## Theory and simulation of dual-channel optical chaotic communication system

Optics Express, Vol. 13, Issue 9, pp. 3445-3453 (2005)

http://dx.doi.org/10.1364/OPEX.13.003445

Acrobat PDF (1707 KB)

### Abstract

A theoretical model based on a novel experiment scheme of dual-channel optical chaotic communication has been presented, and is proved to be reasonable by comparing the numerical simulations with the experimental results. After deducing the transmission function of semiconductor laser by small-signal analysis, how to reasonably select the system parameters has been given in order to realize the effective transmission of signal. Moreover, the cross talk between two channels has been analyzed quantitatively. For a 250MHz modulation message, the numerical simulation shows that it can be hidden efficiently during the transmission and decoded easily in the receiver.

© 2005 Optical Society of America

## 1. Introduction

1. G. D. Van Wiggeren and R. Roy, “Communication with chaotic lasers,” Science **279**, 1198–1200 (1998). [CrossRef]

6. J. Paul, S. Sivaprakasam, and K. A. Shore, “Dual-channel chaotic optical communications using external-cavity semiconductor lasers,” J. Opt. Soc. Am. B **21**, 514–521 (2004). [CrossRef]

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

5. J. Paul, S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, “GHz bandwidth message transmission using chaotic diode lasers,” Electron. Lett. **38**, 28–29 (2002). [CrossRef]

7. L. S. Tsimring and M. M. Sushchik, “Multiplexing chaotic signals using synchronization,” Phys. Lett. A **213**, 155–166 (1996). [CrossRef]

8. Y. Liu and P. Davis, “Dual synchronization of chaos,” Phys. Rev. E **61**, 2176–2179 (2000). [CrossRef]

6. J. Paul, S. Sivaprakasam, and K. A. Shore, “Dual-channel chaotic optical communications using external-cavity semiconductor lasers,” J. Opt. Soc. Am. B **21**, 514–521 (2004). [CrossRef]

9. E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, “Dual and dual-cross synchronizations in chaotic systems,” Opt. Commun. **216**, 179–183 (2003). [CrossRef]

6. J. Paul, S. Sivaprakasam, and K. A. Shore, “Dual-channel chaotic optical communications using external-cavity semiconductor lasers,” J. Opt. Soc. Am. B **21**, 514–521 (2004). [CrossRef]

**21**, 514–521 (2004). [CrossRef]

**21**, 514–521 (2004). [CrossRef]

## 2. Theoretical model

*T*(its subscripts 1, 2 represent two different channels, respectively),

*D*and

*R*correspond to the transmitter laser, decoder laser and receiver laser, respectively,

*E*is the slowly varying field amplitude,

*Φ*is the slowly varying phase,

*N*is the carrier number,

*N*

_{0}is the carrier number at transparency,

*G*=

*g*(

*N*-

*N*

_{0})/(1+

*E*

^{2}/

*g*is the differential gain coefficient,

*E*

_{s}is the saturation field amplitude),

*α*is the line-width enhancement factor,

*γ*

_{P}is the photon loss rate,

*γ*

_{e}is the total carrier loss rate,

*τ*

_{L}is the roundtrip time in laser cavity,

*τ*

_{T}is the roundtrip time in external cavity,

*τ*

_{D}is the transmission time between RL and DEC,

*k*

_{T}is the feedback coefficient of the transmitter lasers,

*k*

_{D}is the injection coefficient from RL to DEC,

*β*is the spontaneous emission rate,

*ω*is the angular frequency of the lasers,

*J*represents the injection carrier rate, ζ is the unity intensity Langevin noise.

