Abstract

We present a detailed analytical self-consistent theory based on wave kinetic equations that describes generation spectrum and output power of a Raman fiber laser (RFL). It is shown both theoretically and experimentally that the quasi-degenerate four-wave mixing (FWM) between different longitudinal modes is the main broadening mechanism in the one-stage RFL at high powers. The shape and power dependence of the intracavity Stokes wave spectrum are in excellent quantitative agreement with predictions of the theory. FWM-induced stochasticity of the amplitude and the phase of each of the 106 longitudinal modes generated in the RFL cavity is an example of a light-wave turbulence in a fiber.

© 2007 Optical Society of America

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  1. E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, "Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber," Opt. Lett. 25, 402-404 (2000).
    [CrossRef]
  2. Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, "Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings," IEEE Photon. Technol. Lett. 15, 383-385 (2003).
    [CrossRef]
  3. J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
    [CrossRef]
  4. Y.-G. Han, T., V. A. Tran, S.-H. Kim, and S. B. Lee, "Development of a multiwavelength Raman fiber laser based on phase-shifted fiber Bragg gratings for long-distance remote-sensing applications," Opt. Lett. 30, 1114-1116 (2005).
    [CrossRef] [PubMed]
  5. A. K. Abeeluck, C. Headley, and C. G. Jorgensen, "High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser," Opt. Lett. 29, 2163-2165 (2004).
    [CrossRef] [PubMed]
  6. C. J. S. de Matos, S. V. Popov, and J. R. Taylor, "Short-pulse, all-fiber, Raman laser with dispersion compensation in a holey fiber," Opt. Lett. 28, 1891-1893 (2003).
    [CrossRef] [PubMed]
  7. P.-L. Hsiung, Y. Chen, T. H. Ko, J. G. Fujimoto, C. J. S. de Matos, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, "Optical coherence tomography using a continuous-wave, high-power, Raman continuum light source," Opt. Express 12, 5287-5295 (2005).
    [CrossRef]
  8. Y. Feng, S. Huang, A. Shirakawa, and K.-I. Ueda, "Multiple-color cw visible lasers by frequency sum-mixing in a cascading Raman fiber laser," Opt. Express 12, 1843-1847 (2005).
    [CrossRef]
  9. D. Georgiev, V. P. Gapontsev, A. G. Dronov, M. Y. Vyatkin, A. B. Rulkov, S. V. Popov, and J. R. Taylor, "Watts-level frequency doubling of a narrow line linearly polarized Raman fiber laser to 589nm," Opt. Express 13, 6772-6776 (2005).
    [CrossRef] [PubMed]
  10. J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
    [CrossRef] [PubMed]
  11. S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, "Homogeneous Raman gain saturation at high pump and Stokes powers," J. Opt. Soc. Am. B 23, 1524-1530 (2006).
    [CrossRef]
  12. V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, "High-power 1.48μm phosphorosilicate-fiber-based laser pumped by laser diodes," Can. J. Phys. 78, 407-413 (2000).
    [CrossRef]
  13. M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
    [CrossRef]
  14. F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.
  15. Q. Wang, Y. Wang, W. Zhang, X. Feng, X. Liu, and B. Zhou, "Inhomogeneous loss mechanism in multiwavelength fiber Raman ring lasers," Opt. Lett. 30, 952-954 (2005).
    [CrossRef] [PubMed]
  16. V. Roy, M. Piche, F. Babin, G. W. Schinn, "Nonlinear wave mixing in a multilongitudinalmode erbium-doped fiber laser," Opt. Express 13, 6791-6797 (2005).
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    [CrossRef]
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    [CrossRef]
  19. S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, "Spectral broadening in Raman fiber lasers," Opt. Lett. 31, 3007-3009 (2006).
    [CrossRef] [PubMed]
  20. V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer-Verlag, 1992).
  21. S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, "Relative intensity noise in cascaded Raman fiber lasers," IEEE Photon. Technol. Lett. 17, 2553-2555 (2005).
    [CrossRef]
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    [CrossRef]
  24. Y. Wang and H. Po, "Impact of cavity losses on cw Raman fiber lasers," Opt. Eng. (Bellingham) 42, 2872-2879 (2003).
    [CrossRef]
  25. P.-C. Peng, H.-Y. Tseng, and S. Chi, "Long-distance FBG sensor system using a linear-cavity fiber raman laser scheme," IEEE Photon. Technol. Lett. 16, 575-577 (2004).
    [CrossRef]
  26. Y.-G. Han, B. S. Lee, D. S. Moon, and Y. Chung, "Investigation of a multiwavelength Raman fiber laser based on few-mode fiber Bragg gratings," Opt. Lett. 30, 2200-2202 (2005).
    [CrossRef] [PubMed]
  27. S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, "Raman gain saturation at high pump and Stokes powers," Opt. Express 13, 6079-6084 (2005).
    [CrossRef] [PubMed]
  28. S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, "Dependence of the spectral parameters of a Raman fibre laser on the Bragg grating temperature," Quantum Electron. 33, 1096-1100 (2003).
    [CrossRef]
  29. Q. Wang, X. Liu, L. Xing, X. Feng, and B. Zhou, "Experimental investigation of an inhomogeneous loss and its influence on multiwavelength fiber lasers," Opt. Lett. 30, 3033-3035 (2005).
    [CrossRef] [PubMed]
  30. Y. Wang, W. Zhang, Q. Wang, X. Feng, X. Liu, and J. Peng, "Broadband source generated by stimulated Raman scattering and four-wave mixing in a highly nonlinear optical fiber ring cavity," Opt. Lett. 29, 842-844 (2004).
    [CrossRef] [PubMed]
  31. B. Barviau, S. Randoux, and P. Suret, "Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber," Opt. Lett. 31, 1696-1698 (2006).
    [CrossRef] [PubMed]

