Abstract

We present an analytical theory based on wave kinetic equations that describes a Raman fiber laser (RFL) generation spectrum. It is shown both theoretically and experimentally that the quasi-degenerate four-wave mixing 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.

© 2006 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, Opt. Lett. 25, 402 (2000).
    [CrossRef]
  2. D. Georgiev, V. P. Gapontsev, A. G. Dronov, M. Y. Vyatkin, A. B. Rulkov, S. V. Popov, and J. R. Taylor, Opt. Express 13, 6772 (2005).
    [CrossRef] [PubMed]
  3. S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, J. Opt. Soc. Am. B 23, 1524 (2006).
    [CrossRef]
  4. V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, Can. J. Phys. 78, 407 (2000).
    [CrossRef]
  5. F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.
  6. Q. Wang, Y. Wang, W. Zhang, X. Feng, X. Liu, and B. Zhou, Opt. Lett. 30, 952 (2005).
    [CrossRef] [PubMed]
  7. P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004).
    [CrossRef]
  8. J.-C. Bouteiller, IEEE Photon. Technol. Lett. 15, 1698 (2003).
    [CrossRef]
  9. S. Huang, Y. Feng, A. Shirakawa, and K.-I. Ueda, Jpn. J. Appl. Phys. Part 2 42, L1439 (2003).
    [CrossRef]
  10. V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer-Verlag, 1992).
  11. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  12. S. A. Babin, D. V. Churkin, and E. V. Podivilov, Opt. Commun. 226, 329 (2003).
    [CrossRef]
  13. S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
    [CrossRef]
  14. Y. Wang and H. Po, Opt. Eng. 42, 2872 (2003).
    [CrossRef]
  15. S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, Quantum Electron. 33, 1096 (2003).
    [CrossRef]

2006 (1)

2005 (3)

2004 (1)

P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004).
[CrossRef]

2003 (5)

J.-C. Bouteiller, IEEE Photon. Technol. Lett. 15, 1698 (2003).
[CrossRef]

S. Huang, Y. Feng, A. Shirakawa, and K.-I. Ueda, Jpn. J. Appl. Phys. Part 2 42, L1439 (2003).
[CrossRef]

S. A. Babin, D. V. Churkin, and E. V. Podivilov, Opt. Commun. 226, 329 (2003).
[CrossRef]

Y. Wang and H. Po, Opt. Eng. 42, 2872 (2003).
[CrossRef]

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, Quantum Electron. 33, 1096 (2003).
[CrossRef]

2000 (2)

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, Opt. Lett. 25, 402 (2000).
[CrossRef]

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, Can. J. Phys. 78, 407 (2000).
[CrossRef]

Agrawal, G. P.

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

Babin, S. A.

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, J. Opt. Soc. Am. B 23, 1524 (2006).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
[CrossRef]

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, Quantum Electron. 33, 1096 (2003).
[CrossRef]

S. A. Babin, D. V. Churkin, and E. V. Podivilov, Opt. Commun. 226, 329 (2003).
[CrossRef]

Bayart, D.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

Borne, S.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

Bouteiller, J.-C.

J.-C. Bouteiller, IEEE Photon. Technol. Lett. 15, 1698 (2003).
[CrossRef]

Bubnov, M. M.

Bufetov, I. A.

Churkin, D. V.

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, J. Opt. Soc. Am. B 23, 1524 (2006).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
[CrossRef]

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, Quantum Electron. 33, 1096 (2003).
[CrossRef]

S. A. Babin, D. V. Churkin, and E. V. Podivilov, Opt. Commun. 226, 329 (2003).
[CrossRef]

Clements, W. R. L.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, Can. J. Phys. 78, 407 (2000).
[CrossRef]

Dianov, E. M.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, Can. J. Phys. 78, 407 (2000).
[CrossRef]

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, Opt. Lett. 25, 402 (2000).
[CrossRef]

Dronov, A. G.

Falkovich, G.

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

Feng, X.

Feng, Y.

S. Huang, Y. Feng, A. Shirakawa, and K.-I. Ueda, Jpn. J. Appl. Phys. Part 2 42, L1439 (2003).
[CrossRef]

Fotiadi, A. A.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
[CrossRef]

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, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

Huang, S.

S. Huang, Y. Feng, A. Shirakawa, and K.-I. Ueda, Jpn. J. Appl. Phys. Part 2 42, L1439 (2003).
[CrossRef]

Kablukov, S. I.

