## Bidirectional chaos communication between two outer semiconductor lasers coupled mutually with a central semiconductor laser |

Optics Express, Vol. 19, Issue 24, pp. 23921-23931 (2011)

http://dx.doi.org/10.1364/OE.19.023921

Acrobat PDF (3436 KB)

### Abstract

Based on a linear chain composed of a central semiconductor laser and two outer semiconductor lasers, chaos synchronization and bidirectional communication between two outer lasers have been investigated under the case that the central laser and the two outer lasers are coupled mutually, whereas there exists no coupling between the two outer lasers. The simulation results show that high-quality and stable isochronal synchronization between the two outer lasers can be achieved, while the cross-correlation coefficients between the two outer lasers and the central laser are very low under proper operation condition. Based on the high performance chaos synchronization between the two outer lasers, message bidirectional transmissions of bit rates up to 20 Gbit/s can be realized through adopting a novel decoding scheme which is different from that based on chaos pass filtering effect. Furthermore, the security of bidirectional communication is also analyzed.

© 2011 OSA

## 1. Introduction

1. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. **64**(8), 821–824 (1990). [CrossRef] [PubMed]

2. I. Fischer, O. Hess, W. Elsaβer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. **73**(16), 2188–2191 (1994). [CrossRef] [PubMed]

37. R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, “Public channel cryptography by synchronization of neural networks and chaotic maps,” Phys. Rev. Lett. **91**(11), 118701 (2003). [CrossRef] [PubMed]

4. S. Tang and J. M. Liu, “Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers,” Opt. Lett. **26**(23), 1843–1845 (2001). [CrossRef] [PubMed]

13. A. Jafari, H. Sedghi, Kh. Mabhouti, and S. Behnia, “Slave-master dynamics of semiconductor laser with short external cavity,” Opt. Commun. **284**(12), 3018–3029 (2011). [CrossRef]

5. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature **438**(7066), 343–346 (2005). [CrossRef] [PubMed]

14. E. Klein, R. Mislovaty, I. Kanter, and W. Kinzel, “Public-channel cryptography using chaos synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **72**(1), 016214 (2005). [CrossRef] [PubMed]

32. V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. **46**(2), 258–264 (2010). [CrossRef]

6. J. Paul, M. W. Lee, and K. A. Shore, “Effect of chaos pass filtering on message decoding quality using chaotic external-cavity laser diodes,” Opt. Lett. **29**(21), 2497–2499 (2004). [CrossRef] [PubMed]

28. I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Zero-lag long-range synchronization via dynamical relaying,” Phys. Rev. Lett. **97**(12), 123902 (2006). [CrossRef] [PubMed]

32. V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. **46**(2), 258–264 (2010). [CrossRef]

## 2. System setup

_{1}) is encoded into the chaotic carrier emitted from OSL1 by using chaos modulation (CM) method [33

33. J. M. Liu, H. F. Chen, and S. Tang, “Synchronized chaotic optical communications at high bit rates,” IEEE J. Quantum Electron. **38**(9), 1184–1196 (2002). [CrossRef]

_{1}) at first. One part is coupled into CSL, and the other part is divided into two parts again by BS

_{2}after passing through an optical isolator (OI

_{1}). One part output from BS

_{2}is injected into photodetector 2 (PD

_{2}) to assist the decoding of message 2 (m

_{2}), while the rest part is transmitted toward the OSL2 side and injects into PD

_{3}through message channel F

_{12}but does not enter into OSL2 because of the existence of OI2. Meantime, a part of signal including m

_{2}and chaotic output from OSL2 injects into PD

_{4}. Through comparing the output of PD

_{3}and PD

_{4}, the difference between m

_{1}and m

_{2}can be obtained under the case that high-quality chaos synchronization between two OSLs has been achieved. Based on this difference, the message m

_{1}can be decoded as long as the message m

_{2}is known. The encoding and decoding process of m

_{2}is the same as that of m

_{1}. As shown in Fig. 1, the messages do not enter into OSLs, therefore the principle of messages decoding is different from that based on chaos pass filtering (CPF) effect.