2006 (4)

2005 (10)

Y. Feng, S. Huang, A. Shirakawa, and K.-I. Ueda, "Multiple-color cw visible lasers by frequency sum-mixing in a cascading Raman fiber laser," Opt. Express 12, 1843-1847 (2005).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, "Relative intensity noise in cascaded Raman fiber lasers," IEEE Photon. Technol. Lett. 17, 2553-2555 (2005).
[CrossRef]

P.-L. Hsiung, Y. Chen, T. H. Ko, J. G. Fujimoto, C. J. S. de Matos, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, "Optical coherence tomography using a continuous-wave, high-power, Raman continuum light source," Opt. Express 12, 5287-5295 (2005).
[CrossRef]

Q. Wang, Y. Wang, W. Zhang, X. Feng, X. Liu, and B. Zhou, "Inhomogeneous loss mechanism in multiwavelength fiber Raman ring lasers," Opt. Lett. 30, 952-954 (2005).
[CrossRef] [PubMed]

Y.-G. Han, T., V. A. Tran, S.-H. Kim, and S. B. Lee, "Development of a multiwavelength Raman fiber laser based on phase-shifted fiber Bragg gratings for long-distance remote-sensing applications," Opt. Lett. 30, 1114-1116 (2005).
[CrossRef] [PubMed]

Y.-G. Han, B. S. Lee, D. S. Moon, and Y. Chung, "Investigation of a multiwavelength Raman fiber laser based on few-mode fiber Bragg gratings," Opt. Lett. 30, 2200-2202 (2005).
[CrossRef] [PubMed]

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, "Raman gain saturation at high pump and Stokes powers," Opt. Express 13, 6079-6084 (2005).
[CrossRef] [PubMed]

D. Georgiev, V. P. Gapontsev, A. G. Dronov, M. Y. Vyatkin, A. B. Rulkov, S. V. Popov, and J. R. Taylor, "Watts-level frequency doubling of a narrow line linearly polarized Raman fiber laser to 589nm," Opt. Express 13, 6772-6776 (2005).
[CrossRef] [PubMed]

