Explicit solution for Raman fiber laser using Lambert W function

doi:10.1364/OE.15.004671

Explicit solution for Raman fiber laser using Lambert W function

Chaohong Huang, Zhiping Cai, Chenchun Ye, and Huiying Xu »View Author Affiliations

Optics Express, Vol. 15, Issue 8, pp. 4671-4676 (2007)
http://dx.doi.org/10.1364/OE.15.004671

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Abstract
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References (14)
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Abstract

In this paper, an approximate explicit solution for the first-order Raman fiber laser is obtained by using Lambert W function. Good agreement between the explicit solution and numerical simulation is demonstrated. Furthermore, the optimal design of Raman fiber laser is discussed using the proposed solution. The optimal values of fiber length, reflectivity of output fiber Bragg grating and power transfer efficiency are obtained under different pump power. There exists a certain tolerance of the optimal parameters, in which the output power decreases only slightly. The optimal fiber length and reflectivity of output FBG decrease with increasing pump power.

OCIS Codes
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3550) Lasers and laser optics : Lasers, Raman

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 14, 2006
Revised Manuscript: March 13, 2007
Manuscript Accepted: March 14, 2007
Published: April 3, 2007

Citation
Chaohong Huang, Zhiping Cai, Chenchun Ye, and Huiying Xu, "Explicit solution for Raman fiber laser using Lambert W function," Opt. Express 15, 4671-4676 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-4671

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References

E. M. Dianov, D. G. Fursa, I. A. Bufetov, S. A. Vasiliev, O. I. Medvedkov, V. G. Plotnichenko, V. V. Koltashev, A. V. Belov, M. M. Bubnov, S. L. Semjonov, and A. M. Prokhorov, "CW high power 1.24μm and 1.48μm Raman lasers based on low loss phosphosilicate fibre," Electron. Lett. 33, 1542-1544 (1997). [CrossRef]
N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, "1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation," Opt. Commun 176, 219-222 (2000). [CrossRef]
M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Elect. 36, 1117-1122 (2000). [CrossRef]
S. Cierullies, H. Renner, and E. Brinkmeyer, "Numerical optimization of multi-wavelength and cascaded Raman fiber lasers," Opt. Commun. 217, 233-238 (2003). [CrossRef]
I. A. Bufetov and E. M. Dianov, "A simple analytic model of a cw multicascade fibre Raman laser," Quantum Elect. 30,873-877 (2000). [CrossRef]
S. A. Babin, D. V. Churkin, and E. V. Podivilov, "Intensity interactions in cascades of a two-stage Raman fiber laser," Opt. Commun. 226, 329-335 (2003). [CrossRef]
B. Burgoyne, N. Godbout, and S. Lacroix, "Theoretical analysis of nth-order cascaded continuous-wave Raman fiber lasers. I. Model and resolution," J. Opt. Soc. Am. B 22, 764-771 (2005). [CrossRef]
B. Burgoyne, N. Godbout, and S. Lacroix, "Theoretical analysis of nth-order cascaded continuous-wave Raman fiber lasers. II. Optimization and design rules," J. Opt. Soc. Am. B 22, 772-776 (2005). [CrossRef]
J. H. Zhou, J. P. Chen, X. W. Li, G. L. Wu, Y. P. Wang, "Exact analytical solution for Raman fiber laser," IEEE Photon. Technol. Lett. 18,1097-1099 (2006). [CrossRef]
C. H. Huang, Z. P. Cai, C. C. Ye, H.Y. Xu, and Z. Q. Luo, "Analytic modeling of the P-doped cascaded Raman fiber lasers," Opt. Fiber Technol. 13, 22-26 (2007). [CrossRef]
S. D. Jackson and P. H. Muir, "Theory and numerical simulation of nth-order cascaded Raman fiber lasers," J. Opt. Soc. Am. B 18, 1297-1306 (2001). [CrossRef]
J. AuYeung and A. Yariv, "Theory of cw Raman oscillation in optical fibers," J. Opt. Soc. Am. B 69, 803-807(1979). [CrossRef]
E. M. Wright, "Solution of the Equation zez=a," Bull. Am. Math. Soc. 65, 89-93(1959). [CrossRef]
J. C. Bouteiller, "Spectral modeling of Raman fiber lasers," IEEE Photon. Technol. Lett. 15, 1698-1700(2003). [CrossRef]