16. R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. **32**(4), 403–405 (2007). [CrossRef] [PubMed]

29. R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three delay-coupled semiconductor lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **78**(6), 066202 (2008). [CrossRef] [PubMed]

*C,*1 and 2 stand for CSL, OSL1 and OSL2, respectively,

*E*is the complex amplitude of the optical field and

*N*represents the carrier number. |…| denotes the amplitude of the complex field.

*K*,

_{C1}*K*

_{C}_{2}are the coupling strengths from CSL to OSL1 and to OSL2, respectively,

*τ*

_{C}_{1},

*τ*

_{C}_{2}are the corresponding coupling delay.

*K*

_{1C},

*K*

_{2C}are the coupling strengths from OSL1 to CSL and from OSL2 to CSL, respectively, and

*τ*,

_{1C}*τ*is the corresponding coupling delay time.

_{2C}*I*is the pump current,

*τ*is the photon lifetime,

_{p}*τ*is the carrier lifetime,

_{e}*β*is the spontaneous emission rate,

*α*is the line width enhancement factor,

*f*is the oscillated frequency of laser at free-running, and

*e*is the electronic charge constant. The nonlinear gain function

*G*is given by

*G = g*(

*N-N*)/[

_{0}*1 + ε |E |*], where

^{2}*g*is the differential gain,

*ε*is the saturation coefficient, and

*N*is the carrier number at the transparency. The frequency detuning between CSL and OSLs is defined as

_{0}*Δf*

_{C}_{1}

_{, C}_{2}

*= f*

_{C}-f_{1}

_{,}_{2}, and the frequency detuning between OSL1 and OSL2 defined as

*Δf*

_{12}

*= f*

_{1}

*-f*

_{2}, χ is Gaussian white noise sources with zero-mean and correlation

34. T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. **86**(5), 795–798 (2001). [CrossRef] [PubMed]

*C*(Δ

_{ij}*t*) [35

35. J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. **40**(6), 640–650 (2004). [CrossRef]

*i*,

*j*( = 1, 2, c) stand for different lasers. The bracket < > denotes the time average,

*Δt*is the time shift, and

*P*(

*t*) is the output intensity and is equals to |

*E*(

*t*)|

^{2}. |

*C*|ranges from 0 to 1, |

_{ij}*C*| = 1 enables a perfect synchronization. If the corresponding time shift of the maximum of cross-correlation Δ

_{ij}*t*

_{max}is positive, laser

*i*is leading to laser

*j*by Δ

*t*

_{max}and vice versa.

*Q*-factor. Here, the

*Q*-factor is defined as [36

36. D. Kanakidis, A. Argyris, and D. Syvridis, “Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration,” J. Lightwave Technol. **21**(3), 750–758 (2003). [CrossRef]

*P*

_{1}〉 and 〈

*P*

_{0}〉 are the average optical powers of bits “1”and “0”, respectively, while σ

_{1}and σ

_{0}are the corresponding standard deviations.

## 3. Results and discussion

*f*

_{1}

*= f*

_{2}

*=*1.94 × 10

^{14}Hz,

*f*= 1.9398 × 10

_{C}^{14}Hz,

*g*

_{C}= g_{1}

*= g*

_{2}= 1.5 × 10

^{4}s

^{−1},

*ε*

_{C}= ε_{1}

*= ε*

_{2}= 5 × 10

^{−7},

*α*

_{C}= α_{1}

*= α*

_{2}= 5,

*τ*= 2ps,

_{p}*τ*2ns,

_{e}=*β*= 1 × 10

^{3}s

^{−1},

*N*= 1.5 × 10

_{0}^{8},

*I*= 36.75mA,

*e*= 1.602 × 10

^{−19}C. The coupling delay times are assumed to be identical in the two coupling branches:

*τ*

_{C}_{1}

*= τ*

_{C}_{2}

*= τ*

_{1}

*=*

_{C}*τ*

_{2}

*= 5ns, and for any pair of mutual coupled lasers, the coupling strength was such that K*

_{C}

_{C}_{1}= K

_{C}_{2}, K

_{1C}= K

_{2C}.