V. Roy, M. Piche, F. Babin, G. W. Schinn, "Nonlinear wave mixing in a multilongitudinalmode erbium-doped fiber laser," Opt. Express 13, 6791-6797 (2005).
[CrossRef] [PubMed]

Q. Wang, X. Liu, L. Xing, X. Feng, and B. Zhou, "Experimental investigation of an inhomogeneous loss and its influence on multiwavelength fiber lasers," Opt. Lett. 30, 3033-3035 (2005).
[CrossRef] [PubMed]

2004 (4)

P.-C. Peng, H.-Y. Tseng, and S. Chi, "Long-distance FBG sensor system using a linear-cavity fiber raman laser scheme," IEEE Photon. Technol. Lett. 16, 575-577 (2004).
[CrossRef]

P. Suret and S. Randoux, "Influence of spectral broadening on steady characteristics of Raman fiber lasers: from experiments to questions about validity of usual models," Opt. Commun. 237, 201-212 (2004).
[CrossRef]

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, "High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser," Opt. Lett. 29, 2163-2165 (2004).
[CrossRef] [PubMed]

Y. Wang, W. Zhang, Q. Wang, X. Feng, X. Liu, and J. Peng, "Broadband source generated by stimulated Raman scattering and four-wave mixing in a highly nonlinear optical fiber ring cavity," Opt. Lett. 29, 842-844 (2004).
[CrossRef] [PubMed]

2003 (7)

C. J. S. de Matos, S. V. Popov, and J. R. Taylor, "Short-pulse, all-fiber, Raman laser with dispersion compensation in a holey fiber," Opt. Lett. 28, 1891-1893 (2003).
[CrossRef] [PubMed]

J.-C. Bouteiller, "Spectral modelling of Raman fiber lasers," IEEE Photon. Technol. Lett. 15, 1698-1700 (2003).
[CrossRef]

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, "Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings," IEEE Photon. Technol. Lett. 15, 383-385 (2003).
[CrossRef]

J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
[CrossRef]

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, "Dependence of the spectral parameters of a Raman fibre laser on the Bragg grating temperature," Quantum Electron. 33, 1096-1100 (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]

Y. Wang and H. Po, "Impact of cavity losses on cw Raman fiber lasers," Opt. Eng. (Bellingham) 42, 2872-2879 (2003).
[CrossRef]

2001 (1)

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

2000 (2)

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, "Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber," Opt. Lett. 25, 402-404 (2000).
[CrossRef]

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, "High-power 1.48μm phosphorosilicate-fiber-based laser pumped by laser diodes," Can. J. Phys. 78, 407-413 (2000).
[CrossRef]

Abeeluck, A. K.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Ania-Castañón, J. D.

J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef] [PubMed]

Babin, F.

Babin, S. A.

S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, "Spectral broadening in Raman fiber lasers," Opt. Lett. 31, 3007-3009 (2006).
[CrossRef] [PubMed]

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, "Homogeneous Raman gain saturation at high pump and Stokes powers," J. Opt. Soc. Am. B 23, 1524-1530 (2006).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, "Relative intensity noise in cascaded Raman fiber lasers," IEEE Photon. Technol. Lett. 17, 2553-2555 (2005).
[CrossRef]

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, "Raman gain saturation at high pump and Stokes powers," Opt. Express 13, 6079-6084 (2005).
[CrossRef] [PubMed]

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, "Dependence of the spectral parameters of a Raman fibre laser on the Bragg grating temperature," Quantum Electron. 33, 1096-1100 (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]

Barviau, B.

Bayart, D.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

Borne, S.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

Bouteiller, J.-C.

J.-C. Bouteiller, "Spectral modelling of Raman fiber lasers," IEEE Photon. Technol. Lett. 15, 1698-1700 (2003).
[CrossRef]

J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
[CrossRef]

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Brar, K.

