## Noise suppressions in synchronized chaos lidars |

Optics Express, Vol. 18, Issue 25, pp. 26155-26162 (2010)

http://dx.doi.org/10.1364/OE.18.026155

Acrobat PDF (1711 KB)

### Abstract

The noise suppressions in the chaos lidar (CLIDAR) and the synchronized chaos lidar (S-CLIDAR) systems with the optoelectronic feedback (OEF) and optical feedback (OF) schemes are studied numerically. Compared with the CLIDAR system, the S-CLIDAR system with the OEF scheme has better correlation coefficients in the large noise regime for SNR < 15 dB. For the S-CLIDAR system with the OF scheme, better detections are also achieved in wide ranges depending on the levels of the phase noise presented in the channel. To have the best synchronization and detection quality, the optimized conditions for the coupling and feedback strengths in the S-CLIDAR system are also discussed.

© 2010 Optical Society of America

## 1. Introduction

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

2. T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. **55**, 1711–1714 (1985). [CrossRef] [PubMed]

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

4. F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. **39**, 562–568 (2003). [CrossRef]

5. S. Tang and J. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. **37**, 329–336 (2001). [CrossRef]

6. F. Y. Lin and J. M. Liu, “Harmonic frequency locking in a semiconductor laser with delayed negative optoelectronic feedback,” Appl. Phys. Lett. **81**, 3128–3130 (2002). [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. V. Annovazzi-Lodi, A. Scire, M. Sorel, and S. Donati, “Dynamic behavior and locking of a semiconductor laser subjected to external injection,” IEEE J. Quantum Electron. **34**, 2350–2357 (1998). [CrossRef]

9. S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. **172**, 279–295 (1999). [CrossRef]

10. N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. **22**, 1382–1386 (1983). [CrossRef] [PubMed]

11. C. Nagasawa, M. Abo, H. Yamamoto, and O. Uchino, “Random modulation cw lidar using new random sequence,” Appl. Opt. **29**, 1466–1470 (1990). [CrossRef] [PubMed]

12. Y. Emery and C. Flesia, “Use of the a1- and the a2-sequences to modulate continuous-wave pseudorandom noise lidar,” Appl. Opt. **37**, 2238–2241 (1998). [CrossRef]

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

13. V. AnnovazziLodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-laser systems and its application to optical cryptography,” IEEE J. Quantum Electron. **32**, 953–959 (1996). [CrossRef]

## 2. Model

*η*and the delay time

_{R}*τ*, where

_{R}*η*= 0 represents cases when the Rx is in an open-loop configuration and

_{R}*η*≠ 0 represents the cases when the Rx is in a close-loop configuration.

_{R}*a*is the normalized optical field,

*ϕ*is the optical phase,

*ñ*is the normalized carrier density,

*J̃*is the normalized dimensionless injection current parameter,

*γ*

_{c}is the cavity decay rate,

*γ*

_{n}is the differential carrier relaxation rate,

*γ*

_{p}is the nonlinear carrier relaxation rate,

*γ*

_{s}is the spontaneous carrier relaxation rate,

*b*is the linewidth enhancement factor,

*η*is the coupling rate,

*τ*is the delay time, and Δ

*ω*is the angular frequency detuning between the Tx and Rx. The subscripts T, R, and C denote the Tx, Rx, and channel, respectively. The laser parameters used here are

*b*= 4,

*γ*

_{n}= 0.667 × 10

^{9}

*s*

^{−1},

*γ*

_{p}= 1.2 × 10

^{9}

*s*

^{−1},

*γ*

_{s}= 1.458 × 10

^{9}

*s*

^{−1},

*γ*

_{c}= 2.4 × 10

^{11}

*s*

^{−1}, Δ

*ω*= 0, and

*J̃*= 0.333 [14

14. T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in fabry–perot semiconductor lasers,” J. Appl. Phys. **73**, 2587–2589 (1993). [CrossRef]

*π*,

*π*], the amplitude and phase noise are added to the respective amplitude

*a*

_{C}(

*t*) and the phase

*ϕ*

_{C}(

*t*) of the received signals, The relative strength of the amplitude noise is defined by the signal-to-noise ratio (SNR) where

*P*

_{s}is the average power of the transmitted signal. The influence of the phase noise is controlled by

*m*, where

*m*= 0 is the case when no phase noise is considered.

*S*

_{T}(

*t*) and

*S*

_{R}(

*t*) are the intensity outputs of the transmitter (yellow dot) and the receiver (blue dot), 〈·〉 denotes the time average, and Δ

*τ*is the relative time difference between the transmitter and the receiver, respectively. The correlation coefficient is bounded with −1 ≤

*ρ*≤ 1, where a larger value of |

*ρ*| indicates better quality of detection.