### 3.1. Chaos synchronization

*C*(a) and

_{1C}*C*(b) as a function of

_{12}*K*and

_{1C}*K*. During the simulations, all the parameters of three SLs are identical except that there exists a frequency detuning

_{C1}*Δf*

_{C1}= Δf_{C2}=**20GHz between CSL and OSLs. Under this condition, all the outputs of three lasers are rendered into chaotic states when**

*-**K*and

_{1C}*K*vary in the range of 10ns

_{C1}^{−1}−60ns

^{−1}. As seen from Fig. 2 (b), good synchronization between two OSLs is always maintained and the influences of

*K*and

_{1C}*K*on synchronization quality are very weak. However, the synchronization quality between OSL1 and CSL is depended strongly on

_{C1}*K*and

_{1C}*K*(see Fig. 2 (a)). Thus, the synchronization quality between OSL1 and CSL can be controlled easily through adjusting

_{C1}*K*and

_{1C}*K*. In order to guarantee high security of messages transmission in this system, the maximum of

_{C1}*C*is expected to be as low as possible. Combing the requirement of high-quality synchronization between two OSLs, an optimal point (labeled as point A in Fig. 2 (a)) can be determined in the parameter space, and the corresponding values of

_{1C}*K*and

_{1C}*K*are 13ns

_{C1}^{−1}and 16ns

^{−1}, respectively. Due to the symmetry of system configuration, the map of the maximum of

*C*in the parameter space of

_{2C}*K*and

_{1C}*K*is similar to Fig. 2 (a).

_{C1}*K*=

_{C1}*K*= 16ns

_{C2}^{−1}and

*K*=

_{1C}*K*= 13ns

_{2C}^{−1}. As seen from Fig. 3 (a1-a3), zero-lag high-quality synchronization between OSL1 and OSL2 can be obtained, where the maximum

*C*= 1 presents at

_{12}*Δt*= 0. On the contrary, from Fig. 3(b1-b3) and (c1-c3), it can be seen that the time series of OSLs are quite different from that of CSL, and the maximum of

*C*is smaller than 0.2 which is much lower than that obtained in Ref [32

_{1C}32. V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. **46**(2), 258–264 (2010). [CrossRef]

### 3.2. Influences of parameter mismatches between OSLs

_{1c}-τ

_{2c}= τ

_{c1}-τ

_{2c}) under τ

_{2c}= τ

_{c2}= 5ns. From this diagram, it can be seen that the synchronization quality is not sensitive to Δτ, and high-quality chaos synchronization between two OSLs can be maintained while the synchronization quality between the CSL and the OSLs is still low. Theoretically, the CSL can locate at such places that this system is convenience to construct and monitor. However, it should be pointed out that above conclusion is drawn only for the short distance coupling case. In practice, we expect that bidirectional long distance secret communication between the two OSLs can be realized via by fiber. Accordingly, the coupling from the CSL to two OSLs may be performed via by long distance fiber. Under these circumstances, if asymmetrical coupling from the CSL to two OSLs is used, the chaos synchronization performance between the two OSLs may worsen due to two different length fiber channels from the CSL to two OSLs. Therefore, the coupling time difference between τ

_{c1}and τ

_{c2}should be as small as possible in reality. Figure 4(b-d) are the cross-correction function between arbitrary two SLs under τ

_{1c}= τ

_{c1}= 3ns and τ

_{2c}= τ

_{c2}= 5ns. Different from the case for symmetric coupling times (see Fig. 3(a3)), the chaos synchronization between two OSLs is not zero-lag synchronization, and the maximum cross-correction coefficient is located at −2ns, which is just equal to τ

_{1c}-τ

_{2c}.

