Abstract

We develop a theoretical framework for modeling of continuous wave Yb-doped fiber lasers with highly nonlinear cavity dynamics. The developed approach has shown good agreement between theoretical predictions and experimental results for particular scheme of Yb-doped laser with large spectral broadening during single round trip. The model is capable to accurately describe main features of the experimentally measured laser outputs such as power efficiency slope, power leakage through fibre Bragg gratings, spectral broadening and spectral shape of generated radiation.

© 2011 OSA

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2010

2009

2008

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008).
[CrossRef] [PubMed]

K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008).
[CrossRef] [PubMed]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

2007

2006

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(11), 1696–1698 (2006).
[CrossRef] [PubMed]

L. M. Zhao and D. Y. Tang, “Generation of 15-nJ bunched noise-like pulses with 93-nm bandwidth in an erbium-doped fiber ring laser,” Appl. Phys. B 83(4), 553–557 (2006).
[CrossRef]

A. A. Fotiadi and P. Mégret, “Self-Q-switched Er-Brillouin fiber source with extra-cavity generation of a Raman supercontinuum in a dispersion-shifted fiber,” Opt. Lett. 31(11), 1621–1623 (2006).
[CrossRef] [PubMed]

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42(11), 1144–1156 (2006).
[CrossRef]

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(2), 023902 (2006).
[CrossRef] [PubMed]

J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48(4), 629–678 (2006).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

S. V. Smirnov, J. D. Ania-Castañón, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

2005

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71(5), 053809 (2005).
[CrossRef]

O. N. Egorova, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, and E. M. Dianov, “Effect of the spectral broadening of the first Stokes component on the efficiency of a two-stage Raman converter,” Quantum Electron. 35(4), 335–338 (2005).
[CrossRef]

2004

V. M. Paramonov, A. S. Kurkov, O. I. Medvedkov, D. A. Grukh, and E. M. Dianov, “Two-frequency fibre Raman laser,” Quantum Electron. 34(3), 213–215 (2004).
[CrossRef]

A. S. Kurkov and E. M. Dianov, “Moderate-power CW fiber lasers,” Quantum Electron. 34(10), 881–900 (2004).
[CrossRef]

N. Kurukitkoson, S. K. Turitsyn, A. S. Kurkov, and E. M. Dianov, “Multiple output wavelength composite Raman fiber converter,” Laser Phys. 14(9), 1227–1230 (2004).

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[CrossRef] [PubMed]

F. Vanholsbeeck, St. Coen, Ph. Emplit, C. Martinelli, F. Leplingard, and T. Sylvestre, “Numerical modeling of a four-wave-mixing-assisted Raman fiber laser,” Opt. Lett. 29(23), 2719–2721 (2004).
[CrossRef] [PubMed]

P. Suret and S. Randoux, “Influence of spectral broadening on steady characteristics of Raman fiber lasers: from experiments to questions about the validity of usual models,” Opt. Commun. 237(1-3), 201–212 (2004).
[CrossRef]

A. A. Fotiadi, P. Mégret, and M. Blondel, “Dynamics of a self-Q-switched fiber laser with a Rayleigh-stimulated Brillouin scattering ring mirror,” Opt. Lett. 29(10), 1078–1080 (2004).
[CrossRef] [PubMed]

2003

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” C. R. Phys. 4(1), 145–161 (2003).
[CrossRef]

J. C. Bouteiller, “Spectral modeling of Raman fiber lasers,” IEEE Photon. Technol. Lett. 15(12), 1698–1700 (2003).
[CrossRef]

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

2002

2001

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (2001).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[CrossRef] [PubMed]

2000

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
[CrossRef]

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36(10), 1117–1122 (2000).
[CrossRef]

1998

1997

1995

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

1992

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28(10), 2086–2096 (1992).
[CrossRef]

1986

K. P. Komarov, “Theory of stationary ultrashort pulses in solid-state lasers with passive mode-locking,” Opt. Spectrosc. 60, 231–234 (1986).

1975

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11(9), 736–746 (1975).
[CrossRef]

Akhmediev, N.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[CrossRef] [PubMed]

Ania-Castanon, J. D.

