## Wavelength division multiplexing of chaotic secure and fiber-optic communications

Optics Express, Vol. 17, Issue 8, pp. 6357-6367 (2009)

http://dx.doi.org/10.1364/OE.17.006357

Acrobat PDF (295 KB)

### Abstract

Wavelength division multiplexing (WDM) transmission of chaotic optical communication (COC) and conventional fiber-optic communication (CFOC) is numerically confirmed and analyzed. For an 80-km-long two-channel communication system, a 1-Gb/s secure message in COC channel and 10-Gb/s digital signal in CFOC channel are simultaneously achieved with 100GHz channel spacing. Our numerical simulations demonstrate that the COC and CFOC can realize no-crosstalk transmission of 80km when the peak power of CFOC channel is less than 8dBm. We also find that the crosstalk between COC and CFOC does not depend on channel spacing when the channel spacing exceeds 100GHz. Moreover, the crosstalk does not limit channel number by comparing the synchronization performance of COC in four- and six-channel WDM systems.

© 2009 Optical Society of America

## 1. Introduction

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

2. T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Shimizu, “Observation of synchronization in laser chaos,” Phys. Rev. Lett. **72**, 3502–3505 (1994). [CrossRef] [PubMed]

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

4. P. Colet and R. Roy, “Digital communication with synchronized chaotic lasers,” Opt. Lett. **19**, 2056–2058 (1994). [CrossRef] [PubMed]

5. J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. **38**, 1141–1154 (2002). [CrossRef]

5. J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. **38**, 1141–1154 (2002). [CrossRef]

6. V. Annovazzi-Lodi, S. Donati, and A. Sciré, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. **33**, 1449–1454 (1997). [CrossRef]

9. 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**, 1633–1635 (2008). [CrossRef]

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

7. H. F. Chen and J. M. Liu, “Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation,” IEEE J. Quantum Electron. **36**, 27–34 (2000). [CrossRef]

5. J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. **38**, 1141–1154 (2002). [CrossRef]

7. H. F. Chen and J. M. Liu, “Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation,” IEEE J. Quantum Electron. **36**, 27–34 (2000). [CrossRef]

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

11. 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]

12. V. Annovazzi-Lodi, M. Benedetti, S. Merlo, M. Norgia, and B. Provinzano, “Optical chaos masking of video signals,” IEEE Photon. Technol. Lett. **17**, 1995–1997 (2005). [CrossRef]

13. C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. **8**, 299–301 (1996). [CrossRef]

14. A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, “Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers,” IEEE J. Quantum Electron. **35**, 292–297 (1999). [CrossRef]

15. A. Bogris, D. Kanakidis, A. Argyris, and D. Syvridis, “Performance characterization of a closed-loop chaotic communication system including fiber transmission in dispersion shifted fibers,” IEEE J. Quantum Electron. **40**, 1326–1336 (2004). [CrossRef]

16. 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 **437**, 343–346 (2005). [CrossRef]

## 2. Theoretical model

*λ*

_{C}. In COC system, transmitter (LD

_{T}) and receiver (LD

_{R}), both of which are composed of a single-mode semiconductor laser with an external reflector, have the same configuration. Transmitter laser (LD

_{T}) emits a chaotic carrier and an optical isolator (ISO) is used to ensure unidirectional transmission. The original message is superposed on chaotic carrier by chaos masking (CMS). The CMS method is implemented by simply adding the message to the output chaotic carrier. The chaotic carrier encoded by message and multiple digital optical signals from lasers LD

_{1}, LD

_{2}, …, LD

_{N}are launched together into the fiber via a WDM multiplexer (MUX), and separated by a WDM demultiplexer (DMUX) after long-haul transmission. An erbium-doped fiber amplifier (EDFA) is placed at the end of the fiber to compensate the fiber loss. The demultiplexed chaotic light is divided into two beams by a beam splitter (BS). One beam is injected into the receiver laser to achieve chaos synchronization. The other beam, as well as the output from the receiver laser, is separately detected by two identical photodiodes. The message can be extracted from the subtraction of the two detected signals.

17. D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, “Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes,” J. Lightwave Technol. **22**, 2256–2263 (2004). [CrossRef]

*E*and

*N*are the slowly varying complex electrical field amplitude and the carrier density in the laser cavity. Subscripts T and R represent the transmitter and receiver, respectively.

*ωτ*is the round-trip phase shift induced by the external feedback, where

*ω*is the angular frequency of the free-running laser and

*τ*is the external cavity round-trip time. The field

*E*

_{ext}is the input signal at the receiver and

*I*is the pump current density of the semiconductor laser.

*k*

_{T,R}of the semiconductor lasers with optical feedback and the injection coefficient

*k*

_{inj}from the transmitter to the receiver are defined as follows:

*τ*

_{in}is the round-trip time in the laser cavity,

*r*

_{0}and

*r*

_{T,R}represent amplitude reflectivity of the laser exit facet and the external reflector respectively,

*r*

_{inj}represents the percentage of the transmitter’s output electrical field amplitude injected into the receiver laser cavity. All the involved laser parameters and their values used in our numerical model are from [18

18. Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. **281**, 2656–2662 (2008). [CrossRef]

*j*,

*k*is chosen to be 1, or 2.