*g*and

_{,}ε*α*of OSL2 and fixing the corresponding parameters of OSL1 and CSL. As a result, the relative parameter mismatches are defined as:

*α*on the synchronization quality between two OSLs is the most severe. These sensitivities of synchronization quality to mismatched parameters are necessary to guarantee the security of communication. At the meantime, as shown in Fig. 5 (b)-(c), one can observe that the cross-correlations between CSL and OSLs always keep smaller than 0.2 for parameter mismatches are varied within the rang of −10%-10%.

### 3.3. Influences of parameter mismatches between CSL and OSLs

*g*and

_{,}ε*α*are defined as:

### 3.4. Bidirectional chaos communication

*F*and

_{12}*F*. At the receiver side, encoded messages are decoded by subtracting the signal of sender from the signal of receiver. It is worth noting that the signals, emitted from one OSL and mixed with message, do not inject into the other OSL, so the principle of messages decoding is not based on chaos pass filtering (CPF) effect. Therefore, the bandwidth limitation induced by CPF is invalid in this system, and then high communication rate may be realized.

_{21}*Q*-factor evolution is given in Fig. 8(a) as a function of message bit rate, and the eye diagrams of message transmission at 5Gbits/s, 10Gbits/s and 15Gbits/s are given in Figs. 8(b)-(d), respectively. It should be noted that the

*Q*-factor always keeps at a high level (above 11) and degrades small with increasing bit rate. The main reason is that the messages do not enter OSLs and the transmission rate of message is not limited by CPF effect, so high bit rate and high

*Q*-factor bidirectional secure communication can be accomplished in this system.

## 4. Conclusions

## Acknowledgements

## References and links

1. | L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. |

2. | I. Fischer, O. Hess, W. Elsaβer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. |

3. | G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science |

4. | S. Tang and J. M. Liu, “Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers,” Opt. Lett. |

5. | 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 |

6. | J. Paul, M. W. Lee, and K. A. Shore, “Effect of chaos pass filtering on message decoding quality using chaotic external-cavity laser diodes,” Opt. Lett. |

7. | G. Q. Xia, Z. M. Wu, and J. G. Wu, “Theory and simulation of dual-channel optical chaotic communication system,” Opt. Express |

8. | J. Ohtsubo, |

9. | Y. H. Hong, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, “GHz bandwidth message transmission using chaotic vertical-cavity surface-emitting lasers,” J. Lightwave Technol. |

10. | 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. |

11. | 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 |

12. | J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express |

13. | A. Jafari, H. Sedghi, Kh. Mabhouti, and S. Behnia, “Slave-master dynamics of semiconductor laser with short external cavity,” Opt. Commun. |

14. | E. Klein, R. Mislovaty, I. Kanter, and W. Kinzel, “Public-channel cryptography using chaos synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

15. | E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

16. | R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. |

17. | W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. |

18. | M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. |

19. | B. B. Zhou and R. Roy, “Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

20. | T. Deng, G. Q. Xia, L. P. Cao, J. G. Chen, X. D. Lin, and Z. M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. |

21. | A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. |

22. | N. Jiang, W. Pan, L. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. |

23. | T. Deng, G. Q. Xia, Z. M. Wu, X. D. Lin, and J. G. Wu, “Chaos synchronization in mutually coupled semiconductor lasers with asymmetrical bias currents,” Opt. Express |

24. | J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. |

25. | R. V. Jensen, “Synchronization of randomly driven nonlinear oscillators,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

26. | C. S. Zhou, J. Kurths, E. Allaria, S. Boccaletti, R. Meucci, and F. T. Arecchi, “Constructive effects of noise in homoclinic chaotic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

27. | A. Uchida, R. McAllister, and R. Roy, “Consistency of nonlinear system response to complex drive signals,” Phys. Rev. Lett. |

28. | I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, “Zero-lag long-range synchronization via dynamical relaying,” Phys. Rev. Lett. |

29. | R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three delay-coupled semiconductor lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

30. | T. Yamamoto, I. Oowada, H. Yip, A. Uchida, S. Yoshimori, K. Yoshimura, J. Muramatsu, S. I. Goto, and P. Davis, “Common-chaotic-signal induced synchronization in semiconductor lasers,” Opt. Express |