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

Ania-Castañón, J. D.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

V. Karalekas, J. D. Ania-Castañón, P. Harper, S. A. Babin, E. V. Podivilov, and S. K. Turitsyn, “Impact of nonlinear spectral broadening in ultra-long Raman fibre lasers,” Opt. Express 15(25), 16690–16695 (2007).
[CrossRef] [PubMed]

S. V. Smirnov, J. D. Ania-Castañón, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

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(2), 023902 (2006).
[CrossRef] [PubMed]

Babin, S. A.

Bale, B. G.

B. G. Bale, S. Boscolo, J. N. Kutz, and S. K. Turitsyn, “Intracavity dynamics in high-power mode-locked fiber lasers,” Phys. Rev. A 81(3), 033828 (2010).
[CrossRef]

Barber, P. R.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

Barviau, B.

Blondel, M.

Boscolo, S.

B. G. Bale, S. Boscolo, J. N. Kutz, and S. K. Turitsyn, “Intracavity dynamics in high-power mode-locked fiber lasers,” Phys. Rev. A 81(3), 033828 (2010).
[CrossRef]

Bouteiller, J. C.

J. C. Bouteiller, “Spectral modeling of Raman fiber lasers,” IEEE Photon. Technol. Lett. 15(12), 1698–1700 (2003).
[CrossRef]

Buckley, J. R.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[CrossRef] [PubMed]

Carman, R. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

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(2), 023902 (2006).
[CrossRef] [PubMed]

Cheng, X.

Churkin, D. V.

Clark, W. G.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[CrossRef] [PubMed]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Coen, St.

Cristiani, I.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36(10), 1117–1122 (2000).
[CrossRef]

Dalloz, N.

Dawes, J. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

Debaes, C.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42(11), 1144–1156 (2006).
[CrossRef]

Degiorgio, V.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36(10), 1117–1122 (2000).
[CrossRef]

Deparis, O.

Dianov, E. M.

O. N. Egorova, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, and E. M. Dianov, “Effect of the spectral broadening of the first Stokes component on the efficiency of a two-stage Raman converter,” Quantum Electron. 35(4), 335–338 (2005).
[CrossRef]

V. M. Paramonov, A. S. Kurkov, O. I. Medvedkov, D. A. Grukh, and E. M. Dianov, “Two-frequency fibre Raman laser,” Quantum Electron. 34(3), 213–215 (2004).
[CrossRef]

A. S. Kurkov and E. M. Dianov, “Moderate-power CW fiber lasers,” Quantum Electron. 34(10), 881–900 (2004).
[CrossRef]

N. Kurukitkoson, S. K. Turitsyn, A. S. Kurkov, and E. M. Dianov, “Multiple output wavelength composite Raman fiber converter,” Laser Phys. 14(9), 1227–1230 (2004).

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (2001).
[CrossRef]

Dudley, J. M.

Eggleton, B. J.

Egorova, O. N.

O. N. Egorova, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, and E. M. Dianov, “Effect of the spectral broadening of the first Stokes component on the efficiency of a two-stage Raman converter,” Quantum Electron. 35(4), 335–338 (2005).
[CrossRef]

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (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(2), 023902 (2006).
[CrossRef] [PubMed]

S. V. Smirnov, J. D. Ania-Castañón, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Emplit, Ph.

Falkovich, G.

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, “Optical turbulence and spectral condensate in long-fiber lasers,” Phys. Rev. A 80(3), 031804(R) (2009).
[CrossRef]

Fedoruk, M.

Fedoruk, M. P.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” C. R. Phys. 4(1), 145–161 (2003).
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K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374(34), 3585–3589 (2010).
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Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28(10), 2086–2096 (1992).
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V. M. Paramonov, A. S. Kurkov, O. I. Medvedkov, D. A. Grukh, and E. M. Dianov, “Two-frequency fibre Raman laser,” Quantum Electron. 34(3), 213–215 (2004).
[CrossRef]

Hammani, K.

