Abstract

We study the fluctuations of pulses in mode-locked lasers using the statistical light-mode dynamics approach. The analysis is based on a decomposition of the laser waveform into three parts: solitary pulse, intracavity noise continuum, and local overlap. We discover significant features in the fluctuation dynamics, beyond those known in existing theories that disregard the continuum component of the waveform, most notably oscillations in the autocorrelation functions of the pulse power and frequency parameters, and an enhancement of the phase jitter diffusion constant. The theoretical results are corroborated by numerical simulations.

© 2010 Optical Society of America

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References

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  1. H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
    [CrossRef]
  2. A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
    [CrossRef] [PubMed]
  3. B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
    [CrossRef] [PubMed]
  4. O. Gat, A. Gordon, and B. Fischer, New J. Phys. 7, 151 (2005).
    [CrossRef]
  5. A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
    [CrossRef] [PubMed]
  6. M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
    [CrossRef] [PubMed]
  7. C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. R. Schibli, and S. T. Cundiff, Opt. Express 15, 6677 (2007).
    [CrossRef] [PubMed]
  8. S. M. Kelly, Electron. Lett. 28, 806 (1992).
    [CrossRef]
  9. A. Hasegawa and Y. Kodama, Solitons in Optical Communication (Oxford U. Press, 1995).
  10. O. Basis and O. Gat, Phys. Rev. E 79, 031126 (2009).
    [CrossRef]
  11. D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
    [CrossRef] [PubMed]
  12. T. Kapitula, Lect. Notes Phys. 661, 407 (2005).
    [CrossRef]
  13. H. Risken, The Fokker-Planck Equation2nd ed., (Springer, 1989).
    [CrossRef]
  14. Note that Eq. (56) in [1] contains an extra 2/w0 factor.
  15. R. Paschotta, Appl. Phys. B 79, 153 (2004).

2009 (1)

O. Basis and O. Gat, Phys. Rev. E 79, 031126 (2009).
[CrossRef]

2007 (1)

2006 (2)

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

2005 (2)

O. Gat, A. Gordon, and B. Fischer, New J. Phys. 7, 151 (2005).
[CrossRef]

T. Kapitula, Lect. Notes Phys. 661, 407 (2005).
[CrossRef]

2004 (2)

R. Paschotta, Appl. Phys. B 79, 153 (2004).

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

2002 (1)

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

1993 (1)

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

1992 (1)

S. M. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

1990 (1)

D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

Basis, O.

O. Basis and O. Gat, Phys. Rev. E 79, 031126 (2009).
[CrossRef]

Bekker, A.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

Cundiff, S. T.

Fischer, B.

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, New J. Phys. 7, 151 (2005).
[CrossRef]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

Gat, O.

O. Basis and O. Gat, Phys. Rev. E 79, 031126 (2009).
[CrossRef]

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, New J. Phys. 7, 151 (2005).
[CrossRef]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

Gordon, A.

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, New J. Phys. 7, 151 (2005).
[CrossRef]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communication (Oxford U. Press, 1995).

Haus, H. A.

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

Kapitula, T.

T. Kapitula, Lect. Notes Phys. 661, 407 (2005).
[CrossRef]

Kartner, F. X.

Katz, M.

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

Kaup, D. J.

D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

Kelly, S. M.

S. M. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communication (Oxford U. Press, 1995).

Mecozzi, A.

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

Menyuk, C. R.

Paschotta, R.

R. Paschotta, Appl. Phys. B 79, 153 (2004).

Risken, H.

H. Risken, The Fokker-Planck Equation2nd ed., (Springer, 1989).
[CrossRef]

Schibli, T. R.

Smith, R. P.

Smulakovsky, V.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

Vodonos, B.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

Wahlstrand, J. K.

Weill, R.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

Willits, J.

Appl. Phys. B (1)

R. Paschotta, Appl. Phys. B 79, 153 (2004).

Electron. Lett. (1)

S. M. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

Lect. Notes Phys. (1)

T. Kapitula, Lect. Notes Phys. 661, 407 (2005).
[CrossRef]

New J. Phys. (1)

O. Gat, A. Gordon, and B. Fischer, New J. Phys. 7, 151 (2005).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (1)

D. J. Kaup, Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (1)

O. Basis and O. Gat, Phys. Rev. E 79, 031126 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, Phys. Rev. Lett. 93, 153901 (2004).
[CrossRef] [PubMed]

Other (3)

A. Hasegawa and Y. Kodama, Solitons in Optical Communication (Oxford U. Press, 1995).

H. Risken, The Fokker-Planck Equation2nd ed., (Springer, 1989).
[CrossRef]

Note that Eq. (56) in [1] contains an extra 2/w0 factor.

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Figures (1)

Fig. 1
Fig. 1

Left, theoretical analysis. Oscillatory part of power (dashed curve) and frequency (solid curve) correlations, in units of T P 0 . The thin gray (red online) curve shows the exponential damping with absorber-dependent rate. Right, numerical simulation. Power autocorrelation functions for a nonlinear coefficient of 2 × 10 3 W 1 , μ = 0.1 , and steady-state pulse peak powers of 72 W (dashed, blue) and 162 W (solid red). The time scale is in round trips.

Equations (9)

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

ψ ̇ = ( i + μ ) ( 1 2 ψ + | ψ | 2 ψ ) + ( g i ϕ 0 ) ψ + ϵ Γ ,
ψ ̇ c = 1 2 ( i + μ ) ψ c + ( g 0 i ϕ 0 ) ψ c + Γ ,
ψ ̇ 1 + x j ψ p x ̇ j μ = L 1 ψ 1 + L 2 ψ 1 * i 1 2 μ v ψ p + g 1 ψ p + f ,
p ̇ = μ P 0 3 4 P p μ d z q Re [ f + P 0 P ( ψ ̇ c f ) ] ,
ϕ ̇ = 2 P 0 μ d z ( q 1 2 P 0 z q z ) Im f ,
v ̇ = μ P 0 2 6 v μ d z q z Im f ,
z ̇ 0 = 2 P 0 μ d z ( z q ) Re f ,
v t + τ v t * = T P 0 ( e μ P 0 2 6 | τ | + π d k k 2 I k ( τ ) ) ,
p t + τ p t * = 2 T P 0 ( P P 0 e μ P 0 3 4 P | τ | + π 2 d k I k ( τ ) ) ,

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