Abstract

I model the nonlinear fiber laser using an expanded Ginzburg-Landau equation (GLE) which includes the self-steepening (SS) and intrapulse Raman scattering (IRS) effects. I show that above a minimum value of the Raman effect, it is possible to find two chirped solitary pulses for the laser system. The smaller chirped solitary wave corresponds to the dispersion-managed (DM) regime whereas the larger chirped solitary wave corresponds to the so-called similariton regime.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Haus, E. P. Ippen, and K. Tamura, "Additive-pulse mode-locking in fiber lasers," IEEE J. Quantum Electron. 30,200-208 (1994).
    [CrossRef]
  2. P. -A. Bélanger, "On the profile of pulses generated by fiber lasers," Opt. Express 13,8089-8096 (2005).
    [CrossRef] [PubMed]
  3. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar evolution of parabolic pulses in a laser," Phys. Rev. Lett. 92,213902 (2004).
    [CrossRef] [PubMed]
  4. F. Ilday, F. Wise, and F. Kaertner, "Possibility of self-similar pulse evolution in a Ti:sapphire laser," Opt. Express 12,2731-2738 (2004).
    [CrossRef] [PubMed]
  5. B. Ortac¸, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ö. Ilday, "Generation of parabolic bound pulses from a Yb-fiber laser," Opt. Express 14,6075-6083 (2006).
    [CrossRef] [PubMed]
  6. N. Akhmediev, and A. Ankiewitz, Solitons, nonlinear pulses and beams (Chapman and Hall, London, 1997).
  7. Z. Li, L. Li, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse formwith self-frequancy shift," Phys. Rev. Lett. 89,263901 (2002).
    [CrossRef] [PubMed]
  8. D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, "Wave-breaking-free pulses in nonlinear optical fibers," J. Opt. Soc. Am. B 10,1185-1190 (1993).
    [CrossRef]
  9. A. Ruehl, O. Prochnow, D. Wandt, D, Kracht, B. Burgoyne, N. Godbout, and S. Lacroix, "Dynamics of parabolic pulses in a ultrafast fiber laser," Opt. Lett. 31,2734-2736 (2006).
    [CrossRef] [PubMed]
  10. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
    [CrossRef] [PubMed]
  11. C. Finot, G. Millot, C. Billet, and J. M. Dudley, "Experimental generation of parabolic pulses via Raman amplification in optical fiber," Opt. Express 11,1547-1552 (2003).
    [CrossRef] [PubMed]
  12. L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, "Gain-guided solitons in dispersion-managed fiber lasers with large net cavity dispersion," Opt. Lett. 31,2957-2959 (2006).
    [CrossRef] [PubMed]
  13. L. M. Zhao, D. Y. Tang, and C. Lu, "Gain-guided solitons in a positive group-dispersion fiber laser," Opt. Lett. 31,1788-1790 (2006).
    [CrossRef] [PubMed]
  14. I. S. Gradshteyn, and I. M. Ryzhik, Tables of Integrals, Series and Products. (Academic press, New York, 2000).

2006 (4)

2005 (1)

2004 (2)

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

F. Ilday, F. Wise, and F. Kaertner, "Possibility of self-similar pulse evolution in a Ti:sapphire laser," Opt. Express 12,2731-2738 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

Z. Li, L. Li, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse formwith self-frequancy shift," Phys. Rev. Lett. 89,263901 (2002).
[CrossRef] [PubMed]

2000 (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
[CrossRef] [PubMed]

1994 (1)

H. A. Haus, E. P. Ippen, and K. Tamura, "Additive-pulse mode-locking in fiber lasers," IEEE J. Quantum Electron. 30,200-208 (1994).
[CrossRef]

1993 (1)

Anderson, D.

Bélanger, P. -A.

Billet, C.

Brunel, M.

Buckley, J. R.

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

Chédot, C.

Cheng, T. H.

Clark, W. G.

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

Desaix, M.

Dudley, J. M.

C. Finot, G. Millot, C. Billet, and J. M. Dudley, "Experimental generation of parabolic pulses via Raman amplification in optical fiber," Opt. Express 11,1547-1552 (2003).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
[CrossRef] [PubMed]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
[CrossRef] [PubMed]

Finot, C.

Harvey, J. D.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus, E. P. Ippen, and K. Tamura, "Additive-pulse mode-locking in fiber lasers," IEEE J. Quantum Electron. 30,200-208 (1994).
[CrossRef]

Hideur, A.

Ilday, F.

Ilday, F. Ö.

B. Ortac¸, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ö. Ilday, "Generation of parabolic bound pulses from a Yb-fiber laser," Opt. Express 14,6075-6083 (2006).
[CrossRef] [PubMed]

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

Ippen, E. P.

H. A. Haus, E. P. Ippen, and K. Tamura, "Additive-pulse mode-locking in fiber lasers," IEEE J. Quantum Electron. 30,200-208 (1994).
[CrossRef]

Kaertner, F.

Karlsson, M.

Kruglov, V. I.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
[CrossRef] [PubMed]

Li, L.

Z. Li, L. Li, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse formwith self-frequancy shift," Phys. Rev. Lett. 89,263901 (2002).
[CrossRef] [PubMed]

Li, Z.

Z. Li, L. Li, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse formwith self-frequancy shift," Phys. Rev. Lett. 89,263901 (2002).
[CrossRef] [PubMed]

Limpert, J.

Lisak, M.

Lu, C.

Millot, G.

Ortac¸, B.

Prochnow, O.

Quiroga-Teixeiro, M. L.

Ruehl, A.

Spatschek, K. H.

Z. Li, L. Li, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse formwith self-frequancy shift," Phys. Rev. Lett. 89,263901 (2002).
[CrossRef] [PubMed]

Tamura, K.

