## A novel algorithm for a multi-cavity Raman fiber laser

Optics Express, Vol. 14, Issue 8, pp. 3427-3432 (2006)

http://dx.doi.org/10.1364/OE.14.003427

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### Abstract

In this paper a Raman Fiber Lasers (RFLs) with several embedded cavities are studied. A novel algorithm is proposed to solve the coupled equations describing the optical power evolution in a RFL. By using some invariant constants as the boundary condition at the output end, the problem of solving ordinary differential equations (ODEs) with guessing boundary value is translated into a two-boundary-condition ODE problem. The algorithm is based on Newton-Raphson method and proved rather fast and stable. Quantitative analysis is performed based on the algorithm.

© 2006 Optical Society of America

## 1. Introduction

1. 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. **7**, 3–16 (2001). [CrossRef]

2. J. AuYeung and A. Yariv, “Theory of CW Raman oscillation in optical fibers,” J. Opt. Soc. Amer. **69**, 803–807)(1979). [CrossRef]

10. F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. **16**, 2601–2603 (2004). [CrossRef]

## 2. Numerical model

*P*

_{i}and

*P*

_{j}are the powers of the ith and jth wave propagating along the fiber, +/- stands for the wave forward/backward propagation,

*g*(

*ν*

_{i},

*ν*

_{j}) is the Raman gain coefficient between frequency

*ν*

_{i}and frequency

*ν*

_{j}:

*A*

_{eff}is the effective area of the fiber, factor 2 stands for the consideration of the polarization effect,

*gr*(

*ν*

_{i}-

*ν*

_{j}) is the Raman gain spectrum measure at the frequency of

*ν*

_{i}which has a peak at the frequency of 14T Hz, R is the reflectivity of corresponding mirrors, subscript 0 and L stand for the input and output ends.

*C*

_{i}, where

*C*

_{i}is a constant along the z axis. By dealing with the boundary condition and resorting to

*C*

_{i}, one can obtain

**J**is defined as

*P*

_{i}(0) by a small disturbance Δ

*P*

_{i}(0) and obtain the output. By subtracting the state output from the output and dividing the result by Δ

*P*

_{i}(0), the ith column of the matrix is obtained.

- Initial guessing values are given at the input.
- The coupled equation is integrated by Runge-Kouta method, and the error between the output and the target output
**Δoutput(**is obtained.*L*) - The Jacobi matrix is calculated and the input is updated by adding
**ΔP(0) = J**^{-1}**Δoutput(L)** - Iteration stops if the error is below a small threshold, else, go to procedure A.

## 3. Simulation results and discussion

12. Yoko Inoue and Shuichi Fujikawa, “Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm,” IEEE J.Quantum Electron. **36**, 751–756 (2000). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | 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. |

2. | J. AuYeung and A. Yariv, “Theory of CW Raman oscillation in optical fibers,” J. Opt. Soc. Amer. |

3. | P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, “Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors,” J. Mod. Opt. |

4. | M. Rini, I. Christiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. |

5. | N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment,” Electron. Lett. |

6. | Michael Krause and Hagen Renner, “Theory and design of double-cavity Raman Fiber Lasers,” IEEE J. Lightwave Technol. |

7. | Bumki Min, Won Jae Lee, and Namkyoo Park. “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. |

8. | Xueming Liu, H. Y zhang, and Y. L Guo. “A novel method for Raman amplifer propagation equations,” IEEE Photon. Technol. Lett. |

9. | Xueming Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” Opt. Express. |

10. | F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. |

11. | G. P. Agrawal, |

12. | Yoko Inoue and Shuichi Fujikawa, “Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm,” IEEE J.Quantum Electron. |

**OCIS Codes**

(140.0140) Lasers and laser optics : Lasers and laser optics

(190.5650) Nonlinear optics : Raman effect

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: January 3, 2006

Revised Manuscript: April 7, 2006

Manuscript Accepted: April 8, 2006

Published: April 17, 2006

**Citation**

Junhe Zhou, Jianping Chen, Xinwan Li, Guiling Wu, Wenning Jiang, Changhai Shi, and Yiping Wang, "A novel algorithm for a multi-cavity Raman fiber laser," Opt. Express **14**, 3427-3432 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3427

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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. 7, 3-16 (2001). [CrossRef]
- J. AuYeung and A. Yariv, "Theory of CW Raman oscillation in optical fibers," J. Opt. Soc. Am. 69, 803-807 (1979). [CrossRef]
- P. N. Kean, B. D. Sinclair, K. Smith, W. Sibbett, C. J. Rowe, and D. C. J. Reid, "Experimental evaluation of a fibre Raman oscillator having fibre grating reflectors," J. Mod. Opt. 35, 397-406 (1988). [CrossRef]
- M. Rini, I. Christiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded Raman fiber lasers," IEEE J. Quantum Electron. 36, 1117-1122 (2000). [CrossRef]
- N. Kurukitkoson, H. Sugahara, S. K. Tusitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, "Optimization of two stage Raman converter based on phosphosilicate core fiber: Modeling and experiment," Electron. Lett. 37, 1281-1283 (2001). [CrossRef]
- M. Krause and H. Renner, "Theory and design of double-cavity Raman Fiber Lasers," J. Lightwave Technol. 23, 2474-2483 (2005). [CrossRef]
- B. Min, W. J. Lee, and N. Park. "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photon. Technol. Lett. 12, 392-394 (2002).
- X. Liu, H. Y Zhang, and Y. L Guo. "A novel method for Raman amplifer propagation equations," IEEE Photon. Technol. Lett. 15, 392-394 (2003). [CrossRef]
- X. Liu and B. Lee, "A fast and stable method for Raman amplifier propagation equations," Opt. Express. 11, 2163-2176 (2003). [CrossRef] [PubMed]
- F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, "Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm," IEEE Photon. Technol. Lett. 16, 2601-2603 (2004). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York, 2001).
- Y. Inoue and S. Fujikawa, "Diode-pumped Nd:YAG laser producing 122W CW power at 1.319μm," IEEE J.Quantum Electron. 36, 751-756 (2000). [CrossRef]

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