

2008 (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, 728–732 (2008).
[Crossref]

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

2007 (1)

2005 (2)

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

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72, 373–377 (2005).
[Crossref]

2004 (3)

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[Crossref]

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

F. Y. Lin and J. M. Liu, “Ambiguity functions of laser-based chaotic radar,” IEEE J. Quantum Electron. 40, 1732–1738 (2004).
[Crossref]

2003 (2)

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

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
[Crossref]

1997 (1)

A. Murakami, J. Ohtsubo, and Y. Liu, “Stability analysis of semiconductor laser with phase-conjugate feedback,” IEEE J. Quantum Electron. 33, 1825–1831 (1997).
[Crossref]

1994 (1)

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. 30, 957–965 (1994).
[Crossref]

1992 (1)

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[Crossref]

1980 (1)

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

Aida, T.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
[Crossref]

Amano, K.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

Annovazzi-Lodi, V.

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

Argyris, A.

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

Cao, L. P.

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282, 3153–3156 (2009).
[Crossref]

Chan, S. C.

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49, 829–838 (2013).
[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, 1930–1935 (2012).
[Crossref]

Chao, Y. K.

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48, 1010–1014 (2012).
[Crossref]

Citrin, D. S.

Colet, P.

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

Danckaert, J.

Davis, P.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
[Crossref]

Deng, T.

Fan, L.

Fischer, I.

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

Garcia-Ojalvo, J.

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

Goedgebuer, J. P.

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 Photon. Technol. Lett. 20, 1633–1635 (2008).
[Crossref]

Heil, T.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
[Crossref]

Hirano, K.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

Hwang, S. K.

S. K. Hwang, J. M. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3-μ m semiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[Crossref]

Inoue, M.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

Kobayashi, K.

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

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, 728–732 (2008).
[Crossref]

Lang, R.

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

Larger, L.

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

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72, 373–377 (2005).
[Crossref]

Li, L.

Li, N.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
[Crossref]

Li, S. S.

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, 1930–1935 (2012).
[Crossref]

Li, X. Z.

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49, 829–838 (2013).
[Crossref]

Liao, Y. H.

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

W. T. Wu, Y. H. Liao, and F. Y. Lin, “Noise suppressions in synchronized chaos lidars,” Opt. Express 18, 26155–26162 (2010).
[Crossref] [PubMed]

Lin, F. Y.

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48, 1010–1014 (2012).
[Crossref]

W. T. Wu, Y. H. Liao, and F. Y. Lin, “Noise suppressions in synchronized chaos lidars,” Opt. Express 18, 26155–26162 (2010).
[Crossref] [PubMed]

F. Y. Lin and J. M. Liu, “Ambiguity functions of laser-based chaotic radar,” IEEE J. Quantum Electron. 40, 1732–1738 (2004).
[Crossref]

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

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[Crossref]

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

Lin, X. D.

Liu, J. M.

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

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

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[Crossref]

F. Y. Lin and J. M. Liu, “Ambiguity functions of laser-based chaotic radar,” IEEE J. Quantum Electron. 40, 1732–1738 (2004).
[Crossref]

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

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. 30, 957–965 (1994).
[Crossref]

S. K. Hwang, J. M. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3-μ m semiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (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, 1930–1935 (2012).
[Crossref]

Liu, Y.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
[Crossref]

A. Murakami, J. Ohtsubo, and Y. Liu, “Stability analysis of semiconductor laser with phase-conjugate feedback,” IEEE J. Quantum Electron. 33, 1825–1831 (1997).
[Crossref]

Locquet, A.

Luo, B.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
[Crossref]

Mark, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[Crossref]

Mirasso, C. R.

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

Mork, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[Crossref]

Mu, P.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

Murakami, A.

A. Murakami, J. Ohtsubo, and Y. Liu, “Stability analysis of semiconductor laser with phase-conjugate feedback,” IEEE J. Quantum Electron. 33, 1825–1831 (1997).
[Crossref]

Naito, S.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

Nguimdo, R. M.