J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
[CrossRef]

Bromage, J.

J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
[CrossRef]

Bubnov, M. M.

Bufetov, I. A.

Chen, X.

J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef] [PubMed]

Chen, Y.

Chi, S.

P.-C. Peng, H.-Y. Tseng, and S. Chi, "Long-distance FBG sensor system using a linear-cavity fiber raman laser scheme," IEEE Photon. Technol. Lett. 16, 575-577 (2004).
[CrossRef]

Chung, Y.

Y.-G. Han, B. S. Lee, D. S. Moon, and Y. Chung, "Investigation of a multiwavelength Raman fiber laser based on few-mode fiber Bragg gratings," Opt. Lett. 30, 2200-2202 (2005).
[CrossRef] [PubMed]

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, "Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings," IEEE Photon. Technol. Lett. 15, 383-385 (2003).
[CrossRef]

Churkin, D. V.

S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, "Spectral broadening in Raman fiber lasers," Opt. Lett. 31, 3007-3009 (2006).
[CrossRef] [PubMed]

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, "Homogeneous Raman gain saturation at high pump and Stokes powers," J. Opt. Soc. Am. B 23, 1524-1530 (2006).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, "Relative intensity noise in cascaded Raman fiber lasers," IEEE Photon. Technol. Lett. 17, 2553-2555 (2005).
[CrossRef]

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, "Raman gain saturation at high pump and Stokes powers," Opt. Express 13, 6079-6084 (2005).
[CrossRef] [PubMed]

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, "Dependence of the spectral parameters of a Raman fibre laser on the Bragg grating temperature," Quantum Electron. 33, 1096-1100 (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]

Clements, W. R. L.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, "High-power 1.48μm phosphorosilicate-fiber-based laser pumped by laser diodes," Can. J. Phys. 78, 407-413 (2000).
[CrossRef]

de Matos, C. J. S.

Dianov, E. M.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, "High-power 1.48μm phosphorosilicate-fiber-based laser pumped by laser diodes," Can. J. Phys. 78, 407-413 (2000).
[CrossRef]

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, "Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber," Opt. Lett. 25, 402-404 (2000).
[CrossRef]

Dronov, A. G.

Eggleton, B. J.

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Ellingham, T. J.

J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef] [PubMed]

Falkovich, G.

V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer-Verlag, 1992).

Feder, K.

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Feng, X.

Feng, Y.

Fotiadi, A. A.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, "Relative intensity noise in cascaded Raman fiber lasers," IEEE Photon. Technol. Lett. 17, 2553-2555 (2005).
[CrossRef]

Fujimoto, J. G.

Gapontsev, V. P.

Georgiev, D.

Grekov, M. V.

Guerin, J.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

Han, Y.-G.

Headley, C.

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, "High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser," Opt. Lett. 29, 2163-2165 (2004).
[CrossRef] [PubMed]

J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
[CrossRef]

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Horn, C.

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Hsiung, P.-L.

Huang, S.

Ibbotson, R.

J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef] [PubMed]

Ismagulov, A. E.

Jorgensen, C. G.

Kablukov, S. I.

Kang, J. U.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, "Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings," IEEE Photon. Technol. Lett. 15, 383-385 (2003).
[CrossRef]

Karpov, V. I.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, "High-power 1.48μm phosphorosilicate-fiber-based laser pumped by laser diodes," Can. J. Phys. 78, 407-413 (2000).
[CrossRef]

Kim, C.-S.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, "Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings," IEEE Photon. Technol. Lett. 15, 383-385 (2003).
[CrossRef]

Kim, S.-H.

Ko, T. H.

Kurkov, A. S.

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, "Dependence of the spectral parameters of a Raman fibre laser on the Bragg grating temperature," Quantum Electron. 33, 1096-1100 (2003).
[CrossRef]

Leclere, C.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

Lee, B. S.

