## Generation of wideband chaos with suppressed time-delay signature by delayed self-interference |

Optics Express, Vol. 21, Issue 7, pp. 8701-8710 (2013)

http://dx.doi.org/10.1364/OE.21.008701

Acrobat PDF (2802 KB)

### Abstract

We demonstrate experimentally and numerically a method using the incoherent delayed self-interference (DSI) of chaotic light from a semiconductor laser with optical feedback to generate wideband chaotic signal. The results show that, the DSI can eliminate the domination of laser relaxation oscillation existing in the chaotic laser light and therefore flatten and widen the power spectrum. Furthermore, the DSI depresses the time-delay signature induced by external cavity modes and improves the symmetry of probability distribution by more than one magnitude. We also experimentally show that this DSI signal is beneficial to the random number generation.

© 2013 OSA

## 1. Introduction

## 2. Experimental setup and theoretical model

*E*(

*t*) =

*A*(

*t*)

*e*

^{i}^{(}

^{ωt}^{+}

^{φ}^{)}, we can deduce the DSI signal as follows,where,

*τ*is the delay time corresponding to the optical path difference in MZI,

_{d}*ω*,

*A*and

*φ*are the angle frequency, amplitude and phase of the laser field. Under optical feedback, the laser field can be numerically governed by the following rate equations based on the Lang-Kobayashi model [12

12. 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]

15. A. Uchida, T. Heil, P. Yun Liu, Davis, and T. Aida, “High-frequency broadband signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. **39**(11), 1462–1467 (2003). [CrossRef]

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

*κ*and

_{f}*τ*are the feedback factor and feedback delay, respectively. The intensity feedback strength is 10log(

_{f}*κ*

_{f}^{2}) dB. The following laser parameters were used in simulations: transparency carrier density

*N*

_{0}= 0.455 × 10

^{6}

*μ*m

^{−3}, differential gain

*g*= 1.414 × 10

^{3}

*μ*m

^{3}ns

^{−1}, gain saturation parameter

*ε*= 5 × 10

^{−5}

*μ*m

^{3}, carrier lifetime

*τ*= 2.5 ns, photon lifetime

_{N}*τ*= 1.17 ps, linewidth enhancement factor

_{p}*α*= 5.0, round-trip time in laser cavity

*τ*= 7.38 ps, threshold current density

_{in}*J*

_{th}= 4.239 × 10

^{5}

*μ*m

^{−3}ns

^{−1},

*ω*= 2π

*c*/

*λ*, where

*λ*= 1550 nm and

*c*= 3 × 10

^{8}m/s.

## 3. Results

*J*= 1.8

*J*

_{th},

*τ*= 5 ns and

_{f}*κ*= 0.08, we obtained a numerical chaotic laser light. Figures 2(a) –2(c) plot the time series, Fourier spectrum, and ACF trace of the laser intensity chaos. As shown in Fig. 2(b), the spectrum has a sharp peak at relaxation frequency

_{f}*f*

_{RO}(about 3.5GHz). That is, the relaxation oscillation dominates the intensity chaos. The relaxation-oscillation signature is also observed by ACF; depicted in Fig. 2(c), the ACF trace has slight fluctuation with a period

*τ*

_{RO}= 1/

*f*

_{RO}. Although this fluctuation can be damped rapidly by increasing feedback strength, the first valley approximately located at

*τ*

_{RO}/2 always exists and thus indicates the relaxation oscillation. Furthermore, the time-delay signature can be identified by the side peak of ACF [12

12. 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]

13. Y. Wu, Y. C. Wang, P. Li, A. B. Wang, and M. J. Zhang, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron. **48**(11), 1371–1379 (2012). [CrossRef]

20. 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]

22. 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]

*τ*exceeds the coherence time of the chaotic laser, the DSI converts the phase dynamics into intensity through a cosine function. We therefore show the time series, Fourier spectrum, and ACF trace of cos(