31. | I. Oowada, H. Ariizumi, M. Li, S. Yoshimori, A. Uchida, K. Yoshimura, and P. Davis, “Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback,” Opt. Express |

32. | V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. |

33. | J. M. Liu, H. F. Chen, and S. Tang, “Synchronized chaotic optical communications at high bit rates,” IEEE J. Quantum Electron. |

34. | T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. |

35. | J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, “Multimode synchronization and communication using unidirectionally coupled semiconductor lasers,” IEEE J. Quantum Electron. |

36. | D. Kanakidis, A. Argyris, and D. Syvridis, “Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration,” J. Lightwave Technol. |

37. | R. Mislovaty, E. Klein, I. Kanter, and W. Kinzel, “Public channel cryptography by synchronization of neural networks and chaotic maps,” Phys. Rev. Lett. |

**OCIS Codes**

(060.4510) Fiber optics and optical communications : Optical communications

(140.5960) Lasers and laser optics : Semiconductor lasers

(190.3100) Nonlinear optics : Instabilities and chaos

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: June 24, 2011

Revised Manuscript: October 5, 2011

Manuscript Accepted: October 27, 2011

Published: November 10, 2011

**Citation**

Ping Li, Jia-Gui Wu, Zheng-Mao Wu, Xiao-Dong Lin, Dao Deng, Yu-Ran Liu, and Guang-Qiong Xia, "Bidirectional chaos communication between two outer semiconductor lasers coupled mutually with a central semiconductor laser," Opt. Express **19**, 23921-23931 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23921

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### References

- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett.64(8), 821–824 (1990). [CrossRef] [PubMed]
- I. Fischer, O. Hess, W. Elsaβer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett.73(16), 2188–2191 (1994). [CrossRef] [PubMed]
- G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science279(5354), 1198–1200 (1998). [CrossRef] [PubMed]
- S. Tang and J. M. Liu, “Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers,” Opt. Lett.26(23), 1843–1845 (2001). [CrossRef] [PubMed]
- 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,” Nature438(7066), 343–346 (2005). [CrossRef] [PubMed]
- J. Paul, M. W. Lee, and K. A. Shore, “Effect of chaos pass filtering on message decoding quality using chaotic external-cavity laser diodes,” Opt. Lett.29(21), 2497–2499 (2004). [CrossRef] [PubMed]
- G. Q. Xia, Z. M. Wu, and J. G. Wu, “Theory and simulation of dual-channel optical chaotic communication system,” Opt. Express13(9), 3445–3453 (2005). [CrossRef] [PubMed]
- J. Ohtsubo, Semiconductor Lasers, Stability, Instability and Chaos, 2nd ed. (Springer-Verlag, 2008).
- Y. H. Hong, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, “GHz bandwidth message transmission using chaotic vertical-cavity surface-emitting lasers,” J. Lightwave Technol.27(22), 5099–5105 (2009). [CrossRef]
- 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]
- 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]
- J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express17(15), 12619–12626 (2009). [CrossRef] [PubMed]
- A. Jafari, H. Sedghi, Kh. Mabhouti, and S. Behnia, “Slave-master dynamics of semiconductor laser with short external cavity,” Opt. Commun.284(12), 3018–3029 (2011). [CrossRef]
- E. Klein, R. Mislovaty, I. Kanter, and W. Kinzel, “Public-channel cryptography using chaos synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(1), 016214 (2005). [CrossRef] [PubMed]
- E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(4), 046201 (2006). [CrossRef] [PubMed]
- R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett.32(4), 403–405 (2007). [CrossRef] [PubMed]
- W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett.33(3), 237–239 (2008). [CrossRef] [PubMed]
- M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron.41(11), 1333–1340 (2005). [CrossRef]
- B. B. Zhou and R. Roy, “Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(2), 026205 (2007). [CrossRef] [PubMed]
- T. Deng, G. Q. Xia, L. P. Cao, J. G. Chen, X. D. Lin, and Z. M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun.282(11), 2243–2249 (2009). [CrossRef]
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