Lee, S. B.

Leplingard, F.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

Liu, X.

Lopez, T.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

L'vov, V. S.

V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer-Verlag, 1992).

Martinelli, C.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

Medvedkov, O. I.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, "Relative intensity noise in cascaded Raman fiber lasers," IEEE Photon. Technol. Lett. 17, 2553-2555 (2005).
[CrossRef]

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, "Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber," Opt. Lett. 25, 402-404 (2000).
[CrossRef]

Mermelstein, M. D.

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Moon, D. S.

Paek, U.-C.

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, "Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings," IEEE Photon. Technol. Lett. 15, 383-385 (2003).
[CrossRef]

Papernyi, S. B.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, "High-power 1.48μm phosphorosilicate-fiber-based laser pumped by laser diodes," Can. J. Phys. 78, 407-413 (2000).
[CrossRef]

Peng, J.

Peng, P.-C.

P.-C. Peng, H.-Y. Tseng, and S. Chi, "Long-distance FBG sensor system using a linear-cavity fiber raman laser scheme," IEEE Photon. Technol. Lett. 16, 575-577 (2004).
[CrossRef]

Piche, M.

Po, H.

Y. Wang and H. Po, "Impact of cavity losses on cw Raman fiber lasers," Opt. Eng. (Bellingham) 42, 2872-2879 (2003).
[CrossRef]

Podivilov, E. V.

Popov, S. V.

Potapov, V. V.

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, "Dependence of the spectral parameters of a Raman fibre laser on the Bragg grating temperature," Quantum Electron. 33, 1096-1100 (2003).
[CrossRef]

Radic, S.

J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
[CrossRef]

Randoux, S.

B. Barviau, S. Randoux, and P. Suret, "Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber," Opt. Lett. 31, 1696-1698 (2006).
[CrossRef] [PubMed]

P. Suret and S. Randoux, "Influence of spectral broadening on steady characteristics of Raman fiber lasers: from experiments to questions about validity of usual models," Opt. Commun. 237, 201-212 (2004).
[CrossRef]

Roy, V.

Rulkov, A. B.

Schinn, G. W.

Shirakawa, A.

Steinvurzel, P.

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Suret, P.

B. Barviau, S. Randoux, and P. Suret, "Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber," Opt. Lett. 31, 1696-1698 (2006).
[CrossRef] [PubMed]

P. Suret and S. Randoux, "Influence of spectral broadening on steady characteristics of Raman fiber lasers: from experiments to questions about validity of usual models," Opt. Commun. 237, 201-212 (2004).
[CrossRef]

Taylor, J. R.

Tran, T. V. A.

Tseng, H.-Y.

P.-C. Peng, H.-Y. Tseng, and S. Chi, "Long-distance FBG sensor system using a linear-cavity fiber raman laser scheme," IEEE Photon. Technol. Lett. 16, 575-577 (2004).
[CrossRef]

Turitsyn, S. K.

J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef] [PubMed]

Ueda, K.-I.

Vasiliev, S. A.

Vyatkin, M. Y.

Wang, Q.

Wang, Y.

Xing, L.

Zakharov, V. E.

V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer-Verlag, 1992).

Zhang, L.

J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef] [PubMed]

Zhang, W.

Zhou, B.

Can. J. Phys. (1)

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, "High-power 1.48μm phosphorosilicate-fiber-based laser pumped by laser diodes," Can. J. Phys. 78, 407-413 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (6)

M. D. Mermelstein, C. Headley, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Y.-G. Han, C.-S. Kim, J. U. Kang, U.-C. Paek, and Y. Chung, "Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period fiber gratings," IEEE Photon. Technol. Lett. 15, 383-385 (2003).
[CrossRef]

J.-C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, "Dual-order Raman pump," IEEE Photon. Technol. Lett. 15, 212-214 (2003).
[CrossRef]