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, J. Opt. Soc. Am. B 23, 1524 (2006).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
[CrossRef]

Karpov, V. I.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, Can. J. Phys. 78, 407 (2000).
[CrossRef]

Kurkov, A. S.

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, Quantum Electron. 33, 1096 (2003).
[CrossRef]

Leclere, C.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

Leplingard, F.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

Liu, X.

Lopez, T.

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

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, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

Medvedkov, O. I.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
[CrossRef]

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, Opt. Lett. 25, 402 (2000).
[CrossRef]

Papernyi, S. B.

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, Can. J. Phys. 78, 407 (2000).
[CrossRef]

Po, H.

Y. Wang and H. Po, Opt. Eng. 42, 2872 (2003).
[CrossRef]

Podivilov, E. V.

S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov, J. Opt. Soc. Am. B 23, 1524 (2006).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
[CrossRef]

S. A. Babin, D. V. Churkin, and E. V. Podivilov, Opt. Commun. 226, 329 (2003).
[CrossRef]

Popov, S. V.

Potapov, V. V.

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, Quantum Electron. 33, 1096 (2003).
[CrossRef]

Randoux, S.

P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004).
[CrossRef]

Rulkov, A. B.

Shirakawa, A.

S. Huang, Y. Feng, A. Shirakawa, and K.-I. Ueda, Jpn. J. Appl. Phys. Part 2 42, L1439 (2003).
[CrossRef]

Suret, P.

P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004).
[CrossRef]

Taylor, J. R.

Ueda, K.-I.

S. Huang, Y. Feng, A. Shirakawa, and K.-I. Ueda, Jpn. J. Appl. Phys. Part 2 42, L1439 (2003).
[CrossRef]

Vasiliev, S. A.

Vyatkin, M. Y.

Wang, Q.

Wang, Y.

Zakharov, V. E.

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

Zhang, W.

Zhou, B.

Can. J. Phys. (1)

V. I. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, Can. J. Phys. 78, 407 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J.-C. Bouteiller, IEEE Photon. Technol. Lett. 15, 1698 (2003).
[CrossRef]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, IEEE Photon. Technol. Lett. 17, 2553 (2005).
[CrossRef]

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

Jpn. J. Appl. Phys. Part 2 (1)

S. Huang, Y. Feng, A. Shirakawa, and K.-I. Ueda, Jpn. J. Appl. Phys. Part 2 42, L1439 (2003).
[CrossRef]

Opt. Commun. (2)

P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004).
[CrossRef]

S. A. Babin, D. V. Churkin, and E. V. Podivilov, Opt. Commun. 226, 329 (2003).
[CrossRef]

Opt. Eng. (1)

Y. Wang and H. Po, Opt. Eng. 42, 2872 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Quantum Electron. (1)

S. A. Babin, A. S. Kurkov, V. V. Potapov, and D. V. Churkin, Quantum Electron. 33, 1096 (2003).
[CrossRef]

Other (3)

F. Leplingard, S. Borne, C. Martinelli, C. Leclere, T. Lopez, J. Guerin, and D. Bayart, in Proceedings of Optical Fiber Communications Conference (Optical Society of America, 2003), pp. 431.

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

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

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Figures (2)

Fig. 1
Fig. 1

a, Effective losses of FBGs forming the RFL cavity. b, Intracavity Stokes wave spectrum at the intracavity power I = 3.8 W : calculation from Eq. (3) (solid curve) and experiment (dotted curve).

Fig. 2
Fig. 2

a, Full width at 1 cosh ( 1 ) level of the intracavity Stokes wave spectrum. b, Spectral power density at its maximum. Experiment (squares) and calculation from Eqs. (5, 6) (solid line). The dashed line is the analytical calculation at low power.

Equations (7)

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τ rt d E n d t 1 2 ( g δ n ) E n ( t ) = i γ L l E n l ( t ) k E k ( t ) E k l * ( t ) ,
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
τ rt d I ( Ω ) d t [ g δ ( Ω ) ] I ( Ω ) = ϵ ( γ L I ) 2 I ( Ω ) + ϵ ( γ L ) 2 I ( Ω 1 ) I ( Ω 2 ) I ( Ω 1 + Ω 2 Ω ) d Ω 1 d Ω 2 ,
I ( Ω ) = δ 2 γ L 2 ϵ cosh ( π Ω δ 2 γ L I 2 ϵ ) .
δ 0 + 1 2 ϵ ( γ I L ) 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 .
Γ = 2 γ L I 2 ϵ π δ 2 ,
I ( 0 ) = δ 2 γ L 2 ϵ .

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