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374(34), 3585–3589 (2010).
[CrossRef]

K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008).
[CrossRef] [PubMed]

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H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

Harper, P.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

V. Karalekas, J. D. Ania-Castañón, P. Harper, S. A. Babin, E. V. Podivilov, and S. K. Turitsyn, “Impact of nonlinear spectral broadening in ultra-long Raman fibre lasers,” Opt. Express 15(25), 16690–16695 (2007).
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H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
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Sh. Namiki, E. P. Ippen, H. A. Haus, and C. X. Yu, “Energy rate equations for mode-locked lasers,” J. Opt. Soc. Am. B 14(8), 2099–2111 (1997).
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H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28(10), 2086–2096 (1992).
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H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11(9), 736–746 (1975).
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Herda, R.

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(2), 023902 (2006).
[CrossRef] [PubMed]

Ilday, F. O.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[CrossRef] [PubMed]

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Sh. Namiki, E. P. Ippen, H. A. Haus, and C. X. Yu, “Energy rate equations for mode-locked lasers,” J. Opt. Soc. Am. B 14(8), 2099–2111 (1997).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28(10), 2086–2096 (1992).
[CrossRef]

Ismagulov, A. E.

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[CrossRef] [PubMed]

Kablukov, S. I.

Karalekas, V.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

V. Karalekas, J. D. Ania-Castañón, P. Harper, S. A. Babin, E. V. Podivilov, and S. K. Turitsyn, “Impact of nonlinear spectral broadening in ultra-long Raman fibre lasers,” Opt. Express 15(25), 16690–16695 (2007).
[CrossRef] [PubMed]

Kibler, B.

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374(34), 3585–3589 (2010).
[CrossRef]

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Kiyan, R. V.

Kobtsev, S. M.

S. V. Smirnov, J. D. Ania-Castañón, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Komarov, A.

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71(5), 053809 (2005).
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Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[CrossRef] [PubMed]

Kukarin, S.

S. V. Smirnov, J. D. Ania-Castañón, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Kurkov, A. S.

O. N. Egorova, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, and E. M. Dianov, “Effect of the spectral broadening of the first Stokes component on the efficiency of a two-stage Raman converter,” Quantum Electron. 35(4), 335–338 (2005).
[CrossRef]

V. M. Paramonov, A. S. Kurkov, O. I. Medvedkov, D. A. Grukh, and E. M. Dianov, “Two-frequency fibre Raman laser,” Quantum Electron. 34(3), 213–215 (2004).
[CrossRef]

A. S. Kurkov and E. M. Dianov, “Moderate-power CW fiber lasers,” Quantum Electron. 34(10), 881–900 (2004).
[CrossRef]

N. Kurukitkoson, S. K. Turitsyn, A. S. Kurkov, and E. M. Dianov, “Multiple output wavelength composite Raman fiber converter,” Laser Phys. 14(9), 1227–1230 (2004).

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (2001).
[CrossRef]

Kurukitkoson, N.

N. Kurukitkoson, S. K. Turitsyn, A. S. Kurkov, and E. M. Dianov, “Multiple output wavelength composite Raman fiber converter,” Laser Phys. 14(9), 1227–1230 (2004).

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (2001).
[CrossRef]

Kutz, J. N.

B. G. Bale, S. Boscolo, J. N. Kutz, and S. K. Turitsyn, “Intracavity dynamics in high-power mode-locked fiber lasers,” Phys. Rev. A 81(3), 033828 (2010).
[CrossRef]

J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48(4), 629–678 (2006).
[CrossRef]

Leblond, H.

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71(5), 053809 (2005).
[CrossRef]

Leplingard, F.

Limpert, J.

Lin, C.

Mackechnie, C. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

Martinelli, C.

Medvedev, S. B.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” C. R. Phys. 4(1), 145–161 (2003).
[CrossRef]

Medvedkov, O. I.

O. N. Egorova, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, and E. M. Dianov, “Effect of the spectral broadening of the first Stokes component on the efficiency of a two-stage Raman converter,” Quantum Electron. 35(4), 335–338 (2005).
[CrossRef]

V. M. Paramonov, A. S. Kurkov, O. I. Medvedkov, D. A. Grukh, and E. M. Dianov, “Two-frequency fibre Raman laser,” Quantum Electron. 34(3), 213–215 (2004).
[CrossRef]

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

Mégret, P.