## 3. Results and discussions

*τ*

_{T}= 9.5 ns and a feedback strength

*η*

_{OEF,T}= 0.123, respectively. For the S-CLIDAR system with the OEF scheme, since the backscattered light is converted to the electric signal before coupling to the Rx, little effect of the phase noise from the channel is found. Under the influence of the amplitude noise with SNR = 0 dB, the detected waveforms in the receivers and their corresponding correlations to the transmitted waveform for the CLIDAR and the S-CLIDAR systems are shown in Figs. 2(c)–(f), respectively. As can be seen, compared with the received waveform in the CLIDAR system that is noisy and severely distorted from the transmitted waveform, the waveform reproduced by the Rx through synchronization in the S-CLIDAR system has little distortion. Correlation coefficients of 0.73 and 0.97 are obtained for the CLIDAR and the S-CLIDAR systems at a delay of 15.5 ns, which is the range delay of the target in the transmission channel

*τ*

_{C}= 15.5 ns under the generalized synchronized condition. Note that, to have the best synchronization for the highest possible correlation coefficient, the coupling strength

*η*

_{OEF,C}and the feedback strength

*η*

_{OEF,R}of the S-CLIDAR system have to be optimized with different levels of noise presented in the channel. Through simulations, for SNR = 0 dB, optimized coupling strength and feedback strength of

*η*

_{OEF,C}= 1.3 and

*η*

_{OEF,R}= 0 are found showing that the S-CLIDAR system has a better synchronization performance under a generalized synchronization condition with an open-loop configuration. Detailed investigations on the optimized coupling strengths under different SNRs for the S-CLIDAR systems with the OEF and the OE schemes will be discussed and given in Fig. 6.

*τ*

_{T}= 9.5 ns and a feedback strength

*η*

_{OF,T}= 0.2, respectively. Unlike in the OEF scheme, the phase noise is found to affect the synchronization significantly in the Rx for the S-CLIDAR system with the OF scheme. With SNR = 0 dB, Figs. 3(c)–(j) show the time series of the detected waveforms and their corresponding correlations to the transmitted waveform for the CLIDAR and the S-CLIDAR systems with the phase noise levels of

*m*= 0, 0.5, and 0.75, respectively. As can be seen, although not being affected by the phase noise, the detected waveform of the CLIDAR system as shown in Fig. 3(c) is distorted severely from the transmitted waveform solely because of the influence of the amplitude noise where a correlation coefficient of only 0.36 is found. On the contrary, the S-CLIDAR system shows good ability in filtering both the amplitude and the phase noises, where correlation coefficients of 0.88, 0.82, and 0.53 are achieved for phase noise levels of

*m*= 0, 0.5, and 0.75, respectively.

*m*= 0, the performance degrades as the level of phase noise increases. For −17 dB < SNR < 15 dB, the correlation coefficient of the CLIDAR system drops quickly even when only affecting by the amplitude noise. Meanwhile, the correlation coefficients of the S-CLIDAR system stay at higher levels benefitted by the synchronization process.

*m*= 0). While the range of suppression gradually decreases as the level of the phase noise increases, suppression ranges of 29.1 and 22.4 dB are still obtained for m = 0.5 and 0.75 in a low SNR regime similar to practical scenarios [15

15. A. B. Utkin, A. Lavrov, and R. Vilar, “Laser rangefinder architecture as a cost-effective platform for lidar fire surveillance,” Opt. Laser Technol. **41**, 862–870 (2009). [CrossRef]

16. T. Cossio, K. Slatton, W. Carter, K. Shrestha, and D. Harding, “Predicting topographic and bathymetric measurement performance for low-snr airborne lidar,” IEEE Trans. Geosci. Remote Sensing **47**, 2298–2315 (2009). [CrossRef]

*η*

_{OEF,C}and

*η*

_{OF,C}for different noise levels, respectively. For the OEF scheme in a low noise regime with SNR > 15 dB, a larger

*η*

_{OEF,C}is desired for better synchronization. As the level of noise increases to SNR < 15 dB, the optimized coupling strength decreases as the noise level increases. In this regime, a strong coupling couples too much noise into the Rx and causes the degradation in synchronization. For the OF scheme, a larger

*η*

_{OF,C}is also desired in the low noise regime when the phase noise is not presented (

*m*= 0). When the phase noise is notable (

*m*= 0.5 and 0.75) or when the amplitude noise increases (lower SNR), lower the coupling strengths are required for optimal synchronization and target detections.