J.-C. Bouteiller, "Spectral modelling of Raman fiber lasers," IEEE Photon. Technol. Lett. 15, 1698-1700 (2003).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, "Relative intensity noise in cascaded Raman fiber lasers," IEEE Photon. Technol. Lett. 17, 2553-2555 (2005).
[CrossRef]

P.-C. Peng, H.-Y. Tseng, and S. Chi, "Long-distance FBG sensor system using a linear-cavity fiber raman laser scheme," IEEE Photon. Technol. Lett. 16, 575-577 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

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]

P. Suret and S. Randoux, "Influence of spectral broadening on steady characteristics of Raman fiber lasers: from experiments to questions about validity of usual models," Opt. Commun. 237, 201-212 (2004).
[CrossRef]

Opt. Eng. (Bellingham) (1)

Y. Wang and H. Po, "Impact of cavity losses on cw Raman fiber lasers," Opt. Eng. (Bellingham) 42, 2872-2879 (2003).
[CrossRef]

Opt. Express (5)

Opt. Lett. (10)

Q. Wang, X. Liu, L. Xing, X. Feng, and B. Zhou, "Experimental investigation of an inhomogeneous loss and its influence on multiwavelength fiber lasers," Opt. Lett. 30, 3033-3035 (2005).
[CrossRef] [PubMed]

B. Barviau, S. Randoux, and P. Suret, "Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber," Opt. Lett. 31, 1696-1698 (2006).
[CrossRef] [PubMed]

Q. Wang, Y. Wang, W. Zhang, X. Feng, X. Liu, and B. Zhou, "Inhomogeneous loss mechanism in multiwavelength fiber Raman ring lasers," Opt. Lett. 30, 952-954 (2005).
[CrossRef] [PubMed]

Y.-G. Han, T., V. A. Tran, S.-H. Kim, and S. B. Lee, "Development of a multiwavelength Raman fiber laser based on phase-shifted fiber Bragg gratings for long-distance remote-sensing applications," Opt. Lett. 30, 1114-1116 (2005).
[CrossRef] [PubMed]

Y.-G. Han, B. S. Lee, D. S. Moon, and Y. Chung, "Investigation of a multiwavelength Raman fiber laser based on few-mode fiber Bragg gratings," Opt. Lett. 30, 2200-2202 (2005).
[CrossRef] [PubMed]

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, "High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser," Opt. Lett. 29, 2163-2165 (2004).
[CrossRef] [PubMed]

S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, "Spectral broadening in Raman fiber lasers," Opt. Lett. 31, 3007-3009 (2006).
[CrossRef] [PubMed]

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, "Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber," Opt. Lett. 25, 402-404 (2000).
[CrossRef]

C. J. S. de Matos, S. V. Popov, and J. R. Taylor, "Short-pulse, all-fiber, Raman laser with dispersion compensation in a holey fiber," Opt. Lett. 28, 1891-1893 (2003).
[CrossRef] [PubMed]

Y. Wang, W. Zhang, Q. Wang, X. Feng, X. Liu, and J. Peng, "Broadband source generated by stimulated Raman scattering and four-wave mixing in a highly nonlinear optical fiber ring cavity," Opt. Lett. 29, 842-844 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, "Ultralong Raman fiber lasers as virtually lossless optical media," Phys. Rev. Lett. 96, 023902 (2006).
[CrossRef] [PubMed]

Quantum Electron. (1)

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, "Dependence of the spectral parameters of a Raman fibre laser on the Bragg grating temperature," Quantum Electron. 33, 1096-1100 (2003).
[CrossRef]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer-Verlag, 1992).

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, "FWM-assisted Raman laser for second-order Raman pumping," in Proceedings of the Optical Fiber Communications Conference (Optical Society of America, 2003), paper ThB4.

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Figures (7)

Fig. 1
Fig. 1

One-stage RFL based on a phosphosilicate fiber.

