Abstract

We derive a general characterization of the intracavity pulse dynamics for passively mode-locked fiber lasers based on the use of the variational principle. As a first application this method is used for an efficient simulation of the laser dynamics of stretched pulse and similariton lasers and evaluation of its stability.

© 2007 Optical Society of America

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References

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  1. H. A. Haus, "Mode-Locking of Lasers," IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
    [CrossRef]
  2. H. A. Haus, K. Tamura, L. E. Nelson and E. P. Ippen "Stretched-Pulse Additive Pulse Mode-Locking in Fiber Abstruct- Stretched-pulse Ring Lasers: Theory and Experiment," IEEE J. QuantumElectron. 31, 591-598 (1995).
    [CrossRef]
  3. V. I. Kruglov, A. C. Peacock, J. M. Dudley and J. D. Harvey, "Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers, "Opt. Lett. 25, 1753-1755 (2000).
    [CrossRef]
  4. 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]
  5. J. N. Kutz, P. Holmes, S. G. Evangelides, J. P. Gordon, " Hamiltonian dynamics of dispersion-managed breathers," J. Opt. Soc. Am. B 15, 87-96 (1998).
    [CrossRef]
  6. C. Jirauscheck, U. Morgner and F. X. Kärtner, "Variational analysis of spatio-temporal pulse dynamics in dispersive Kerr media," J. Opt. Soc. Am. B 19, 1716-1721 (2002).
    [CrossRef]
  7. C. Jirauscheck, U. Morgner and F. X. Kärtner, "Spatiotemporal Gaussian pulse dynamics in Kerr-lens modelocked lasers," J. Opt. Soc. Am. B 20, 1356-1368 (2003).
    [CrossRef]
  8. C. Jirauscheck and F. X. Kärtner, "Gaussian pulse dynamics in gain media with Kerr nonlinearity," J. Opt. Soc. Am. B 23, 1776-1784 (2006).
    [CrossRef]
  9. J- G. Caputo, N. Flytzanis, M. P. Sorensen, "Ring laser configuration studied by collective coordinates," J. Opt. Soc. Am. B 12, 139-145 (1995).
    [CrossRef]
  10. S. Waiyapot and M. Matsumoto, "Jitter and time stability of an actively mode-locked dispersion-managed fiber laser," Opt. Commun. 188, 167-180 (2001).
    [CrossRef]
  11. M. Horowitz and C. R. Menyuk, "Analysis of pulse dropout in harmonically mode-locked fiber lasers by use of the Lyapunov method," Opt. Lett. 25, 40-42 (2000).
    [CrossRef]
  12. C. Jirauschek and F. Ö. Ilday, "Theory of the Self-Similar Laser Oscillator," CLEO 2005, Paper JWB65 (2005).
  13. K. Tamura, E. P. Ippen, H. A. Haus and L. Nelson, "77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser," Opt. Lett. 18, 1080-1082 (1993).
    [CrossRef] [PubMed]
  14. Introduction to numerical analysis, ser. Texts in Applied Mathematics, vol. 12, Springer (2002).
  15. Advanced Synergetics, ser. Springer Series, vol. 20, Springer-Verlag (1983).

2006 (1)

2004 (1)

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]

2003 (1)

2002 (1)

2001 (1)

S. Waiyapot and M. Matsumoto, "Jitter and time stability of an actively mode-locked dispersion-managed fiber laser," Opt. Commun. 188, 167-180 (2001).
[CrossRef]

2000 (3)

1998 (1)

1995 (2)

H. A. Haus, K. Tamura, L. E. Nelson and E. P. Ippen "Stretched-Pulse Additive Pulse Mode-Locking in Fiber Abstruct- Stretched-pulse Ring Lasers: Theory and Experiment," IEEE J. QuantumElectron. 31, 591-598 (1995).
[CrossRef]

J- G. Caputo, N. Flytzanis, M. P. Sorensen, "Ring laser configuration studied by collective coordinates," J. Opt. Soc. Am. B 12, 139-145 (1995).
[CrossRef]

1993 (1)

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]

Caputo, J- G.

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]

Dudley, J. M.

Evangelides, S. G.

Flytzanis, N.

Gordon, J. P.

Harvey, J. D.

Haus, H. A.

H. A. Haus, "Mode-Locking of Lasers," IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson and E. P. Ippen "Stretched-Pulse Additive Pulse Mode-Locking in Fiber Abstruct- Stretched-pulse Ring Lasers: Theory and Experiment," IEEE J. QuantumElectron. 31, 591-598 (1995).
[CrossRef]

K. Tamura, E. P. Ippen, H. A. Haus and L. Nelson, "77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser," Opt. Lett. 18, 1080-1082 (1993).
[CrossRef] [PubMed]

Holmes, P.

Horowitz, M.

Ilday, F. Ö.

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, K. Tamura, L. E. Nelson and E. P. Ippen "Stretched-Pulse Additive Pulse Mode-Locking in Fiber Abstruct- Stretched-pulse Ring Lasers: Theory and Experiment," IEEE J. QuantumElectron. 31, 591-598 (1995).
[CrossRef]

K. Tamura, E. P. Ippen, H. A. Haus and L. Nelson, "77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser," Opt. Lett. 18, 1080-1082 (1993).
[CrossRef] [PubMed]

Jirauscheck, C.

Kärtner, F. X.