*et al.*have carried out the theoretical and experimental investigations about a single-mode laser subject to external light injection form several lasers [11

11. J. Troger, L. Thevenaz, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. **17**, 629–636 (1999) [CrossRef]

11. J. Troger, L. Thevenaz, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. **17**, 629–636 (1999) [CrossRef]

*k*

_{ij}(

*i*,

*j*=1,2) indicates the injection coefficient of TL

_{j}to RL

_{i}, and then the rate equations of RL can be expressed as

*E*

_{R1,R2}(

*t*),

*Φ*

_{R1,R2}(

*t*) and

*N*

_{R1,R2}(

*t*) are the electrical amplitude, the phase and the carrier density, respectively, the subscripts

*R1*and

*R2*indicate the received system synchronized with TL1 or TL2, respectively, (

*Δω*)

_{R1,R2}is the angular frequency deviation between TL1 and TL2, (

*Δω*)

*R*

_{1}=

*ω*

_{R}-

*ω*

_{1}, (

*Δω*)

*R*

_{2}=

*ω*

_{R}-

*ω*

_{2},

*τ*

_{inj}is the transmission time from TL to RL. In this paper, in order to make the theory be suitable for the case of small channel interval, the effect of the cross injection has been taken into account though it can be ignored for the case of large channel interval. If the system is assumed to be symmetric for the two channels, matrix

*k*

_{inj}is the injection coefficient of the same channel, and

*k*

_{cro}is the cross injection coefficient between two different channels, then Eq. (2) can be divided into two identical equations. When the received system synchronizes with TL1, Eq. (2) can be expressed as:

## 3. Transmission function

12. S. Tang, H. F. Chen, S. K. Hwang, and J. M. Liu, “Message encoding and decoding through chaos modulation in chaotic optical communications,” IEEE Trans. Circuits Syst. I **49**, 163–169 (2002). [CrossRef]

13. S. Sivaprakasam and K. A. Shore, “Message encoding and decoding using chaotic external-cavity diode lasers,” IEEE J. Quantum Electron. **36**, 35–39 (2000). [CrossRef]

14. A. Uchida, Y. Liu, and P. Davis, “Characteristics of chaotic masking in synchronized semiconductor lasers,” IEEE J. Quantum Electron. **39**, 963–970 (2003). [CrossRef]

*δE*

_{1}(

*t*), then

15. S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, “Regimes of chaotic synchronization in external-cavity laser diodes,” IEEE J. Quantum Electron. **38**, 1155–1160 (2002). [CrossRef]

*Φ*

_{R2}can be ignored. Taking the Laplace transform to Eq. (4), the complex transmission function is

## 4. Results and discussion

### 4.1Chaos synchronization of lasers in the same channel

*g*=3.2×10

^{3}s

^{-1},

*α*=3.0,

*N*

_{0}=1.25×10

^{8},

*E*

_{s}=2.0352×10

^{3},

*γ*

_{P}=2.38×10

^{11}s

^{-1},

*γ*

_{e}=6.21×10

^{8}s

^{-1},

*τ*

_{L}=8.5ps,

*τ*=4ns,

*τ*

_{inj}=4ns,

*τ*

_{D}=4ns,

*β*=5×10

^{2}s

^{-1},

*f*

_{1}=

*ω*

_{1}/2

*π*=1.9355×10

^{5}GHz,

*f*

_{2}=

*ω*

_{2}/2

*π*=1.9345×10

^{5}GHz,

*k*

_{1}=

*k*

_{inj}=

*k*

_{D}=0.187,

*J*/

*J*

_{th}=1.059 (where

*J*

_{th}is the threshold injection carrier rate,

*J*

_{th}=1.99×10

^{8}s

^{-1}), (

*Δf*)

_{D}=(

*Δω*)

_{D}/

*2π*=0GHz, Δ

*f*

_{R1}=(Δ

*ω*)

_{R1}/2

*π*=0GHz, Δ

*f*

_{R2}=(Δ

*ω*)

_{R2}/2

*π*=100GHz. Figures 2(a)-2(d) give the chaotic temporal waveforms, the chaotic attractors of TL1, synchronization errors of TL1 to RL, and synchronization errors of TL1 to DEC, respectively. From these diagrams, it can be seen that both RL and DEC can be synchronized with TL1 after experiencing a transient process (about 10-20ns), which is coincided with the experimental results in Ref. [16

