## Frequency domain model to calculate the pump to signal RIN transfer in multi-pump Raman fiber amplifiers

Optics Express, Vol. 14, Issue 23, pp. 11024-11035 (2006)

http://dx.doi.org/10.1364/OE.14.011024

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### Abstract

In this paper, a novel frequency domain model to compute the pump to signal relative intensity noise (RIN) transfer in multi-pump Raman fiber amplifiers (RFAs) is proposed. The analytical expressions for RFAs with single pump and single signal channel are derived as a specific case of the model. The formulas exactly agree with the published results both for the co-pumped and counter-pumped RFAs. Afterwards, the pump to signal RIN transfer in multi-pump RFAs is studied numerically with thorough discussions.

© 2006 Optical Society of America

## 1. Introduction

2. C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to Signal RIN Transfer in Raman Fiber Amplifiers,” IEEE, J. Lightwave Technol. **19**, 1140–1148 (2001). [CrossRef]

5. X. Zhou, C. Lu, P. Shum, and TH. Cheng, “A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier,” IEEE Photon. Technol. Lett. **13**, 945–947 (2001). [CrossRef]

11. M. Karásek and M. Menif, “Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation,” IEEE J. Lightwave Technol. **20**, 1680–1688 (2002). [CrossRef]

9. Jaehyoung Park, Pilhan Kim, Jonghan Park, H. Lee, and Namkyoo Park, “Closed Integral form expansion of Raman equation for efficient gain optimization Process,” IEEE Photon. Tech. Lett. **16**, 1649–1651 (2004). [CrossRef]

2. C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to Signal RIN Transfer in Raman Fiber Amplifiers,” IEEE, J. Lightwave Technol. **19**, 1140–1148 (2001). [CrossRef]

## 2. Mathematical modeling

*v*is the group velocity at frequency

_{g,i}*ν*,

_{i}*α*is the attenuation coefficient at frequency

_{i}*ν*,

_{i}*g*(

*ν*,

_{i}*ν*) is the Raman gain coefficient between the frequencies

_{j}*ν*and

_{i}*ν*:

_{j}*gr*(

*ν*,

_{i}*ν*) is the Raman gain spectrum,

_{j}*A*is the effective area of the fiber, factor 2 stands for the polarization effect.

_{eff}*P*(

_{i}*z*), whose derivative of t is zero. The RIN power on each pump as well as the consequent transferred RIN power on each signal channel is denoted as Δ

*P*(

_{i}*z*,

*t*), which has the nonzero derivative of t, Δ

*P*(

_{i}*z*,

*t*)+

*P*(

_{i}*z*) satisfies equation (2), and if the second order term is omitted, we have:

**M**

*can be evaluated numerically via forward Euler method, Runge-Kutta method or Picard method. For the co-pumped RFAs,*

_{RIN}**ΔP**(0,

*ω*) is known and the RIN transfer

**ΔP**

_{s}(

*L*,

*ω*) can be simply calculated by multiplying the matrix. For the counter-pumping scheme, the RIN transfer can also be evaluated. We achieve this by separating the vector

**ΔP**(0,

*ω*) into

**ΔP**(

*L*,

*ω*) into

**M**

*into*

_{RIN}**ΔP**

*(0,*

_{s}*ω*)=0, therefore the Eq. (5) becomes:

## 3. Analytical formula for RIN transfer in RFAs with single pump and single signal channel

*et al.*[2

2. C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to Signal RIN Transfer in Raman Fiber Amplifiers,” IEEE, J. Lightwave Technol. **19**, 1140–1148 (2001). [CrossRef]

**19**, 1140–1148 (2001). [CrossRef]

**19**, 1140–1148 (2001). [CrossRef]

## 4. Numerical results and discussion

*β*

_{2}and the third order dispersion coefficient

*β*

_{3}are -20.4071711919

*ps*

^{2}/

*km*and 0.17348694743

*ps*

^{3}/

*km*at the wavelength of 1550nm. 80 channels of signals are launched into the fiber with 100GHz channel spacing. The input signal power for each channel is –10dbm. Different pumping schemes are investigated upon this piece of fiber sharing the same pumping wavelength, i.e. 1425nm, 1440nm, 1450nm, 1465nm and 1490nm. The data of Raman gain spectrum comes from the published literature [13]. The gain profile of the RFA is optimized using the matrix-based algorithms [9

9. Jaehyoung Park, Pilhan Kim, Jonghan Park, H. Lee, and Namkyoo Park, “Closed Integral form expansion of Raman equation for efficient gain optimization Process,” IEEE Photon. Tech. Lett. **16**, 1649–1651 (2004). [CrossRef]