Mezentsev, V. K.

E. G. Turitsyna, S. K. Turitsyn, and V. K. Mezentsev, “Numerical investigation of the impact of reflectors on spectral performance of Raman fibre laser,” Opt. Express 18(5), 4469–4477 (2010).
[CrossRef] [PubMed]

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, “Optical turbulence and spectral condensate in long-fiber lasers,” Phys. Rev. A 80(3), 031804(R) (2009).
[CrossRef]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” C. R. Phys. 4(1), 145–161 (2003).
[CrossRef]

Millot, G.

Namiki, Sh.

Okhotnikov, O.

Ortaç, B.

Panajotov, K.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42(11), 1144–1156 (2006).
[CrossRef]

Paramonov, V. M.

O. N. Egorova, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, and E. M. Dianov, “Effect of the spectral broadening of the first Stokes component on the efficiency of a two-stage Raman converter,” Quantum Electron. 35(4), 335–338 (2005).
[CrossRef]

V. M. Paramonov, A. S. Kurkov, O. I. Medvedkov, D. A. Grukh, and E. M. Dianov, “Two-frequency fibre Raman laser,” Quantum Electron. 34(3), 213–215 (2004).
[CrossRef]

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (2001).
[CrossRef]

Pask, H. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

Picozzi, A.

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374(34), 3585–3589 (2010).
[CrossRef]

Podivilov, E. V.

Randoux, S.

Rini, M.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical modeling and optimization of cascaded Raman fiber lasers,” IEEE J. Quantum Electron. 36(10), 1117–1122 (2000).
[CrossRef]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[CrossRef] [PubMed]

Sanchez, F.

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71(5), 053809 (2005).
[CrossRef]

Schreiber, T.

Shapiro, E. G.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” C. R. Phys. 4(1), 145–161 (2003).
[CrossRef]

Shtyrina, O.

Shum, P. P.

Smirnov, S. V.

D. V. Churkin, S. V. Smirnov, and E. V. Podivilov, “Statistical properties of partially coherent cw fiber lasers,” Opt. Lett. 35(19), 3288–3290 (2010).
[CrossRef] [PubMed]

S. V. Smirnov, J. D. Ania-Castañón, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[CrossRef] [PubMed]

Sugahara, H.

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (2001).
[CrossRef]

Suret, P.

Sylvestre, T.

Tang, D. Y.

L. M. Zhao and D. Y. Tang, “Generation of 15-nJ bunched noise-like pulses with 93-nm bandwidth in an erbium-doped fiber ring laser,” Appl. Phys. B 83(4), 553–557 (2006).
[CrossRef]

Tang, M.

Thienpont, H.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42(11), 1144–1156 (2006).
[CrossRef]

Tian, X.

Town, G.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[CrossRef] [PubMed]

Tropper, A. C.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers—versatile sources for the 1-1.2 μm region,” IEEE J. Sel. Top. Quantum Electron. 1(1), 2–13 (1995).
[CrossRef]

Tünnermann, A.

Turitsyn, S.

Turitsyn, S. K.

E. G. Turitsyna, S. K. Turitsyn, and V. K. Mezentsev, “Numerical investigation of the impact of reflectors on spectral performance of Raman fibre laser,” Opt. Express 18(5), 4469–4477 (2010).
[CrossRef] [PubMed]

B. G. Bale, S. Boscolo, J. N. Kutz, and S. K. Turitsyn, “Intracavity dynamics in high-power mode-locked fiber lasers,” Phys. Rev. A 81(3), 033828 (2010).
[CrossRef]

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, “Optical turbulence and spectral condensate in long-fiber lasers,” Phys. Rev. A 80(3), 031804(R) (2009).
[CrossRef]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

V. Karalekas, J. D. Ania-Castañón, P. Harper, S. A. Babin, E. V. Podivilov, and S. K. Turitsyn, “Impact of nonlinear spectral broadening in ultra-long Raman fibre lasers,” Opt. Express 15(25), 16690–16695 (2007).
[CrossRef] [PubMed]

S. V. Smirnov, J. D. Ania-Castañón, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

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(2), 023902 (2006).
[CrossRef] [PubMed]

N. Kurukitkoson, S. K. Turitsyn, A. S. Kurkov, and E. M. Dianov, “Multiple output wavelength composite Raman fiber converter,” Laser Phys. 14(9), 1227–1230 (2004).