_{d}*φ*) in Figs. 2(d)–2(f). Unlike the intensity chaos, the phase dynamics has a flat and wide spectrum (Fig. 2(e)) without any peak or dominant component. Correspondingly, the ACF trace in Fig. 2(f) has no periodic fluctuation and obvious valley. The disappearance of the relaxation-oscillation signature can be attributed to the nonlinear phase feedback. On the right side of Eq. (3), the feedback term including the factor sin[

*ωτ*+

_{f}*φ*(

*t*)−

*φ*(

*t*−

*τ*)] is nonlinear which will induce change of frequency and excite new oscillations. As the feedback strength increases, the effects of nonlinear feedback on the variation of phase will exceed that of the carrier change, and then the relaxation oscillation in phase signal is no longer dominant. In addition, the size of the ACF peak at

_{f}*τ*is a little smaller than that of intensity chaos [26

_{f}26. R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett. **36**(22), 4332–4334 (2011). [CrossRef] [PubMed]

*τ*= 8.75ns. We can find that the spectrum of the DSI signal is expanded and flattened, and that the ACF trace is cleaned without signatures of relaxation oscillation and feedback delay. In the following, we will quantitatively study the DSI signal of chaotic OFSL both experimentally and numerically.

_{d}### 3.1 Flattening spectrum and enhancing bandwidth

### 3.2 Signatures suppression

*μ*s which is about 40 times feedback delay of 73.88 ns. As shown in the dotted blue line, the ACF trace of the chaotic laser has five side peaks separately at

*τ*, 2

_{f}*τ*, 3

_{f}*τ*, 4

_{f}*τ*, and 5

_{f}*τ*with gradually reduced height. In comparison, the ACF trace of the DSI signal has only two shortened peaks located at

_{f}*τ*and 2

_{f}*τ*, depicted by the red solid line. This means the time-delay signature is depressed. Note that there is no peak appearing at 2.74ns in the red ACF trace, which means that ACF does not disclose the information about the OPD. In addition, as plotted with dotted line in the insets, the ACF trace of chaotic laser has an obvious valley located at about

_{f}*τ*

_{RO}/2 after the peak. In contrast, the ACF trace of the DSI signal no longer has obvious valleys, that is, the relaxation oscillation signature is dispelled.

*τ*to denote the level of the time-delay signature. Figure 7(a) shows the experimental peak height as function of feedback strength for chaotic laser (open squares) and DSI signal (filled squares). The crosses represent the three times standard deviation of the ACF background noise. We can find that the time-delay signature is depressed for any feedback state, the peak size decreased about 30-40%. Figure 7(b) displays the corresponding numerical results. Shown in open squares, the ACF peak size of chaotic laser decreases at first and then increases as feedback strength increases (similar results were found in [12

_{f}12. 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]

### 3.3 Improvement on symmetry of probability distribution

### 3.4 Demonstration of application in RNG

^{−3}indicating a low correlation. For comparison, we also extract random number from the chaotic laser light in Fig. 8 with the same digitization and extraction procedure. We then use the National Institute of Standards and Technology (NIST) battery of statistical tests [27] to evaluate the randomness of each significant bit. The tests are accomplished using 1000 samples of 1Mbit sequences and the significance level of 0.01 [27].

23. N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. **36**(23), 4632–4634 (2011). [CrossRef] [PubMed]

## 4. Discussion and conclusion

5. F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. **10**(5), 991–997 (2004). [CrossRef]

8. A. B. Wang, M. J. Zhang, H. Xu, and Y. C. Wang, “Location of wire faults using chaotic signal,” IEEE Electron Device Lett. **32**(3), 372–374 (2011). [CrossRef]

## Acknowledgments

## References and links

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 |

2. | A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. |

3. | 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 |

4. | I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. |

5. | F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. |

6. | F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. |

7. | Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett. |

8. | A. B. Wang, M. J. Zhang, H. Xu, and Y. C. Wang, “Location of wire faults using chaotic signal,” IEEE Electron Device Lett. |

9. | A. B. Wang, N. Wang, Y. B. Yang, B. J. Wang, M. J. Zhang, and Y. C. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol. |

