Abstract

It is shown that additive noise can inhibit modulation instability in laser equations of motion. A related self-starting condition for pulsation is obtained by employing a fluctuation–dissipation relation between noise and losses and a statistical mechanics approach. Entropy considerations are shown to play a crucial role. The quantum limit for self-starting is estimated.

© 2003 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).
  2. H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
    [CrossRef]
  3. H. Haken, Synergetics, 2nd enlarged ed. (Springer-Verlag, Berlin, 1978).
    [CrossRef]
  4. G. P. Agrawal, IEEE Photon. Technol. Lett. 4, 562 (1992).
    [CrossRef]
  5. T. Kapitula, J. N. Kutz, and B. Sandstede, J. Opt. Soc. Am. B 19, 740 (2002).
    [CrossRef]
  6. C. J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 20, 350 (1995).
    [CrossRef]
  7. F. Krausz, T. Brabec, and C. Spilmann, Opt. Lett. 16, 235 (1991).
    [CrossRef] [PubMed]
  8. H. A. Haus and E. P. Ippen, Opt. Lett. 16, 1331 (1991).
    [CrossRef] [PubMed]
  9. J. Herrmann, Opt. Commun. 98, 111 (1993).
    [CrossRef]
  10. K. Tamura, J. Jacobson, E. P. Ippen, H. A. Haus, and J. G. Fujimoto, Opt. Lett. 18, 220 (1993).
    [CrossRef]
  11. F. Krausz and T. Brabec, Opt. Lett. 18, 888 (1993).
    [CrossRef]
  12. Y.-F. Chou, J. Wang, H.-H. Liu, and N.-P. Kuo, Opt. Lett. 19, 566 (1994).
    [CrossRef] [PubMed]
  13. A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
    [CrossRef]
  14. A. Gordon and B. Fischer, Opt. Commun. (to be published).
  15. For simplicity of notation Gm is defined here differently from Ref. ; here the Gm have a power of unity.
  16. This is obtained from Stratonovich calculus. Intuitively, Re[a*m(eW)/(2N) Gm] is the rate at which the noise supplies energy to the m th mode, which is (eW)/(2N), the power of the noise. The summation on m adds a factor of N.
  17. E. Desurvire, Erbium Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).

2002 (2)

T. Kapitula, J. N. Kutz, and B. Sandstede, J. Opt. Soc. Am. B 19, 740 (2002).
[CrossRef]

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

2001 (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

2000 (1)

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

1995 (1)

1994 (2)

E. Desurvire, Erbium Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).

Y.-F. Chou, J. Wang, H.-H. Liu, and N.-P. Kuo, Opt. Lett. 19, 566 (1994).
[CrossRef] [PubMed]

1993 (3)

1992 (1)

G. P. Agrawal, IEEE Photon. Technol. Lett. 4, 562 (1992).
[CrossRef]

1991 (2)

1978 (1)

H. Haken, Synergetics, 2nd enlarged ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

G. P. Agrawal, IEEE Photon. Technol. Lett. 4, 562 (1992).
[CrossRef]

Brabec, T.

Chen, C. J.

Chou, Y.-F.

Desurvire, E.

E. Desurvire, Erbium Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).

Fischer, B.

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

A. Gordon and B. Fischer, Opt. Commun. (to be published).

Fujimoto, J. G.

Gordon, A.

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

A. Gordon and B. Fischer, Opt. Commun. (to be published).

Haken, H.

H. Haken, Synergetics, 2nd enlarged ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

Haus, H. A.

Herrmann, J.

J. Herrmann, Opt. Commun. 98, 111 (1993).
[CrossRef]

Ippen, E. P.

Jacobson, J.

Kapitula, T.

T. Kapitula, J. N. Kutz, and B. Sandstede, J. Opt. Soc. Am. B 19, 740 (2002).
[CrossRef]

Krausz, F.

Kuo, N.-P.

Kutz, J. N.

T. Kapitula, J. N. Kutz, and B. Sandstede, J. Opt. Soc. Am. B 19, 740 (2002).
[CrossRef]

Liu, H.-H.

Menyuk, C. R.

Sandstede, B.

T. Kapitula, J. N. Kutz, and B. Sandstede, J. Opt. Soc. Am. B 19, 740 (2002).
[CrossRef]

Spilmann, C.

Tamura, K.

Wai, P. K. A.

Wang, J.

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

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. P. Agrawal, IEEE Photon. Technol. Lett. 4, 562 (1992).
[CrossRef]

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

T. Kapitula, J. N. Kutz, and B. Sandstede, J. Opt. Soc. Am. B 19, 740 (2002).
[CrossRef]

Opt. Commun. (2)

J. Herrmann, Opt. Commun. 98, 111 (1993).
[CrossRef]

A. Gordon and B. Fischer, Opt. Commun. (to be published).

Opt. Lett. (6)

Phys. Rev. Lett. (1)

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

Other (5)

For simplicity of notation Gm is defined here differently from Ref. ; here the Gm have a power of unity.

This is obtained from Stratonovich calculus. Intuitively, Re[a*m(eW)/(2N) Gm] is the rate at which the noise supplies energy to the m th mode, which is (eW)/(2N), the power of the noise. The summation on m adds a factor of N.

E. Desurvire, Erbium Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).

H. Haken, Synergetics, 2nd enlarged ed. (Springer-Verlag, Berlin, 1978).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

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Figures (1)

Fig. 1
Fig. 1

Plot of the free energy, obtained from the mean field theory,13,14 as a function of the order parameter M for different values of T. The number near each curve is the corresponding value of T/γsP02. The behavior of the curves near M=0 is shown in the inset: M=0 remains a local minimum of the free energy and thus a metastable state.

Equations (9)

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

damdt=fmat-P-P0amt+TΓ˜mt,
Γ˜mt1Γ˜n*t2=2δmnδt1-t2,  Γ˜mt1Γ˜nt2=0.
damdt=fmat-P-P0amt+W2N1/2Γ˜mt,
12dPdt=  Ream*fma-P-P0P+W2N1/2 Ream*Γ˜m,
P=P0+P0W2+Ream*fma+O2.
damdt=fma-Reak*fkaP0am+TΓ˜m-W2P0am.
γP02>W,
M=1NP0mam.
FM-F0NTM2-NγsP023M4.

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