16. S. Sivaprakasam and K. A. Shore, “Cascaded synchronization of external-cavity laser diodes,” Opt. Lett. **66**, 253–255 (2001). [CrossRef]

## 4.2 Analysis of signal transmission function

*k*

_{inj}, the frequency detuning Δ

*f*

_{R1}and Δ

*f*

_{R2}. Figure 3 shows the transmission functions for different

*k*

_{inj}, Δ

*f*

_{R1}and Δ

*f*

_{R2}. The data used in calculation are: Δ

*f*

_{R1}=Δ

*f*

_{D}=0GHz, Δ

*f*

_{R2}=Δ

*f*

_{R1}+100GHz,

*J*/

*J*

_{th}=1.059,

*k*

_{cro}=0.1×

*k*

_{inj},

*k*

_{1}=

*k*

_{inj}=

*k*

_{D}=

*k*, and the other data are the same as Fig. 2. From this diagram, it can be seen that, for different

*k*, Δ

*f*

_{R1}and Δ

*f*

_{R2}, the transmittance curves have different distributions and frequency resonant humps, so the quantity of the attenuation in the RL can be adjusted through changing

*k*and Δ

*f*

_{R1}. With the same method, the transmission function of the DEC can also be obtained. Because the DEC has the similar parameters as the RL, the transmission function of the DEC has the similar behaviors as Fig. 3. As mentioned above, the demodulation of message is achieved by comparing the intensity difference between the input and output of DEC, and then the attenuation of message in the DEC is necessary (i.e., the transmittance should be smaller than 0dB). Therefore, for given

*k*and Δ

*f*

_{R1}, the suitable range of the message frequency can be roughly estimated from this diagram.

## 4.3 Numerical analysis of cross talk between two channels

*C*is, the higher quality of synchronization will be. If C is equal to 1, the system is synchronized completely. As shown in Fig. 4, the quality of synchronization decreases with the increase of the

*k*

_{cro}/

*k*

_{inj}value. When

*k*

_{cro}/

*k*

_{inj}varies within the regime of 0~0.3, the system is well synchronized (C≥0.99). With the further increase of

*k*

_{cro}/

*k*

_{inj}, the quality of synchronization decreases gradually.

## 5. Conclusions

## Acknowledgments

## References and links

1. | G. D. Van Wiggeren and R. Roy, “Communication with chaotic lasers,” Science |

2. | S. Tang and J. M. Liu, “Effects of message encoding and becoding on synchronized chaotic optical communications,” IEEE J. Quantum Electron. |

3. | J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. |

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

5. | J. Paul, S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, “GHz bandwidth message transmission using chaotic diode lasers,” Electron. Lett. |

6. | J. Paul, S. Sivaprakasam, and K. A. Shore, “Dual-channel chaotic optical communications using external-cavity semiconductor lasers,” J. Opt. Soc. Am. B |

7. | L. S. Tsimring and M. M. Sushchik, “Multiplexing chaotic signals using synchronization,” Phys. Lett. A |

8. | Y. Liu and P. Davis, “Dual synchronization of chaos,” Phys. Rev. E |

9. | E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, “Dual and dual-cross synchronizations in chaotic systems,” Opt. Commun. |

10. | G. P. Agrawal and N. K. Dutta, |

11. | J. Troger, L. Thevenaz, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. |

12. | S. Tang, H. F. Chen, S. K. Hwang, and J. M. Liu, “Message encoding and decoding through chaos modulation in chaotic optical communications,” IEEE Trans. Circuits Syst. I |

13. | S. Sivaprakasam and K. A. Shore, “Message encoding and decoding using chaotic external-cavity diode lasers,” IEEE J. Quantum Electron. |

14. | A. Uchida, Y. Liu, and P. Davis, “Characteristics of chaotic masking in synchronized semiconductor lasers,” IEEE J. Quantum Electron. |