H. A. Haus, E. P. Ippen, and K. Tamura, "Additive-pulse mode-locking in fiber lasers," IEEE J. Quantum Electron. 30,200-208 (1994).
[CrossRef]

Tang, D. Y.

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
[CrossRef] [PubMed]

Tünnermann, A.

Wandt, D.

Wise, F.

Wise, F. W.

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

Zhao, L. M.

Zhou, G.

Z. Li, L. Li, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse formwith self-frequancy shift," Phys. Rev. Lett. 89,263901 (2002).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

H. A. Haus, E. P. Ippen, and K. Tamura, "Additive-pulse mode-locking in fiber lasers," IEEE J. Quantum Electron. 30,200-208 (1994).
[CrossRef]

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

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84,6010-6013 (2000).
[CrossRef] [PubMed]

Z. Li, L. Li, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse formwith self-frequancy shift," Phys. Rev. Lett. 89,263901 (2002).
[CrossRef] [PubMed]

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

Other (2)

N. Akhmediev, and A. Ankiewitz, Solitons, nonlinear pulses and beams (Chapman and Hall, London, 1997).

I. S. Gradshteyn, and I. M. Ryzhik, Tables of Integrals, Series and Products. (Academic press, New York, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Chirp parameter β as a function of the IRS effect TRω 0. The different operating regimes can be seen for TRω 0=5. The solitonic regime corresponding to the case where β=0 is also included in the figure.

Fig. 2.
Fig. 2.

Spectral [(a) and (c)] (given by Eq. (2) of Ref. [2]) and phase distribution ((b) and (d)) for different values of β ranging from 0–60. The amplitude of the various depicted spectra, while being arbitrary, ensures that all the shown spectra have the same energy.

Fig. 3.
Fig. 3.

Spectral (a) profile given by Eqs. (6a) and (6b) and corresponding temporal profile (b) calculated from the inverse Fourier transform of Eq. (6a).

Equations (34)

Equations on this page are rendered with MathJax. Learn more.

i V x + β 2 2 V ττ i ( g l ) ν γ V 2 V + i β 3 6 V τττ i γ 0 ω 0 ( V 2 V ) τ + γ 0 T R ( V 2 ) τ V = 0
V ( τ , x ) = V 0 { sech [ α ( τ + bx ) ] } 1 i β exp [ i ( a τ Γ x ) ]
T R ω 0 = β 4 ( β 2 + 9 ) ( β 2 1 )
ν f = 2 α π 2 arcsinh [ cosh ( π 2 β ) ]
ν f α β π
V ̂ ( ν ) = V ̂ 0 exp ( 1.386 ν 2 ν f 2 ) for ν ν f 2
V ̂ ( ν ) = 0 for ν > ν f 2
τ f ν f = 0.9309
V ( τ ) = V 0 sech ( α τ ) exp { i β ln [ sech ( α τ ) ] }
α β = π ν f = 22
( γ 0 L ) V 0 2 = ( Γ L )
( Γ L ) = π 2 ν f 2 2 ( β ¯ L )
2 g L T 0 2 0.05 ν g 2
ν f 2 ν g 2 12 ( Γ L ) β
C = 0.66 ( g l ) L β ¯ L
C = 1.22 ( g l ) L β ¯ L
α 2 ( 1 i β ) ( i β 2 ) = 2 V 0 2 ( γ γ 0 a ω 0 ) ( β 2 β 3 a )
α 2 ( 1 i β ) 2 = 2 [ Γ a 2 2 ( β 2 β 3 a 3 ) i ( g l ) ( β 2 β 3 a ) ]
α 2 ( 1 i β ) ( i β 2 ) = 6 γ 0 V 0 2 β 3 ω 0 ( β 2 + 9 ) [ ( β 2 + 9 ) 2 T R ω 0 β + 6 i T R ω 0 ]
α 2 ( 1 i β ) 2 = 6 β 3 ( β 2 a β 3 a 2 2 + b )
β 4 ( β 2 + 9 ) ( β 2 1 ) = T R ω 0
a 2 ω 0 2 a ω 0 [ 1 ε 0 ( β 2 2 ) 3 β ] = α 2 ( β 2 + 1 ) ( β 2 + 4 ) 6 ( β 2 1 )
Γ = ( g l ) ( β 2 + 2 ) β
γ 0 V 0 2 = 3 ( g l ) ( β 2 + 4 ) [ 3 β ε 0 ( β 2 2 ) ]
α 2 = 3 ( g l ) g T 0 ( β 2 + 1 )
b = β ¯ a ( β 2 + 1 ) [ β ε 0 ( β 2 + 2 ) ] 2 β [ ( β 2 2 ) + 3 β ε 0 ]
g T 0 2 = β ¯ 2 [ 3 β ε 0 ( β 2 2 ) ] [ ( β 2 2 ) + 3 β ε 0 ]
β 3 ω 0 = 3 β ¯ ( β 2 + 1 ) ( β 2 + 4 ) 2 ( β 2 1 ) [ ( β 2 2 ) + 3 β ε 0 ]
V x = ε 0 γ 0 V 2 V
F T [ V 2 V ] = [ ( 1 i β ) 2 + ( 2 π ν α ) 2 ] ( 2 i β ) ( 1 i β ) V ̂
V ̂ = V ̂ i exp [ ε 0 γ 0 x 0 V 0 2 ( 2 π ν α ) 2 ( 2 i β ) ( 1 i β ) ]
V ̂ = V ̂ i exp [ ε 0 γ 0 x 0 V 0 2 ( 4 ν 2 ν f 2 ) ]
V ̂ ( ν ) = V ̂ 0 exp ( 1.386 ν 2 ν f 2 ) for ν ν f 2
V ̂ ( ν ) = 0 for ν > ν f 2

Metrics