Fig. 2
Fig. 2

Effective losses of FBGs forming the RFL cavity: Measurements (thin curve) and parabolic approximation (thick curve).

Fig. 3
Fig. 3

Measured (∎) and calculated (curve) upon Eqs. (11, 12) total intracavity Stokes wave power.

Fig. 4
Fig. 4

a, Intracavity Stokes wave spectrum near the generation threshold: P 0 = 0.4 W . b–d, Measured (dots) and calculated (solid curve) upon Eqs. (8, 9) intracavity Stokes wave spectrum at different input pump power P 0 : b, P 0 = 1 W ; c, P 0 = 2 W ; and d, P 0 = 3 W .

Fig. 5
Fig. 5

a, Full width at 1 cosh ( 1 ) = 0.648 level of the intracavity Stokes wave spectrum. b, Spectral power density at its maximum. Experiment (◻, ∎) and calculation (curve) upon Eqs. (9, 10).

Fig. 6
Fig. 6

Measured (∎) and calculated (solid curve) upon Eqs. (15) effective transmission coefficient T e f f .

Fig. 7
Fig. 7

Pump wave spectrum, a, before and, b, after transmission trough RFL (input pump power P 0 = 1.5 W ).

Equations (38)

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E ( z , t ) = 1 2 ( E + ( z , t ) e i k ( c t z ) + E ( z , t ) e i k ( c t + z ) ) + c.c. ,
( 1 c d d t ± d d z ) E ± ( z , t ) = ( g R P ( z ) α 2 ) E + ( z , t ) i 2 γ [ I ± ( z , t ) + 2 I ( z , t ) ] E ± ( z , t ) + i β d 2 E ± ( z , t ) d t 2 ,
E ± ( z , t ) = 1 2 n E n ( t ) exp ( i n Δ t i κ z n ) exp ( i ν n t ) ,
τ r t d E n d t 1 2 ( g δ n ) E n ( t ) = i 2 γ L l 0 E n l ( t ) m 0 E n m ( t ) E n m l * ( t ) exp ( 2 i β m l Δ 2 c t ) ,
g = 2 g R P ¯ L 2 α L .
P ¯ = P 0 1 exp ( 2 α p L 2 λ λ p g R L I ) ( α p + λ λ p g R I ) L ,
[ δ ( Ω ) + α 2 L + δ N L ] I ( Ω ) = 2 g R L P ¯ I ( Ω ) + δ N L I 2 I ( Ω 1 ) I ( Ω 2 ) I ( Ω 1 + Ω 2 Ω ) d Ω 1 d Ω 2 ,
δ N L = 2 3 γ I L 1 + ( 8 β L Ω 2 ¯ 3 δ N L ) 2 .
I ( Ω ) = 2 I π Γ cosh ( 2 Ω Γ ) ,
Γ = 2 π 2 δ N L δ 2
I ( 0 ) = 2 I π Γ .
δ N L = 2 3 γ I L 1 + ( 4 β L 3 δ 2 ) 2 .
δ 0 + δ N L ( I ) 2 + 2 α L = 2 g R P 0 1 exp ( 2 α p L 2 λ λ p g R L I ) α p + λ λ p g R I ,
I 1 , 2 o u t ( Ω ) = δ 0 + δ 2 Ω 2 2 I π Γ cosh ( 2 Ω Γ ) .