## 4. Conclusions

## Acknowledgments

## References and links

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

2. | T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. |

3. | B. T. J. Mork and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. |

4. | F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. |

5. | S. Tang and J. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. |

6. | F. Y. Lin and J. M. Liu, “Harmonic frequency locking in a semiconductor laser with delayed negative optoelectronic feedback,” Appl. Phys. Lett. |

7. | F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. |

8. | V. Annovazzi-Lodi, A. Scire, M. Sorel, and S. Donati, “Dynamic behavior and locking of a semiconductor laser subjected to external injection,” IEEE J. Quantum Electron. |

9. | S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. |

10. | N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. |

11. | C. Nagasawa, M. Abo, H. Yamamoto, and O. Uchino, “Random modulation cw lidar using new random sequence,” Appl. Opt. |

12. | Y. Emery and C. Flesia, “Use of the a1- and the a2-sequences to modulate continuous-wave pseudorandom noise lidar,” Appl. Opt. |

13. | V. AnnovazziLodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-laser systems and its application to optical cryptography,” IEEE J. Quantum Electron. |

14. | T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in fabry–perot semiconductor lasers,” J. Appl. Phys. |

15. | A. B. Utkin, A. Lavrov, and R. Vilar, “Laser rangefinder architecture as a cost-effective platform for lidar fire surveillance,” Opt. Laser Technol. |

16. | T. Cossio, K. Slatton, W. Carter, K. Shrestha, and D. Harding, “Predicting topographic and bathymetric measurement performance for low-snr airborne lidar,” IEEE Trans. Geosci. Remote Sensing |

**OCIS Codes**

(010.3640) Atmospheric and oceanic optics : Lidar

(140.1540) Lasers and laser optics : Chaos

(140.5960) Lasers and laser optics : Semiconductor lasers

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: October 13, 2010

Revised Manuscript: November 24, 2010

Manuscript Accepted: November 26, 2010

Published: November 30, 2010

**Citation**

Wen-Ting Wu, Yi-Huan Liao, and Fan-Yi Lin, "Noise suppressions in synchronized chaos lidars," Opt. Express **18**, 26155-26162 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-25-26155

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### References

- F. Y. Lin, and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004). [CrossRef]
- T. Mukai, and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscil- lation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. 55, 1711–1714 (1985). [CrossRef] [PubMed]
- B. T. J. Mork, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992). [CrossRef]
- F. Y. Lin, and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39, 562–568 (2003). [CrossRef]
- S. Tang, and J. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37, 329–336 (2001). [CrossRef]
- F. Y. Lin, and J. M. Liu, “Harmonic frequency locking in a semiconductor laser with delayed negative optoelectronic feedback,” Appl. Phys. Lett. 81, 3128–3130 (2002). [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]
- V. Annovazzi-Lodi, A. Scire, M. Sorel, and S. Donati, “Dynamic behavior and locking of a semiconductor laser subjected to external injection,” IEEE J. Quantum Electron. 34, 2350–2357 (1998). [CrossRef]
- S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279–295 (1999). [CrossRef]
- N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. 22, 1382–1386 (1983). [CrossRef] [PubMed]
- C. Nagasawa, M. Abo, H. Yamamoto, and O. Uchino, “Random modulation cw lidar using new random sequence,” Appl. Opt. 29, 1466–1470 (1990). [CrossRef] [PubMed]
- Y. Emery, and C. Flesia, “Use of the a1- and the a2-sequences to modulate continuous-wave pseudorandom noise lidar,” Appl. Opt. 37, 2238–2241 (1998). [CrossRef]
- V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-laser systems and its application to optical cryptography,” IEEE J. Quantum Electron. 32, 953–959 (1996). [CrossRef]
- T. B. Simpson, and J. M. Liu, “Phase and amplitude characteristics of nearly degenerate four-wave mixing in fabry–perot semiconductor lasers,” J. Appl. Phys. 73, 2587–2589 (1993). [CrossRef]
- A. B. Utkin, A. Lavrov, and R. Vilar, “Laser rangefinder architecture as a cost-effective platform for lidar fire surveillance,” Opt. Laser Technol. 41, 862–870 (2009). [CrossRef]
- T. Cossio, K. Slatton, W. Carter, K. Shrestha, and D. Harding, “Predicting topographic and bathymetric measurement performance for low-snr airborne lidar,” IEEE Trans. Geosci. Rem. Sens. 47, 2298–2315 (2009). [CrossRef]

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