## Fiber-bragg-grating-based dispersion-compensated and gain-flattened raman fiber amplifier

Optics Express, Vol. 15, Issue 19, pp. 12356-12361 (2007)

http://dx.doi.org/10.1364/OE.15.012356

Acrobat PDF (370 KB)

### Abstract

In this paper, we propose a novel signal/pump double-pass Raman fiber amplifier using fiber Brag gratings (FBGs). In order to compensate the dispersion slop mismatch among channels in lightwave system, FBGs embedded in different positions along dispersion compensated fiber are used to control the travel length of each WDM signal. Gain equalization can be achieved by optimizing the reflectivity of each FBG. Maximum output power variation among channels is less than ±0.5 dB after appropriate optimization. Finally, a wavelength division multiplexing (WDM) system using 40-Gb/s x 8 ch non return-to-zero (NRZ) signal transmission in a 100-km transmission fiber is simulated to confirm the system performance. Using proposed dispersion compensation method, it may lead to 2 dB improvement in Q value. Such kind of RFA may find vast applications in WDM system where dispersion management is a crucial issue.

© 2007 Optical Society of America

## 1. Introduction

## 2. Proposed scheme implementation

_{smf}(λ) and L

_{smf}are the dispersion parameter and the length of SMF respectively, and D

_{dcf}(λ) is dispersion parameter of the DCF. Because the WDM signals pass through the DCF twice, there is a 1/2 factor in this expression path of the round-trip design. Figure 1 depicts the configuration of our proposed RFA. The WDM signals are fed into a 50 km SMF via a WDM multiplexer, and then travel through port 1 to port 2 of the optical circulator (OC). Together with the signals, Raman pump is launched into the dispersion compensation module (DCM) via a Raman coupler. The DCM is composed of several FBGs, several segments of DCF and a FBG-based pump reflector. Each FBG is matched with a certain signal channel separated. Inside the DCM, different signals travel through different lengths of DCF. For example, signal 1 only passes through the DCF 1 and then is reflected by the FBG 1, while signal 2 passes both the DCF 1 and DCF 2 and then is only reflected by the FBG 2 and so forth. The length of each segment of DCF is determined by using equation (1) to eliminate the residual dispersion of WDM signal channels. The Raman pump passes through the whole DCF and FBGs in the DCM firstly, and then the residual pump power comes back from the DCF again. Thus, the pump power double-passes the gain medium of the DCF to increase the pumping efficiency. In the double-pass scheme RFA, the forward and backward power evolution of pump, signals can be expressed in terms of the following equation [8

8. L. Dou, S.-K. Liaw, M. Li, Y.-T. Lin, and A. Xu, “Parameters optimization of high efficiency discrete Raman fiber amplifier by using the coupled steady-state equations,” Opt. Commun. **273**, 149–152 (2007). [CrossRef]

^{+}(z,v

_{i}) and P

^{-}(z,v

_{i}) are optical power of the forward and the backward propagating waves within infinitesimal bandwidth around v

_{i}respectively. α(v

_{i}) is the attenuation coefficient of the corresponding wavelength v

_{i}. A

_{eff}is effective area of optical fiber; g

_{R}(v

_{i}-v

_{m}) is Raman gain parameter at frequency v

_{i}due to pump at frequency v

_{m}; the factor Γ accounts for polarization randomization effect, which value lies between 1 and 2. Besides dispersion compensation, we may also carry out the gain equalization by adjusting the reflectivity of each FBG. Here, the objective function is

_{i}(R) is the signal power of the ith WDM at FBG with reflectivity R

_{i}, and our aim is to minimize the objective function to zero. Considering possible large channel number in a real WDM system, we use Broyden method [9

9. C. G. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Mathematics of Computation **19**, 577–593 (1965). [CrossRef]

## 3. Simulation results and discussion

11. L. G-Nielsen, M. Wandel, P. Kristensen, C. Jørgensen, L.Vilbrad Jørgensen, B. Edvold, B. Pálsdóttir, and D. Jakobsen, “Dispersion-Compensating Fibers,” J. of Lightwave Technol. **23**, 3566–3579 (2005). [CrossRef]

12. E.M. Dianov, “Advances in Raman fibers,” J. Lightwave Technol. **20**, 1457–1462 (2002). [CrossRef]

^{2}; and the dispersion of DCF is -95 ps/nm/km at 1550 nm with dispersion slope of -0.62 ps/km/nm