10. | A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor Laser with optical feedback,” IEEE Photon. Technol. Lett. |

11. | K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express |

12. | 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. |

13. | Y. Wu, Y. C. Wang, P. Li, A. B. Wang, and M. J. Zhang, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron. |

14. | R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. |

15. | A. Uchida, T. Heil, P. Yun Liu, Davis, and T. Aida, “High-frequency broadband signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. |

16. | Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. |

17. | A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. |

18. | M. J. Zhang, T. G. Liu, P. Li, A. B. Wang, J. Z. Zhang, and Y. C. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photon. Technol. Lett. |

19. | S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. |

20. | 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. |

21. | 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 |

22. | 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 |

23. | N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. |

24. | S.-S. Li, Q. Liu, and S.-C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE J. Photonics |

25. | R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. |

26. | R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett. |

27. | A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dary, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800–22 Revision 1a (2010). |

**OCIS Codes**

(140.1540) Lasers and laser optics : Chaos

(140.5960) Lasers and laser optics : Semiconductor lasers

(260.3160) Physical optics : Interference

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: December 4, 2012

Revised Manuscript: February 22, 2013

Manuscript Accepted: March 18, 2013

Published: April 2, 2013

**Citation**

Anbang Wang, Yibiao Yang, Bingjie Wang, Beibei Zhang, Lei Li, and Yuncai Wang, "Generation of wideband chaos with suppressed time-delay signature by delayed self-interference," Opt. Express **21**, 8701-8710 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8701

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### References

- 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,” Nature437(7066), 343–346 (2005). [CrossRef] [PubMed]
- A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett.100(19), 194101 (2008). [CrossRef] [PubMed]
- 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. Photonics2(12), 728–732 (2008). [CrossRef]
- I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103(2), 024102 (2009). [CrossRef] [PubMed]
- F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron.10(5), 991–997 (2004). [CrossRef]
- F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron.40(6), 815–820 (2004). [CrossRef]
- Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett.20(19), 1636–1638 (2008). [CrossRef]
- A. B. Wang, M. J. Zhang, H. Xu, and Y. C. Wang, “Location of wire faults using chaotic signal,” IEEE Electron Device Lett.32(3), 372–374 (2011). [CrossRef]
- A. B. Wang, N. Wang, Y. B. Yang, B. J. Wang, M. J. Zhang, and Y. C. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol.30(21), 3420–3426 (2012). [CrossRef]
- A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor Laser with optical feedback,” IEEE Photon. Technol. Lett.20(19), 1633–1635 (2008). [CrossRef]
- K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010). [CrossRef] [PubMed]
- 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]
- Y. Wu, Y. C. Wang, P. Li, A. B. Wang, and M. J. Zhang, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron.48(11), 1371–1379 (2012). [CrossRef]
- R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81(3), 558–561 (1998). [CrossRef]
- A. Uchida, T. Heil, P. Yun Liu, Davis, and T. Aida, “High-frequency broadband signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron.39(11), 1462–1467 (2003). [CrossRef]
- Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett.28(5), 319–321 (2003). [CrossRef] [PubMed]
- A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett.34(8), 1144–1146 (2009). [CrossRef] [PubMed]
- M. J. Zhang, T. G. Liu, P. Li, A. B. Wang, J. Z. Zhang, and Y. C. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photon. Technol. Lett.23(24), 1872–1874 (2011). [CrossRef]
- S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron.48(8), 1069–1076 (2012). [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(20), 2960–2962 (2007). [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. Express18(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. Express17(22), 20124–20133 (2009). [CrossRef] [PubMed]
- N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett.36(23), 4632–4634 (2011). [CrossRef] [PubMed]
- S.-S. Li, Q. Liu, and S.-C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE J. Photonics4(5), 1930–1935 (2012). [CrossRef]
- R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16(3), 347–355 (1980). [CrossRef]
- R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett.36(22), 4332–4334 (2011). [CrossRef] [PubMed]
- A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dary, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800–22 Revision 1a (2010).

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