Kruglov, V. I.

Kutz, J. N.

Matsumoto, M.

S. Waiyapot and M. Matsumoto, "Jitter and time stability of an actively mode-locked dispersion-managed fiber laser," Opt. Commun. 188, 167-180 (2001).
[CrossRef]

Menyuk, C. R.

Morgner, U.

Nelson, L.

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson and E. P. Ippen "Stretched-Pulse Additive Pulse Mode-Locking in Fiber Abstruct- Stretched-pulse Ring Lasers: Theory and Experiment," IEEE J. QuantumElectron. 31, 591-598 (1995).
[CrossRef]

Peacock, A. C.

Sorensen, M. P.

Tamura, K.

H. A. Haus, K. Tamura, L. E. Nelson and E. P. Ippen "Stretched-Pulse Additive Pulse Mode-Locking in Fiber Abstruct- Stretched-pulse Ring Lasers: Theory and Experiment," IEEE J. QuantumElectron. 31, 591-598 (1995).
[CrossRef]

K. Tamura, E. P. Ippen, H. A. Haus and L. Nelson, "77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser," Opt. Lett. 18, 1080-1082 (1993).
[CrossRef] [PubMed]

Waiyapot, S.

S. Waiyapot and M. Matsumoto, "Jitter and time stability of an actively mode-locked dispersion-managed fiber laser," Opt. Commun. 188, 167-180 (2001).
[CrossRef]

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]

IEEE J. QuantumElectron. (1)

H. A. Haus, K. Tamura, L. E. Nelson and E. P. Ippen "Stretched-Pulse Additive Pulse Mode-Locking in Fiber Abstruct- Stretched-pulse Ring Lasers: Theory and Experiment," IEEE J. QuantumElectron. 31, 591-598 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. A. Haus, "Mode-Locking of Lasers," IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

S. Waiyapot and M. Matsumoto, "Jitter and time stability of an actively mode-locked dispersion-managed fiber laser," Opt. Commun. 188, 167-180 (2001).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

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 (3)

Introduction to numerical analysis, ser. Texts in Applied Mathematics, vol. 12, Springer (2002).

Advanced Synergetics, ser. Springer Series, vol. 20, Springer-Verlag (1983).

C. Jirauschek and F. Ö. Ilday, "Theory of the Self-Similar Laser Oscillator," CLEO 2005, Paper JWB65 (2005).

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Figures (3)

Fig. 1.
Fig. 1.

(a)Schematic diagram for the stretched pulse laser. (b) Intracavity pulse dynamics: (i) Energy, (ii) rms pulsewitdth and (iii) bandwidth. Solid lines are the solution to Eqs. (8)-(10); dashed lines refer to full numerical simulations.

Fig. 2.
Fig. 2.

Same as fig. 1 for the similariton laser oscillator.

Fig. 3.
Fig. 3.

Solid lines are the boundary of the stable region, whereas dashed lines correspond to the stable cw gain G cw = 0.9 for (a) stretched pulse laser and (b) similariton laser. Corresponding, insets show the negative real part of the Floquet coefficients λi (solid lines) and λΩ (dot-dashed lines) normalized to the total fiber length L t.

Equations (16)

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u z = g s ( z ) u + g s ( z ) Ω g 2 2 u t 2 + i β ( z ) 2 2 u t 2 u 2 u .
( u , u z ; u * , u z * ) = i 2 ( u u * z u * u z ) + β 2 u t 2 + γ 2 u 4 ,
u = E τ f ( t t 0 τ ) exp [ i ρ 2 ( t t 0 ) 2 + i Ω t + ] ,
I k = s k f 2 ( s ) d s
J k = λ k f ˜ ( λ ) 2 d λ 2 π .
L = E [ I 2 2 τ 2 d ρ d z + d ϕ d z + t 0 d Ω d z ] + γ P 4 2 E 2 τ + β 2 [ J 2 τ 2 + I 2 τ 2 ρ 2 + Ω 2 ] E ,
L x d d z L x z = 2 Im { + g s ( u + 1 Ω g 2 2 u t 2 ) u * x d t } ,
d E d z = 2 g s ( z ) E 2 g s ( z ) Ω 2 + 2 Ω g 2 E ,
d τ d z = β ( z ) ρτ + ( 1 S + I 2 J 2 I 2 I 4 I 2 2 I 2 ρ 2 τ 4 ) g s ( z ) τ Ω g 2 ,
d ρ d z = β ( z ) ( ρ 2 J 2 I 2 τ 4 ) g s ( z ) Ω g 2 ρ τ 2 4 S 1 I 2 γ P 4 2 I 2 E τ 3 ,
d Ω d z = 4 g s ( z ) 2 Ω g 2 Ω
d t 0 d z = 2 [ β ( z ) 2 + 2 I 2 ρ τ 2 g s ( z ) Ω g 2 ] Ω
A + A = ( 1 l 0 1 + f 0 2 A 2 P sat )
τ 2 τ + 2 = 1 + 2 l 0 f 0 2 A 2 P sat ( 1 + f 0 2 A 2 P sat ) ( 1 + f 0 2 A 2 P sat l 0 ) ,
d Δ x d z = [ A ( z ) + B L n δ ( z z L n L t ) ] Δ x
G cw = exp [ 2 0 L g g s ( z ) d z ] ( 1 l 0 ) 2 Γ SA < 1 ,

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