E. M. Dianov, A. S. Kurkov, O. I. Medvedkov, V. M. Paramonov, O. N. Egorova, N. Kurukitkoson, and S. K. Turitsyn, “Raman fiber source for the 1.6-1.75 micrometer spectral region,” Laser Phys. 13(3), 397–400 (2003).

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” C. R. Phys. 4(1), 145–161 (2003).
[CrossRef]

N. Kurukitkoson, H. Sugahara, S. K. Turitsyn, O. N. Egorova, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Optimisation of two-stage Raman converter based on phosphosilicate core fibre: modelling and experiment,” Electron. Lett. 37(21), 1281–1283 (2001).
[CrossRef]

Turitsyna, E. G.

E. G. Turitsyna, S. K. Turitsyn, and V. K. Mezentsev, “Numerical investigation of the impact of reflectors on spectral performance of Raman fibre laser,” Opt. Express 18(5), 4469–4477 (2010).
[CrossRef] [PubMed]

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, “Optical turbulence and spectral condensate in long-fiber lasers,” Phys. Rev. A 80(3), 031804(R) (2009).
[CrossRef]

Vanholsbeeck, F.

Vermeulen, N.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42(11), 1144–1156 (2006).
[CrossRef]

Wise, F. W.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[CrossRef] [PubMed]

Yu, C. X.

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(2), 023902 (2006).
[CrossRef] [PubMed]

Zhao, L. M.

L. M. Zhao and D. Y. Tang, “Generation of 15-nJ bunched noise-like pulses with 93-nm bandwidth in an erbium-doped fiber ring laser,” Appl. Phys. B 83(4), 553–557 (2006).
[CrossRef]

Appl. Phys. B

L. M. Zhao and D. Y. Tang, “Generation of 15-nJ bunched noise-like pulses with 93-nm bandwidth in an erbium-doped fiber ring laser,” Appl. Phys. B 83(4), 553–557 (2006).
[CrossRef]

C. R. Phys.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” C. R. Phys. 4(1), 145–161 (2003).
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Figures (6)

Fig. 1
Fig. 1

(left) Experimental setup, (right) transmission spectrum.

Fig. 2
Fig. 2

(top) Measured laser output power and (middle and bottom rows) output spectra for various pumping power at the flat end and at the FBG cavity edge.

Fig. 3
Fig. 3

Effective equivalent scheme used in modeling.

Fig. 4
Fig. 4

Power distribution inside laser cavity for maximal pump power (22.6 W at z = 0).

Fig. 5
Fig. 5

Computed and measures output power as a function of pump at z = 0. Upper curve shows the output through the flat end, bottom curve correspond to the leakage through FBG.

Fig. 6
Fig. 6

Output spectra as a function of pumping power.

Equations (19)

