## Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser

Optics Express, Vol. 18, Issue 7, pp. 6661-6666 (2010)

http://dx.doi.org/10.1364/OE.18.006661

Acrobat PDF (349 KB)

### Abstract

The time delay (TD) signature concealment of optical feedback induced chaos in an external cavity semiconductor laser is experimentally demonstrated. Both the evolution curve and the distribution map of TD signature are obtained in the parameter space of external feedback strength and injection current. The optimum parameter scope of the TD signature concealment is also specified. Furthermore, the approximately periodic evolution relation between TD signature and external cavity length is observed and indicates that the intrinsic relaxation oscillation of semiconductor laser may play an important role during the process of TD signature suppression.

© 2010 OSA

## 1. Introduction

1. R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. **41**(4), 541–548 (2005). [CrossRef]

2. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcıa-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature **437**(7066), 343–346 (2005). [CrossRef]

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

4. 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]

5. 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]

4. 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]

5. 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]

6. M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **54**(4), R3082–3085 (1996). [CrossRef] [PubMed]

7. 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]

8. M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D **203**(3-4), 209–223 (2005). [CrossRef]

## 2. Experimental setup

*I*) by an ultra-low-noise current source (ILX-Lightwave, LDX-3620) and stabilized at 20.14°C by a thermoelectric controller (ILX-Lightwave, LDT-5412). The lasing wavelength of the solitary SL is measured to be about 1549.6nm by an optical spectrum analyzer (Ando AQ6317C). The emission of SL is firstly collimated by an aspheric lens and about 43% of optical energy is incident on an external cavity mirror by a beam splitter (BS). The external feedback strength (

_{th}*F*), defined as the ratio of reflected power and the solitary SL output power, is controlled by a variable neutral density filter and monitored at point T by an optical power meter. An optical isolator (OI) (isolation>55dB) is also used to avoid the unwanted reflected disturbance from the front face of signal detection part. In the signal detection part, the optical signal is firstly transformed into electronic signal by a wide bandwidth photodetector (PD, New Focus 1544-B, bandwidth 12 GHz) and then analyzed by a 6 GHz digital oscilloscope (Agilent 54855A, sample interval 50ps). During experiment, the external cavity length is firstly set as about

_{ext}*L*= 300mm, which corresponds a TD (

_{cav}*T*) of about 2ns.

_{delay}## 3. Experimental results and discussion

*F*≈0.038 and Fig. 2 (B1) for

_{ext}*F*≈0.0013. Both time series behave intricately. However, from the power spectrum (Fig. 2 (A2)) corresponding to

_{ext}*F*≈0.038, some uniform spacing frequency peaks emerge upon the background and reveal the external cavity characteristic frequency

_{ext}*f*≈500MHz. Thus, the value of

_{cav}*T*could be estimated as

_{delay}*T*= 1/

_{delay}*f*≈2 ns. In contrast, for the TD suppressed intensity time series in Fig. 2 (B1), the according power spectrum (Fig. 2 (B2)) becomes relatively smooth and has no significant frequency peaks upon background.

_{cav}11. J. G. Wu, G. Q. Xia, L. P. Cao, and Z.-M. Wu, “Z. and 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**(15), 3153–3156 (2009). [CrossRef]

12. 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]

*T*≈2 ns) is clearly exhibited. Combining all SF and MI curves, one can observe that the TD signatures are gradually suppressed as

_{delay}*F*decreasing from 0.038 to 0.0013. Especially, for the case of

_{ext}*F*≈0.0013 in Figs. 3(D), the TD signature is almost shielded completely into the background fluctuations. In this situation, an eavesdropper would be quite difficult to accurately identify the

_{ext}*T*of the SL dynamical system. Further decreasing

_{delay}*F*to 0.0003 as shown in Fig. 3(E), the TD signature arise reversely again. In addition, the small periodical troughs of SF curves relate closely to the relaxation oscillation of SL [12

_{ext}12. 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]

_{RO}) of SL, and could be estimated as about 0.55ns from Fig. 3(E2).

*F*in a time window of 1.0 ns around

_{ext}*T*. Such a time window is sufficiently large to capture the possible shift of the SF peak and also sufficiently narrow to measure only the SF peak. From these two curves in Fig. 4, the evolution of TD signature could be roughly divided into three regions. For

_{delay}*F*>0.019 (region I), the TD signature is obvious and the identified

_{ext}*T*well conforms to expected

_{delay}*T*≈2ns. For 0.0013<

_{delay}*F*<0.019 (region II), the TD signature attenuates significantly with the decrease of

_{ext}*F*, and the weakest TD signature is obtained for

_{ext}*F*0.003. Meantime, the identified

_{ext}≈*T*begins to deviate from the expected

_{delay}*T*≈2ns. As for

_{delay}*F*<0.0013 (region III), the TD signature booms again. However, the deviation between identified

_{ext}*T*and expected

_{delay}*T*becomes larger than above two regions. These results confirm qualitatively with the theoretical prediction [12

_{delay}12. 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]

*F*values (colored as the dark blue region). We could name it as TD signature suppression (TDSS) region. Additionally, with the increasing of injection current, the TDSS region gradually expands and the minimum TD signature point has a tendency to monotonically move towards a higher

_{ext}*F*level. From Fig. 5(B), it could be observed that the identified

_{ext}*T*always deviates from the expected

_{delay}*T*for

_{delay}*F*bellow a key value about 0.01. Based on these two diagrams, one can specify the optimal parameter scope of chaotic output with weak and pseudo TD signature. Moreover, above results show that weak TD signature region usually locates around relatively low

_{ext}*F*level. However, from the viewpoint of the information dimension of chaotic attractor, low

_{ext}*F*may decrease the Kaplan-Yorke dimension [1

_{ext}1. R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. **41**(4), 541–548 (2005). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. |

2. | A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcıa-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature |

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

4. | 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 |

5. | I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics |

6. | M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

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

8. | M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D |

9. | M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. |

10. | 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 |

11. | J. G. Wu, G. Q. Xia, L. P. Cao, and Z.-M. Wu, “Z. and M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. |

12. | 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. |

13. | 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. |

**OCIS Codes**

(140.5960) Lasers and laser optics : Semiconductor lasers

(190.3100) Nonlinear optics : Instabilities and chaos

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: January 5, 2010

Revised Manuscript: February 5, 2010

Manuscript Accepted: March 9, 2010

Published: March 16, 2010

**Citation**

Jia-Gui Wu, Guang-Qiong Xia, Xi Tang, Xiao-Dong Lin, Tao Deng, Li Fan, and Zheng-Mao Wu, "Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser," Opt. Express **18**, 6661-6666 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-6661

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### References

- R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005). [CrossRef]
- A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcıa-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005). [CrossRef]
- F. Y. Lin and J. M. Liu, “chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40(6), 815–820 (2004). [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]
- 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]
- M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–3085 (1996). [CrossRef] [PubMed]
- 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]
- M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D 203(3-4), 209–223 (2005). [CrossRef]
- M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005). [CrossRef]
- J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009). [CrossRef] [PubMed]
- J. G. Wu, G. Q. Xia, L. P. Cao, and Z.-M. Wu, Z. Wu, and 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(15), 3153–3156 (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(20), 2960–2962 (2007). [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]

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