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. Quantum Electron. 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. 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, 213902 (2004).
    [Crossref] [PubMed]
  5. J. N. Kutz, P. Holmes, S. G. Evangelides, and 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 mode-locked 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, and 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. 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, 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)

J- G. Caputo, N. Flytzanis, and M. P. Sorensen, “Ring laser configuration studied by collective coordinates,” J. Opt. Soc. Am. B 12, 139–145 (1995).
[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. Quantum Electron. 31, 591–598 (1995).
[Crossref]

1993 (1)

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, 213902 (2004).
[Crossref] [PubMed]

Caputo, J- G.

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, 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. Quantum Electron. 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. 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, 213902 (2004).
[Crossref] [PubMed]

Ilday, F. ö.

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

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. Quantum Electron. 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.

Jirauschek, C.

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

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. Quantum Electron. 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. Quantum Electron. 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. 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, 213902 (2004).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (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. Quantum Electron. 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. 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, 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.

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Fig. 2.
Fig. 2.

Same as fig. 1 for the similariton laser oscillator.

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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.

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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 − iγ ∣ u ∣ 2 u .
ℒ ( 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 + iϕ ] ,
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 + ℬ 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 ) ℬ 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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