*A*is the slowly varying complex electrical field amplitude,

_{j}*z*is the propagation distance, and

*T*is the time measured in a reference frame moving at the group velocity.

*α*,

*β*

_{2},

*γ*are the fiber attenuation coefficient, the second-order dispersion parameter and the nonlinear coefficient, respectively. The two terms on the right-hand side of Eq. (6) are due to self-phase modulation (SPM) and cross-phase modulation (XPM), respectively. The factor of 2 shows that XPM is twice as effective as SPM for the same intensity. In our numerical simulations, we consider nonzero dispersion-shifted fiber (NZ-DSF) with typical values of

*α*=0.2dB/km,

*β*

_{2}=5.1ps

^{2}/km and

*γ*=1.5W

^{-1}/km as transmission link. The wavelengths of the emitted signals are set on the International Telecommunication Union (ITU) grid with a spacing of 0.8nm (100GHz). The channel,

*λ*=1550.12nm, is viewed as transmission channel of chaotic light, and the channel,

*λ*=1550.92nm, as transmission channel of conventional digital optical signal. The optical spectra corresponding to two channels are shown in Fig. 2. Optical spectrum of semiconductor laser is broadened owing to optical feedback. Thus, the linewidth of chaotic optical spectrum is as much as 11.8GHz. However, this value is still smaller than channel spacing, 100GHz.

## 3. Numerical results and discussions

_{10}(a/b), where a and b are the maximum eye opening measured for the decoded message without and with transmission. Value of the EOP smaller than 3dB can be considered fairly good. The synchronization performance of COC system can be evaluated by introducing the correlation coefficient defined as

*P*

_{T}(

*t*) and

*P*

_{R}(

*t*) are the outputs of the transmitter and the receiver, respectively, and 〈〉 denotes the time average. The correlation coefficient is bounded as -1≤

*ρ*≤1.A larger value of ∣

*ρ*∣ indicates a higher synchronization quality.

### 3.1 Numerical realization of COC and CFOC WDM

20. P. Grassberger and I. Procaccia, “Characterization of strange attractors,” Phys. Rev. Lett. **50**, 346–349 (1983). [CrossRef]

^{-1}. The mean optical power of the chaotic carrier is about 7dBm. A 1-Gb/s pseudorandom nonreturn-to-zero (NRZ) bit sequence [Fig. 3(c)] is embedded into the output chaotic carrier by CMS method, as shown in Fig. 3(b). The amplitude of the NRZ sequence is set to 9% of the mean amplitude of chaotic carrier. This small value ensures security, and moreover alleviates destructive influence on the system synchronization. Figure 4(a) shows a pseudorandom NRZ sequence at the OC-192 standard bit rate of 10 Gb/s. The laser LD

_{1}that functions as an emitter launches the optical carrier of wavelength λ=1550.92nm when the current of the laser is biased at 14.4mA. By using the 10-Gb/s NRZ bit stream chosen to encode the optical carrier, the digital optical signal with 8dBm peak power is obtained. Now, chaotic light encoding the message in COC channel and the digital optical signal in CFOC channel are multiplexed together into the fiber for 80-km-long WDM transmission. The fiber dispersion and nonlinearity effects distort chaotic carrier characteristics and degrade the synchronization performance between the transmitter and receiver. So, the decoded 1-Gb/s pseudorandom message of COC has high-frequency noises. Similarly, the received 10-Gb/s pseudorandom signal at the receiver end for CFOC takes on high-frequency noises due to the fiber dispersion and nonlinearity effects, shown in Fig. 4(b). However, the quality of the extracted messages can be effectively improved via a low-pass filter. For COC, a low-pass Chebyshev ☐ filter with 1.5GHz pass-band cut-off frequency is utilized to filter out the high-frequency temporal oscillations and the decoded message after filtering is shown in Fig. 3(d). The corresponding EOP is 2.5dB by calculation. For CFOC, the fast temporal oscillations can be effectively removed by a same type low-pass filter with 11.0 GHz pass-band cut-off frequency. The received signal after filtering is shown in Fig. 4(c). Obviously, the recovered signal at the receiving end is in good agreement with the encoded pseudorandom signal at the transmitter end except for the sharp fast oscillations. Moreover, the corresponding EOP is as low as 2.7dB. We can see that the high-quality pseudorandom messages are separately recovered at the receiver end for COC and CFOC WDM transmission. This indicates that COC and CFOC can simultaneously be realized within the same fiber link.