Ohtsubo, J.

A. Murakami, J. Ohtsubo, and Y. Liu, “Stability analysis of semiconductor laser with phase-conjugate feedback,” IEEE J. Quantum Electron. 33, 1825–1831 (1997).
[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, 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, 879–891 (2009).
[Crossref]

Pan, W.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

Pesquera, L.

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

Rontani, D.

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, 879–891 (2009).
[Crossref]

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, 2960–2962 (2007).
[Crossref] [PubMed]

Sciamanna, M.

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, 879–891 (2009).
[Crossref]

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, 2960–2962 (2007).
[Crossref] [PubMed]

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, 728–732 (2008).
[Crossref]

Shore, K. A.

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

Simpson, T. B.

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. 30, 957–965 (1994).
[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, 728–732 (2008).
[Crossref]

Syvridis, D.

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

Tang, X.

Tromborg, B.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[Crossref]

Uchida, A.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
[Crossref]

Udaltsov, V. S.

Van der Sande, G.

Verschaffelt, G.

Wang, A.

A. Wang, Y. Yang, B. Wang, B. Zhang, L. Li, and Y. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express,  21, 8701–8710 (2013).
[Crossref] [PubMed]

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

Wang, B.

Wang, Y.

A. Wang, Y. Yang, B. Wang, B. Zhang, L. Li, and Y. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express,  21, 8701–8710 (2013).
[Crossref] [PubMed]

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

White, J. K.

S. K. Hwang, J. M. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3-μ m semiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[Crossref]

Wu, J. G.

Wu, T. C.

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48, 1010–1014 (2012).
[Crossref]

Wu, W. T.

Wu, Z. M.

Xia, G. Q.

Xiang, S.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

Yan, L.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
[Crossref]

Yang, Y.

Yoshimori, S.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

Yoshimura, K.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[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, 728–732 (2008).
[Crossref]

Zhang, B.

Zhang, L.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

Zou, X.

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

IEEE J. Quantum Electron. (12)

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

A. Murakami, J. Ohtsubo, and Y. Liu, “Stability analysis of semiconductor laser with phase-conjugate feedback,” IEEE J. Quantum Electron. 33, 1825–1831 (1997).
[Crossref]

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[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, 879–891 (2009).
[Crossref]

F. Y. Lin and J. M. Liu, “Ambiguity functions of laser-based chaotic radar,” IEEE J. Quantum Electron. 40, 1732–1738 (2004).
[Crossref]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 1367–1379 (2009).
[Crossref]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39, 1462–1467 (2003).
[Crossref]

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49, 829–838 (2013).
[Crossref]

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

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. 30, 957–965 (1994).
[Crossref]

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, X. Zou, L. Zhang, and P. Mu, “Photonic generation of wideband time-delay-signature-eliminated chaotic signals utilizing an optically injected semiconductor laser,” IEEE J. Quantum Electron. 48, 1339–1345 (2012).
[Crossref]

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48, 1010–1014 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[Crossref]

IEEE Photon. Technol. Lett. (2)

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

N. Li, W. Pan, S. Xiang, L. Yan, B. Luo, and X. Zou, “Loss of time delay signature in broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 24, 2187–2190 (2012).
[Crossref]

IEEE Photonics J. (1)

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, 1930–1935 (2012).
[Crossref]

J. Opt. Technol. (1)

Nat. Photonics (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, 728–732 (2008).
[Crossref]

Nature (1)

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

Opt. Commun. (2)

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

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282, 3153–3156 (2009).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Other (1)