^{2}. In a conventional configuration, the dispersion compensation is carried out by using only one segment of DCF, transmission bandwidth or transmission speed is surely restricted. As shown in Fig. 2, if we want to minimize the system residual dispersion in the conventional configuration, the length of DCF is equal to 9.1 km. In this condition, the maximum absolution of residual dispersion, which appears both in the longest and the shortest wavelengths are +62 ps/nm and -62 ps/nm, respectively. So, the maximum transmission speed Rb is limited to 23 Gbit/s, as could be predicted by the following equation [13]:

8. L. Dou, S.-K. Liaw, M. Li, Y.-T. Lin, and A. Xu, “Parameters optimization of high efficiency discrete Raman fiber amplifier by using the coupled steady-state equations,” Opt. Commun. **273**, 149–152 (2007). [CrossRef]

2. L. Dou, M. Li, Z. Li, A. Xu, C.-Y. David Lan, and S.-K. Liaw, “Improvement in characteristics of a distributed Raman fiber amplifier by using signal-pump double-pass scheme,” Optical Engineering **45**, No. 094201 (2006). [CrossRef]

^{23}-1 non-return-to zero (NRZ) formats is applied to intensity modulation of WDM channels in 40 Gb/s speed for each channel. The total signal envelope propagates through the fiber span including 100 km SMF is modeled by the modified nonlinear Schrödinger equation (NLSE) [14].

_{gj}is group velocity of jth channel, β

_{2j}is group velocity dispersion (GVD) parameter, β

_{3j}is third-order dispersion (TOD) parameter,

*γ*is nonlinear coefficient, and α accounts the loss. We incorporate the signal/pump double-pass Raman amplification effect by adding the distributed RFA gain coefficient into the NLSE [3

3. M. Tang, Y. D. Gong, and P. Shum, “Design of Double-Pass Dispersion-Compensated Raman Amplifiers for Improved Efficiency: Guidelines and Optimizations,” J. Lightwave Technology **22**, 1899–1908 (2004). [CrossRef]

^{-11}) could be obtained as non-return-to-aero (NRZ) data format is used. On the other hand, without residual dispersion compensation will lead to worse system performance both for the shortest and the longest wavelengths. In our simulation, only three kinds of impairments such as amplifier accompany noise, residual dispersion and nonlinearity are considered to be the overall impacts to close the eye diagram. In such condition, the noise will be a Gaussian distribution [15

15. C. J. Anderson and J. A. Lyle, “Technique for evaluating system performance using Q in numerical simulations exhibiting intersymbol interference,” Electron. Lett. **30**, 71–72 (1994). [CrossRef]

^{-12}to 10

^{-7}for both the longest and the shortest wavelengths. These results confirm the feasibility of RFA we proposed.

## 4. Conclusion

^{23}-1 NRZ formats is applied to intensity modulation the WDM channels in 40 Gb/s x 100-km SMF system to confirm the ability of residual dispersion compensation. We find that the Q value is improved by nearly 2 dB corresponding to BER is improved from about 10

^{-7}to 10

^{-12}for both the longest and the shortest wavelengths. Such kind of RFA may find vast application in WDM system where dispersion management and power equalization is a crucial issue.

## Acknowledgments

## References and links

1. | Y. Sun, J.W. Y., A.K. Sulhoff, J.L. Srivastava, T.A. Zyskind, J.R. Strasser, C. Pedrazzani, J. Wolf, J.B. Zhou, R.P. Judkins, A.M. Espindola, and Vengsarkar, “80 nm ultra-wide-band erbium-doped silica fiber amplifier,” Electron. Lett. |

2. | L. Dou, M. Li, Z. Li, A. Xu, C.-Y. David Lan, and S.-K. Liaw, “Improvement in characteristics of a distributed Raman fiber amplifier by using signal-pump double-pass scheme,” Optical Engineering |

3. | M. Tang, Y. D. Gong, and P. Shum, “Design of Double-Pass Dispersion-Compensated Raman Amplifiers for Improved Efficiency: Guidelines and Optimizations,” J. Lightwave Technology |

4. | V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. |

5. | S. Wen and S. Chi, “DCF-based fiber Raman amplifiers with fiber grating reflectors for tailoring accumulated-dispersion spectra,” Opt. Commun. |

6. | S.-K. Liaw, K.-P. Ho, and S. Chi, “Dynamic power-equalized EDFA modules using strain tunable fiber gratings,” IEEE Photon. Technol. Lett. |

7. | M. Rochette, M. Guy, S. LaRochelle, J. Lauzon, and F. Trépanier, “Gain equalization of EDFAs’ with Bragg gratings,” Photon. Technol. Lett. |