15. | S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, “Regimes of chaotic synchronization in external-cavity laser diodes,” IEEE J. Quantum Electron. |

16. | S. Sivaprakasam and K. A. Shore, “Cascaded synchronization of external-cavity laser diodes,” Opt. Lett. |

17. | J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, “Optically modulated chaotic communication scheme with external-cavity length as a key to security,” J. Opt. Soc. Am. B |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(140.1540) Lasers and laser optics : Chaos

(140.2020) Lasers and laser optics : Diode lasers

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 5, 2005

Revised Manuscript: April 17, 2005

Published: May 2, 2005

**Citation**

Guangqiong Xia, Zhengmao Wu, and Jiagui Wu, "Theory and simulation of dual-channel optical chaotic communication system," Opt. Express **13**, 3445-3453 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-9-3445

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### References

- G. D. Van Wiggeren, and R. Roy, �??Communication with chaotic lasers,�?? Science 279, 1198-1200 (1998). [CrossRef]
- S. Tang and J. M. Liu, �??Effects of message encoding and becoding on synchronized chaotic optical communications,�?? IEEE J. Quantum Electron. 39, 1468-1474 (2003). [CrossRef]
- J. Ohtsubo, �??Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,�?? IEEE J. Quantum Electron. 38, 1141-1153 (2002). [CrossRef]
- J. M. Liu, H. F. Chen, and S. Tang, �??Synchronized chaotic optical communications at high bit rates,�?? IEEE J. Quantum Electron. 38, 1184-1196 (2002). [CrossRef]
- J. Paul, S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, �??GHz bandwidth message transmission using chaotic diode lasers,�?? Electron. Lett. 38, 28-29 (2002). [CrossRef]
- J. Paul, S. Sivaprakasam, and K. A. Shore, �??Dual-channel chaotic optical communications using external-cavity semiconductor lasers,�?? J. Opt. Soc. Am. B 21, 514-521 (2004). [CrossRef]
- L. S. Tsimring, and M. M. Sushchik, �??Multiplexing chaotic signals using synchronization,�?? Phys. Lett. A 213, 155-166 (1996). [CrossRef]
- Y. Liu, and P. Davis, �??Dual synchronization of chaos,�?? Phys. Rev. E 61, 2176-2179 (2000). [CrossRef]
- E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, �??Dual and dual-cross synchronizations in chaotic systems,�?? Opt. Commun. 216, 179-183 (2003). [CrossRef]
- G. P. Agrawal, and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993).
- J. Troger, L. Thevenaz, P. A. Robert, �??Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,�?? J. Lightwave Technol. 17, 629-636 (1999) [CrossRef]
- S. Tang, H. F. Chen, S. K. Hwang, and J. M. Liu, �??Message encoding and decoding through chaos modulation in chaotic optical communications,�?? IEEE Trans. Circuits Syst. I 49, 163-169 (2002). [CrossRef]
- S. Sivaprakasam, and K. A. Shore, �??Message encoding and decoding using chaotic external-cavity diode lasers,�?? IEEE J. Quantum Electron. 36, 35-39 (2000). [CrossRef]
- A. Uchida, Y. Liu, and P. Davis, �??Characteristics of chaotic masking in synchronized semiconductor lasers,�?? IEEE J. Quantum Electron. 39, 963-970 (2003). [CrossRef]
- S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, �??Regimes of chaotic synchronization in external-cavity laser diodes,�?? IEEE J. Quantum Electron. 38, 1155-1160 (2002). [CrossRef]
- S. Sivaprakasam, and K. A. Shore, �??Cascaded synchronization of external-cavity laser diodes,�?? Opt. Lett. 66, 253-255 (2001). [CrossRef]
- J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, �??Optically modulated chaotic communication scheme with external-cavity length as a key to security,�?? J. Opt. Soc. Am. B 20, 497-503 (2003). [CrossRef]

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