Babin, S. A.
Belov, A. V.
Bouteiller, J. C.
Brinkmeyer, E.
Bubnov, M. M.
Bufetov, I. A.
Burgoyne, B.
Cai, Z. P.
Chen, J. P.
Churkin, D. V.
Cierullies, S.
Cristiani, I.
Degiorgio, V.
Dianov, E. M.
Fursa, D. G.
Godbout, N.
Huang, C. H.
Jackson, S. D.
Kim, N. S.
Koltashev, V. V.
Lacroix, S.
Li, C.
Li, X. W.
Luo, Z. Q.
Medvedkov, O. I.
Muir, P. H.
Plotnichenko, V. G.
Podivilov, E. V.
Prabhu, M.
Prokhorov, A. M.
Renner, H.
Rini, M.
Semjonov, S. L.
Song, J.
Ueda, K.
Vasiliev, S. A.
Wang, Y. P.
Wright, E. M.
Wu, G. L.
Xu, H.Y.
Ye, C. C.
Zhou, J. H.

Bull. Am. Math. Soc.

E. M. Wright, "Solution of the Equation zez=a," Bull. Am. Math. Soc. 65, 89-93(1959). [CrossRef]

Electron. Lett.

E. M. Dianov, D. G. Fursa, I. A. Bufetov, S. A. Vasiliev, O. I. Medvedkov, V. G. Plotnichenko, V. V. Koltashev, A. V. Belov, M. M. Bubnov, S. L. Semjonov, and A. M. Prokhorov, "CW high power 1.24μm and 1.48μm Raman lasers based on low loss phosphosilicate fibre," Electron. Lett. 33, 1542-1544 (1997). [CrossRef]

IEEE J. Quantum Elect.

M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Elect. 36, 1117-1122 (2000). [CrossRef]

IEEE Photon. Technol. Lett.

J. H. Zhou, J. P. Chen, X. W. Li, G. L. Wu, Y. P. Wang, "Exact analytical solution for Raman fiber laser," IEEE Photon. Technol. Lett. 18,1097-1099 (2006). [CrossRef]
J. C. Bouteiller, "Spectral modeling of Raman fiber lasers," IEEE Photon. Technol. Lett. 15, 1698-1700(2003). [CrossRef]

J. Opt. Soc. Am. B

S. D. Jackson and P. H. Muir, "Theory and numerical simulation of nth-order cascaded Raman fiber lasers," J. Opt. Soc. Am. B 18, 1297-1306 (2001). [CrossRef]
J. AuYeung and A. Yariv, "Theory of cw Raman oscillation in optical fibers," J. Opt. Soc. Am. B 69, 803-807(1979). [CrossRef]
B. Burgoyne, N. Godbout, and S. Lacroix, "Theoretical analysis of nth-order cascaded continuous-wave Raman fiber lasers. I. Model and resolution," J. Opt. Soc. Am. B 22, 764-771 (2005). [CrossRef]
B. Burgoyne, N. Godbout, and S. Lacroix, "Theoretical analysis of nth-order cascaded continuous-wave Raman fiber lasers. II. Optimization and design rules," J. Opt. Soc. Am. B 22, 772-776 (2005). [CrossRef]

Opt. Commun

N. S. Kim, M. Prabhu, C. Li, J. Song, and K. Ueda, "1239/1484 nm cascaded phosphosilicate Raman fiber laser with CW output power of 1.36 W at 1484 nm pumped by CW Yb-doped double-clad fiber laser at 1064 nm and spectral continuum generation," Opt. Commun 176, 219-222 (2000). [CrossRef]

Opt. Commun.

S. Cierullies, H. Renner, and E. Brinkmeyer, "Numerical optimization of multi-wavelength and cascaded Raman fiber lasers," Opt. Commun. 217, 233-238 (2003). [CrossRef]
S. A. Babin, D. V. Churkin, and E. V. Podivilov, "Intensity interactions in cascades of a two-stage Raman fiber laser," Opt. Commun. 226, 329-335 (2003). [CrossRef]

Opt. Fiber Technol.

C. H. Huang, Z. P. Cai, C. C. Ye, H.Y. Xu, and Z. Q. Luo, "Analytic modeling of the P-doped cascaded Raman fiber lasers," Opt. Fiber Technol. 13, 22-26 (2007). [CrossRef]

Quantum Elect.

I. A. Bufetov and E. M. Dianov, "A simple analytic model of a cw multicascade fibre Raman laser," Quantum Elect. 30,873-877 (2000). [CrossRef]

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