8. | L. Dou, S.-K. Liaw, M. Li, Y.-T. Lin, and A. Xu, “Parameters optimization of high efficiency discrete Raman fiber amplifier by using the coupled steady-state equations,” Opt. Commun. |

9. | C. G. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Mathematics of Computation |

10. | W. H. Press, |

11. | L. G-Nielsen, M. Wandel, P. Kristensen, C. Jørgensen, L.Vilbrad Jørgensen, B. Edvold, B. Pálsdóttir, and D. Jakobsen, “Dispersion-Compensating Fibers,” J. of Lightwave Technol. |

12. | E.M. Dianov, “Advances in Raman fibers,” J. Lightwave Technol. |

13. | L Kazovsky, S. Benedetto, and A. Willner, |

14. | G. P. Agrawal, |

15. | C. J. Anderson and J. A. Lyle, “Technique for evaluating system performance using Q in numerical simulations exhibiting intersymbol interference,” Electron. Lett. |

**OCIS Codes**

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

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

(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 25, 2007

Revised Manuscript: September 4, 2007

Manuscript Accepted: September 4, 2007

Published: September 13, 2007

**Citation**

Shien-Kuei Liaw, Liang Dou, and Anshi Xu, "Fiber-bragg-grating-based dispersion-compensated and gain-flattened raman fiber Amplifier," Opt. Express **15**, 12356-12361 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-12356

Sort: Year | Journal | Reset

### References

- Y. Sun, J. W. Sulhoff, A. K. Srivastava, J. L. Zyskind, T. A. Strasser, J. R. Pedrazzani, C. Wolf, J. Zhou, J. B. Judkins, R. P. Espindola and A. M. Vengsarkar, "80 nm ultra-wide-band erbium-doped silica fiber amplifier," Electron. Lett. 33, 1965-1967 (1997). [CrossRef]
- L. Dou, M. Li, Z. Li, A. Xu, C.-Y. David Lan and S.-K. Liaw, "Improvement in characteristics of a distributed Raman fiber amplifier by using signal-pump double-pass scheme," Opt. Eng. 45, 094201 (2006). [CrossRef]
- M. Tang, Y. D. Gong, and P. Shum, "Design of Double-Pass Dispersion-Compensated Raman Amplifiers for Improved Efficiency: Guidelines and Optimizations," J. Lightwave Technol. 22, 1899-1908 (2004). [CrossRef]
- V. E. Perlin and H. G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," J. Lightwave Technol. 20, 250-254 (2002). [CrossRef]
- S. Wen and S. Chi, "DCF-based fiber Raman amplifiers with fiber grating reflectors for tailoring accumulated-dispersion spectra," Opt. Commun. 272, 247-251 (2007). [CrossRef]
- S.-K. Liaw, K.-P. Ho and S. Chi, "Dynamic power-equalized EDFA modules using strain tunable fiber gratings," IEEE Photon. Technol. Lett. 11, 797-799 (1999) [CrossRef]
- M. Rochette, M. Guy, S. LaRochelle, J. Lauzon, and F. Trépanier, "Gain equalization of EDFAs' with Bragg gratings," Photon. Technol. Lett. 11, 536-538 (1999). [CrossRef]
- L. Dou, S.-K. Liaw, M. Li, Y.-T. Lin and A. Xu, "Parameters optimization of high efficiency discrete Raman fiber amplifier by using the coupled steady-state equations," Opt. Commun. 273, 149-152 (2007). [CrossRef]
- C. G. Broyden, "A class of methods for solving nonlinear simultaneous equations," Mathematics of Computation 19, 577-593 (1965). [CrossRef]
- W. H. Press, Numerical Recipes in C: the art of scientific computing, (Cambridge University Press, New York 1995).
- L. G-Nielsen, M. Wandel, P.Kristensen, C. Jørgensen, L.Vilbrad Jørgensen, B. Edvold, B. Pálsdóttir, and D. Jakobsen, "Dispersion-Compensating Fibers," J. Lightwave Technol. 23, 3566-3579 (2005). [CrossRef]
- E. M. Dianov, "Advances in Raman fibers," J. Lightwave Technol. 20, 1457-1462 (2002). [CrossRef]
- L Kazovsky, S. Benedetto, and A. Willner, Optical fiber Communication Systems, 1st ed. (Artech House Publishers, Norwood, 1996).
- G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).
- C. J. Anderson, and J. A. Lyle, "Technique for evaluating system performance using Q in numerical simulations exhibiting intersymbol interference," Electron. Lett. 30, 71-72 (1994). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.