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    A + z + β 1 A + t + i β 2 2 2 A + t 2 i γ { | A + | 2 + 2 | A | 2 } A + = g ( | A + | 2 + | A | 2 ) A + α 2 A +
A z + β 1 A t + i β 2 2 2 A t 2 i γ { | A | 2 + 2 | A + | 2 } A = g ( | A + | 2 + | A | 2 ) A α 2 A
A L ( ω ) = 1 R L ( ω ) A ( ω ) ,    A R ( ω ) = 1 R R ( ω ) A + ( ω )
      d P + d z = g ( P ) P + α P +
d P d z = g ( P ) P α P
d N 2 ( z , t ) d t = ( σ 12 ( p ) ρ p ( 0 ) P p ( z ) h ν p + σ 12 ( s ) ρ s ( 0 ) P s + ( z ) + P s ( z ) h ν s ) N ( ( σ 21 ( p ) + σ 12 ( p ) ) ρ p ( 0 ) P p ( z ) h ν p + ( σ 21 ( s ) + σ 12 ( s ) ) ρ s ( 0 ) P s + ( z ) + P s ( z ) h ν s + 1 T Y b ) N 2 ( z , t ) d P p ( z ) d z = ( σ 21 ( p ) + σ 12 ( p ) ) ρ p ( 0 ) N 2 ( z , t ) P p ( z ) σ 12 ( p ) ρ p ( 0 ) N P p ( z ) d P s ± ( z ) d z = ± ( σ 21 ( s ) + σ 12 ( s ) ) ρ s ( 0 ) N 2 ( z , t ) P s ± ( z ) σ 12 ( s ) ρ s ( 0 ) N P s ± ( z )
N 2 ( z ) = N ( σ 12 ( p ) ρ p ( 0 ) h ν p P p ( z ) + σ 12 ( s ) ρ s ( 0 ) h ν s ( P s + ( z ) + P s ( z ) ) ) ( σ 21 ( p ) + σ 12 ( p ) ) ρ p ( 0 ) h ν p P p ( z ) + ( σ 21 ( p ) + σ 12 ( p ) ) ρ s ( 0 ) h ν s ( P s + ( z ) + P s ( z ) ) + 1 T
d P p ( z ) d z = α p P p ( z ) P s a t ( p ) + α p μ P s + ( z ) + P s ( z ) P s a t ( s ) 1 + P s + ( z ) + P s ( z ) P s a t ( s ) + P p ( z ) P s a t ( p ) P p ( z ) α p P p ( z )
d P s ± ( z ) d z = ± α s μ     P p ( z ) P s a t ( p ) + α s P s + ( z ) + P s ( z ) P s a t ( s ) 1 + P s + ( z ) + P s ( z ) P s a t ( s ) + P p ( z ) P s a t ( p ) P s ± ( z ) α s P s ± ( z ) = ± g ( P ) P s ± ( z ) α s P s ± ( z )
[ P p ( z ) P p ( 0 ) ] η P s ( z ) P s ( 0 ) / P s + ( z ) P s + ( 0 ) = [ P p ( z ) P p ( 0 ) ] η ( P s + ( z ) P s + ( 0 ) ) 1 = exp [ α s ( 1 μ ) z ] .
P s ( z ) = P s + ( z ) + P s ( z ) = P s + ( 0 ) × e α s ( 1 μ ) z × [ P p ( z ) P p ( 0 ) ] η + P s ( 0 ) × e α s ( 1 μ ) z × [ P p ( z ) P p ( 0 ) ] η .
α p = α s μ ( ln 1 β ln ( 1 1 R ) ) α s L ( μ 1 ) ln ( 1 R )
η d ln f d x = μ + ( 1 μ ) h ( x ) 1 + f ( x ) + h ( x )
d ln h ± d x = ± 1 + ( μ 1 ) f ( x ) 1 + f ( x ) + h ( x )
f ( 0 ) = f 0 = P p ( 0 ) / P s a t ( p ) , h ( l 0 = L α s ) = R h ( l 0 ) , h ( 0 ) = h + ( 0 ) .
A + ( n ) z + β 1 A + ( n ) t + i β 2 2 2 A + ( n ) t 2 i γ { | A + ( n ) | 2 + 2 | A ( n 1 ) | 2 } A + = g ( A + ( n ) , A ( n 1 ) ) 2 A + ( n ) α 2 A + ( n )
A ( n ) z + β 1 A ( n ) t + i β 2 2 2 A ( n ) t 2 i γ { | A ( n ) | 2 + 2 | A + ( n 1 ) | 2 } A = g ( A + ( n ) , A ( n ) ) 2 A ( n ) α 2 A ( n )
g ( P + , P ) = α s μ     P p ( z ) P s a t ( p ) + α s P + ( z ) + P ( z ) P s a t ( s ) 1 + P + ( z ) + P ( z ) P s a t ( s ) + P p ( z ) P s a t ( p ) ,    P ± ( z ) = 1 T | A ± ( z , t ) | 2 d t
A f ( n ) ( 0 , t ) = R 4 % A b ( n 1 ) ( L , t ) ,    A b ( n ) ( 0 , ω ) = R ( ω ) A f ( n ) ( L , ω )

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