### 3.2 Inter-channel crosstalk between COC and CFOC

### 3.3 Dependence on channel spacing and channel number

## 4. Conclusions

21. J. Z. Zhang, Y. C. Wang, and A. B. Wang, “Improving performance of optical fibre chaotic communication by dispersion compensation techniques,” Chin. Phys. B **17**, 3264–3269 (2008). [CrossRef]

## Acknowledgments

## References and links

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

2. | T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Shimizu, “Observation of synchronization in laser chaos,” Phys. Rev. Lett. |

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

4. | P. Colet and R. Roy, “Digital communication with synchronized chaotic lasers,” Opt. Lett. |

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

6. | V. Annovazzi-Lodi, S. Donati, and A. Sciré, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. |

7. | H. F. Chen and J. M. Liu, “Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation,” IEEE J. Quantum Electron. |

8. | V. Annovazzi-Lodi, S. Donati, and A. Sciré, “Synchronization of chaotic injected-laser systems and its application to optical cryptography,” IEEE J. Quantum Electron. |

9. | 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. |

10. | J. Mørk, B. Tromborg, and J. Mark, ”Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. |

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

12. | V. Annovazzi-Lodi, M. Benedetti, S. Merlo, M. Norgia, and B. Provinzano, “Optical chaos masking of video signals,” IEEE Photon. Technol. Lett. |

13. | C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photon. Technol. Lett. |

14. | A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, “Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers,” IEEE J. Quantum Electron. |

15. | A. Bogris, D. Kanakidis, A. Argyris, and D. Syvridis, “Performance characterization of a closed-loop chaotic communication system including fiber transmission in dispersion shifted fibers,” IEEE J. Quantum Electron. |

16. | 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 |

17. | D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, “Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes,” J. Lightwave Technol. |

18. | Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. |

19. | G. P. Agrawal, |

20. | P. Grassberger and I. Procaccia, “Characterization of strange attractors,” Phys. Rev. Lett. |

21. | J. Z. Zhang, Y. C. Wang, and A. B. Wang, “Improving performance of optical fibre chaotic communication by dispersion compensation techniques,” Chin. Phys. B |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.4230) Fiber optics and optical communications : Multiplexing

(140.5960) Lasers and laser optics : Semiconductor lasers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 21, 2009

Revised Manuscript: March 14, 2009

Manuscript Accepted: March 17, 2009

Published: April 2, 2009

**Citation**

Jian-Zhong Zhang, An-Bang Wang, Juan-Fen Wang, and Yun-Cai Wang, "Wavelength division multiplexing of chaotic secure and fiber-optic communications," Opt. Express **17**, 6357-6367 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6357

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### References

- L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990). [CrossRef] [PubMed]
- T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Shimizu, "Observation of synchronization in laser chaos," Phys. Rev. Lett. 72, 3502-3505 (1994). [CrossRef] [PubMed]
- G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998). [CrossRef] [PubMed]
- P. Colet and R. Roy, "Digital communication with synchronized chaotic lasers," Opt. Lett. 19, 2056-2058 (1994). [CrossRef] [PubMed]
- J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002). [CrossRef]
- V. Annovazzi-Lodi, S. Donati, and A. Sciré, "Synchronization of chaotic lasers by optical feedback for cryptographic applications," IEEE J. Quantum Electron. 33, 1449-1454 (1997). [CrossRef]
- H. F. Chen and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000). [CrossRef]
- V. Annovazzi-Lodi, S. Donati, and A. Sciré, "Synchronization of chaotic injected-laser systems and its application to optical cryptography," IEEE J. Quantum Electron. 32, 953-959 (1996). [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, 1633-1635 (2008). [CrossRef]
- J. Mørk, B. Tromborg, and J. Mark,"Chaos in semiconductor lasers with optical feedback: theory and experiment," IEEE J. Quantum Electron. 28, 93-108 (1992). [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]
- V. Annovazzi-Lodi, M. Benedetti, S. Merlo, M. Norgia, and B. Provinzano, "Optical chaos masking of video signals," IEEE Photon. Technol. Lett. 17, 1995-1997 (2005). [CrossRef]
- C. R. Mirasso, P. Colet, and P. García-Fernández, "Synchronization of chaotic semiconductor lasers: application to encoded communications," IEEE Photon. Technol. Lett. 8, 299-301 (1996). [CrossRef]
- A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, "Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers," IEEE J. Quantum Electron. 35, 292-297 (1999). [CrossRef]
- A. Bogris, D. Kanakidis, A. Argyris, and D. Syvridis, "Performance characterization of a closed-loop chaotic communication system including fiber transmission in dispersion shifted fibers," IEEE J. Quantum Electron. 40, 1326-1336 (2004). [CrossRef]
- 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 437, 343-346 (2005). [CrossRef]
- D. Kanakidis, A. Bogris, A. Argyris, and D. Syvridis, "Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes," J. Lightwave Technol. 22, 2256-2263 (2004). [CrossRef]
- Y. L. Li, Y. C. Wang, and A. B. Wang, "Message filtering characteristics of semiconductor laser as receiver in optical chaos communication," Opt. Commun. 281, 2656-2662 (2008). [CrossRef]
- G. P. Agrawal, Nonlinear fiber optics, 3rd Edition (Academic Press, San Diego, 2001) Chap. 2.
- P. Grassberger and I. Procaccia, "Characterization of strange attractors," Phys. Rev. Lett. 50, 346-349 (1983). [CrossRef]
- J. Z. Zhang, Y. C. Wang, and A. B. Wang, "Improving performance of optical fibre chaotic communication by dispersion compensation techniques," Chin. Phys. B 17, 3264-3269 (2008). [CrossRef]

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