**19**, 1140–1148 (2001). [CrossRef]

*r*and

_{s}*r*are defined in Eq. (14). Since

_{p}*r*is proportional to

_{s}*r*, the RIN transfer value

_{p}### 4.1 co-pumping

### 4.2 Counter-pumping

## 5. Conclusion

## Acknowledgments

## References and links

1. | S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelengthdivision-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. |

2. | C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to Signal RIN Transfer in Raman Fiber Amplifiers,” IEEE, J. Lightwave Technol. |

3. | M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, “RIN transfer analysis in pump depletion regime for Raman fiber amplifiers,” Electron. Lett. |

4. | Bruno Bristiel, Shifeng Jiang, Philippe Gallion, and Erwan Pincemin, “New Model of Noise Figure and RIN Transfer in Fiber Raman Amplifiers,” IEEE Photon. Technol. Lett. |

5. | X. Zhou, C. Lu, P. Shum, and TH. Cheng, “A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier,” IEEE Photon. Technol. Lett. |

6. | M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, “Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps,” IEEE Photon. Technol. Lett. |

7. | V.E Perlin and H.G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” IEEE, J. lightwave technol. |

8. | V.E. Perlin and H.G. Winful, “On distributed raman amplification for ultrabroad-band long-haul wdm systems,” IEEE, J. lightwave technol. |

9. | Jaehyoung Park, Pilhan Kim, Jonghan Park, H. Lee, and Namkyoo Park, “Closed Integral form expansion of Raman equation for efficient gain optimization Process,” IEEE Photon. Tech. Lett. |

10. | Jian Chen, Xueming Liu, Chao Lu, Yixin Wang, and Zhaohui Li, “Design of Multistage Gain-Flattened Fiber Raman Amplifiers,” IEEE, J. lightwave technol. |

11. | M. Karásek and M. Menif, “Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation,” IEEE J. Lightwave Technol. |

12. | G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York, 2001) |

13. | C. Fludger, A. Maroney, N. Jolley, and R. Mears, “An analysis of the improvements in OSNR from distributed Raman amplifiers using modern transmission fibers,” in |

**OCIS Codes**

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

(290.5910) Scattering : Scattering, stimulated Raman

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: July 14, 2006

Revised Manuscript: September 6, 2006

Manuscript Accepted: September 21, 2006

Published: November 13, 2006

**Citation**

Junhe Zhou, Jianping Chen, Xinwan Li, Guiling Wu, Yiping Wang, and Wenning Jiang, "Frequency domain model to calculate the pump to signal RIN transfer in multi-pump Raman fiber amplifiers," Opt. Express **14**, 11024-11035 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11024

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### References

- S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Top.Quantum Electron. l 7, 3-16 (2001).
- C. R. S. Fludger, V. Handerek, and R. J. Mears, "Pump to Signal RIN Transfer in Raman Fiber Amplifiers," IEEE, J. Lightwave Technol. 19, 1140-1148 (2001). [CrossRef]
- M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, "RIN transfer analysis in pump depletion regime for Raman fiber amplifiers," Electron. Lett. 38, 403-405, (2002). [CrossRef]
- Bruno Bristiel, Shifeng Jiang, Philippe Gallion, and Erwan Pincemin, "New Model of Noise Figure and RIN Transfer in Fiber Raman Amplifiers," IEEE Photon. Technol. Lett. 18, 980-982 (2006). [CrossRef]
- X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001). [CrossRef]
- M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001). [CrossRef]
- V.E Perlin, H.G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," IEEE, J. lightwave technol. 20, 250 - 254 (2002). [CrossRef]
- V.E. Perlin, H.G. Winful, "On distributed raman amplification for ultrabroad-band long-haul wdm systems," IEEE, J. lightwave technol. 20, 409-417 (2002). [CrossRef]
- Jaehyoung Park, Pilhan Kim, Jonghan Park, H. Lee, and Namkyoo Park, "Closed Integral form expansion of Raman equation for efficient gain optimization Process," IEEE Photon. Tech. Lett. 16, 1649 - 1651 (2004). [CrossRef]
- Jian Chen, Xueming Liu, Chao Lu, Yixin Wang, and Zhaohui Li, "Design of Multistage Gain-Flattened Fiber Raman Amplifiers," IEEE, J. lightwave technol. 24, 935-944 (2006). [CrossRef]
- M. Karásek and M. Menif, "Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation," IEEE J. Lightwave Technol. 20, 1680-1688 (2002). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York, 2001)
- C. Fludger, A. Maroney, N. Jolley, and R. Mears, "An analysis of the improvements in OSNR from distributed Raman amplifiers using modern transmission fibers," in Optical Fiber Communication Conference Technical Digest (Optical Society of America, 2000) 100-102.

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