δ e f f 2 ( I 1 o u t + I 2 o u t ) I = δ ( Ω ) I ( Ω ) d Ω I = δ 0 + δ N L ( I ) 2 .
T e f f δ N L 4 ,
τ r t d I n d t ( g δ n ) I n ( t ) = Re [ i γ L l 0 , m 0 E n l ( t ) E n m ( t ) E n m l * ( t ) E n * ( t ) exp ( 2 i β m l Δ 2 c t ) ] .
δ E n ( t ) = i γ L 2 t l 0 , m 0 E n l ( t ) E n m ( t ) E n m l * ( t ) exp ( 2 i β m l Δ 2 c t ) d t τ r t .
τ r t d I ( Ω ) d t = [ g δ ( Ω ) ] I ( Ω ) + S F W M ( Ω ) = 0 ,
S F W M ( Ω ) = δ N L I ( Ω ) + ( γ L ) 2 I ( Ω Ω 1 ) I ( Ω Ω 2 ) I ( Ω Ω 1 Ω 2 ) ( 3 τ r t τ ) [ 1 + ( 4 τ L β 3 τ r t ) 2 Ω 1 2 Ω 2 2 ] d Ω 1 d Ω 2 ,
δ N L = ( γ L ) 2 [ I ( Ω Ω 1 ) + I ( Ω Ω 2 ) ] I ( Ω Ω 1 Ω 2 ) I ( Ω Ω 1 ) I ( Ω Ω 2 ) ( 3 τ r t τ ) [ 1 + ( 4 τ L β 3 τ r t ) 2 Ω 1 2 Ω 2 2 ] d Ω 1 d Ω 2 .
F ( Ω ) = n 0 D F n π [ D 2 + ( Ω n Δ ) 2 ] ,
τ r t τ δ N L 2 ,
γ I L 4 β L Ω 2 ¯ ,
Ω 2 ¯ = Ω 2 I ( Ω ) d Ω I .
δ ( Ω ) = δ 0 + δ 2 Ω 2 .
δ 0 + δ 2 Ω 2 ¯ = g = 2 g R L P ¯ 2 α L .
3 2 δ N L B ( γ I L ) 2 4 β L Ω 2 ¯ ln ( 8 β L Ω 2 ¯ 3 δ N L ) γ I L 4 β L Ω 2 ¯ ,
S F W M ( 0 ) I ( 0 ) = ( γ L ) 2 d Ω 1 d Ω 2 I ( Ω 1 ) I ( Ω 2 ) [ I ( Ω 1 + Ω 2 ) I ( 0 ) + 1 ] [ I ( Ω 1 ) + I ( Ω 2 ) ] I ( Ω 1 + Ω 2 ) ( 3 δ N L 2 ) [ 1 + ( 8 L β 3 δ N L ) 2 Ω 1 2 Ω 2 2 ] .
g δ 0 = S F W M ( 0 ) I ( 0 ) = 3 2 A δ N L ( γ I L 4 β L Ω 2 ¯ ) 2 δ N L ,
Ω 2 ¯ = γ I 4 β [ 4 β L δ 2 A B ln ( 4 β L A δ 2 B ) ] 1 4
δ N L = 2 3 γ I L [ B ln ( 4 β L A δ 2 B ) ] 3 4 ( 4 β L A δ 2 ) 1 4 ,
2 g R P ¯ ( I ) L = 2 α L + δ 0 + γ I L [ A B ln ( 4 β L A δ 2 B ) ] 1 4 ( 4 β L δ 2 ) 3 4 ,
4 β L δ 2 1 ,
τ r t d E n ( t ) d t = g δ n 2 E n ( t ) 2 i γ L l 0 p l ( t ) exp [ i l ( κ c 1 Δ ) t ] E n l ( t ) .
τ r t d I n d t = ( g δ n ) I n 2 γ L l 0 [ i p l ( t ) e i l ( κ c 1 Δ ) t E n l ( t ) E n * ( t ) + c.c. ] .
δ E n ( t ) = 2 i γ L t l 0 p l ( t ) e i l ( κ c 1 Δ ) t E n l ( t ) d t τ r t .
τ r t d I ( Ω ) d t [ g δ ( Ω ) ] I ( Ω ) = 2 τ 1 τ r t ( 2 γ L ) 2 d Ω F p ( Ω ) [ I ( Ω Ω ) I ( Ω ) ] 1 + [ τ 1 ( c 1 c 1 ) Ω ] 2 ,

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