S. K. Hwang, J. M. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3-μ m semiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic setups of chaos generation for Path O: original chaos, Path H1: heterodyned chaos, and Path H2: mixed chaos. SL: semiconductor laser; M: mirror; PD: photode-tector; SG: signal generator; A: microwave amplifier; LPF: low pass filter.
Fig. 2
Fig. 2 (a) Power spectrum, (b) autocorrelation function, and (c) delayed mutual information of the original chaos generated with a feedback strength ξ = 0.09 and a feedback delay time τ = 1 ns after filtered by the acquisition bandwidth. As the reference, the dashed curve in (a) is the power spectrum of the original chaos before filtered by the acquisition bandwidth.
Fig. 3
Fig. 3 (a) Power spectra, (b) autocorrelation functions, and (c) delayed mutual information of the heterodyned chaos (blue solid curves) obtained from the first heterodyne scheme with different fLO (green solid lines): 5.94 GHz (first row), 6.21 GHz (second row), 6.44 GHz (third row), and 6.53 GHz (fourth row). As the reference, the black dashed curves show the (a) power spectrum of the original chaos before filtering, and the (b) autocorrelation function and (c) delayed mutual information of the original chaos after filtering.
Fig. 4
Fig. 4 (a) Absolute amplitudes of the first (bright blue) and second (dark blue) TDS peaks of the autocorrelation functions, (b) ρTDS, and (c) effective bandwidths of the heterodyned chaos under different fLO. The black solid lines in (b) and (c) show the ρTDS and effective bandwidth obtained from the original chaos for reference. The gray dashed lines show the multiples of floop/2.
Fig. 5
Fig. 5 (a) Power spectra, (b) autocorrelation functions, and (c) delayed mutual information of the mixed chaos (red solid curves) obtained from the second heterodyne scheme for different fLO (green solid lines): 5.94 GHz (first row), 6.21 GHz (second row), 6.44 GHz (third row), and 6.53 GHz (fourth row), when A = 0.1 dB. As the reference, the black dashed curves show the (a) power spectrum of the original chaos before filtering, and the (b) autocorrelation function and (c) delayed mutual information of the original chaos after filtering.
Fig. 6
Fig. 6 (a) ρTDS and (c) effective bandwidth of the mixed chaos for different A and fLO, where the arrows on the right of the color bars indicate the ρTDS and effective bandwidth for the original chaos. (b) Minimum ρTDS and (d) maximum effective bandwidths of the mixed chaos obtained under optimal A for different fLO, where the black solid lines in (b) and (d) show the ρTDS and effective bandwidth of the original chaos for reference. The gray dashed lines show the multiples of floop/2.
Fig. 7
Fig. 7 (a) ρTDS and (b) effective bandwidths of the original chaos (black), the heterodyned chaos from the first heterodyne scheme (blue), and the mixed chaos from the second heterodyne scheme (red) under different feedback strengths. The fLO and A are optimized to have the minimum ρTDS in the heterodyned chaos and the mixed chaos.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

da dt = 1 2 [ γ c γ n γ s J ˜ n ˜ - γ p ( 2 a + a 2 ) ] ( 1 + a ) + ξ γ c [ 1 + a ( t - τ ) ] cos [ ϕ ( t - τ ) - ϕ ( t ) ]
d ϕ dt = - b 2 [ γ c γ n γ s J ˜ n ˜ - γ p ( 2 a + a 2 ) ] + ξ γ c [ 1 + a ( t - τ ) ] 1 + a sin [ ϕ ( t - τ ) - ϕ ( t ) ]
d n ˜ dt = - γ s n ˜ - γ n ( 1 + a ) 2 n ˜ - γ s J ˜ ( 2 a + a 2 ) + γ s γ p γ s J ˜ ( 2 a + a 2 ) ( 1 + a ) 2
S O ( t ) = LPF [ I ( t ) ] ,
S H 1 ( t ) = LPF [ I ( t ) × cos ( 2 π f LO t ) ] ,
S H 2 ( t ) = LPF [ I ( t ) × ( 1 + A cos ( 2 π f LO t ) ) ] ,
ρ TDS = | ρ 1 | + | ρ 2 | + | ρ 3 | + | ρ 4 | 4

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