Abstract

Fiber lasers emit soliton pulses that exhibit discrete spectral sidebands generated through dispersive-wave resonances. The position of these soliton sidebands is shown to be affected by the amount of chirp acquired by the pulse, and the degree of chirp is determined by total cavity losses and gain dispersion. Our results show that the soliton chirp shifts the sideband frequencies and that sidebands can be generated even in the case of normal dispersion. The long- and short-cavity cases are discussed separately so that our results are applicable to all laser configurations.

© 1995 Optical Society of America

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References

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  1. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  2. N. Pandit, D. U. Noske, S. M. J. Kelly, J. R. Taylor, Electron. Lett. 28, 455 (1992).
    [CrossRef]
  3. S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
    [CrossRef]
  4. D. U. Noske, N. Pandit, J. R. Taylor, Opt. Lett. 17, 1515 (1992).
    [CrossRef] [PubMed]
  5. N. J. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
    [CrossRef]
  6. M. L. Dennis, I. N. Duling, IEEE J. Quantum Electron. 30, 1469 (1994).
    [CrossRef]
  7. H. A. Haus, E. P. Ippen, K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
    [CrossRef]
  8. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  9. P. A. Bélanger, L. Gagnon, C. Paré, Opt. Lett. 14, 943 (1989).
    [CrossRef] [PubMed]
  10. G. P. Agrawal, Phys. Rev. E 48, 2316 (1993).
    [CrossRef]
  11. M. Hofer, M. H. Ober, F. Haberl, M. E. Fermann, IEEE J. Quantum Electron. 28, 720 (1992).
    [CrossRef]

1994 (2)

M. L. Dennis, I. N. Duling, IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

H. A. Haus, E. P. Ippen, K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

1993 (1)

G. P. Agrawal, Phys. Rev. E 48, 2316 (1993).
[CrossRef]

1992 (6)

M. Hofer, M. H. Ober, F. Haberl, M. E. Fermann, IEEE J. Quantum Electron. 28, 720 (1992).
[CrossRef]

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

D. U. Noske, N. Pandit, J. R. Taylor, Opt. Lett. 17, 1515 (1992).
[CrossRef] [PubMed]

N. Pandit, D. U. Noske, S. M. J. Kelly, J. R. Taylor, Electron. Lett. 28, 455 (1992).
[CrossRef]

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

N. J. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

1989 (1)

Agrawal, G. P.

G. P. Agrawal, Phys. Rev. E 48, 2316 (1993).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Andonovic, I.

N. J. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Bélanger, P. A.

Blow, K. J.

N. J. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Dennis, M. L.

M. L. Dennis, I. N. Duling, IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

Duling, I. N.

M. L. Dennis, I. N. Duling, IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

Fermann, M. E.

M. Hofer, M. H. Ober, F. Haberl, M. E. Fermann, IEEE J. Quantum Electron. 28, 720 (1992).
[CrossRef]

Gagnon, L.

Gordon, J. P.

Haberl, F.

M. Hofer, M. H. Ober, F. Haberl, M. E. Fermann, IEEE J. Quantum Electron. 28, 720 (1992).
[CrossRef]

Haus, H. A.

H. A. Haus, E. P. Ippen, K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

Hofer, M.

M. Hofer, M. H. Ober, F. Haberl, M. E. Fermann, IEEE J. Quantum Electron. 28, 720 (1992).
[CrossRef]

Ippen, E. P.

H. A. Haus, E. P. Ippen, K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

Kelly, S. M. J.

N. Pandit, D. U. Noske, S. M. J. Kelly, J. R. Taylor, Electron. Lett. 28, 455 (1992).
[CrossRef]

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

Noske, D. U.

D. U. Noske, N. Pandit, J. R. Taylor, Opt. Lett. 17, 1515 (1992).
[CrossRef] [PubMed]

N. Pandit, D. U. Noske, S. M. J. Kelly, J. R. Taylor, Electron. Lett. 28, 455 (1992).
[CrossRef]

Ober, M. H.

M. Hofer, M. H. Ober, F. Haberl, M. E. Fermann, IEEE J. Quantum Electron. 28, 720 (1992).
[CrossRef]

Pandit, N.

N. Pandit, D. U. Noske, S. M. J. Kelly, J. R. Taylor, Electron. Lett. 28, 455 (1992).
[CrossRef]

D. U. Noske, N. Pandit, J. R. Taylor, Opt. Lett. 17, 1515 (1992).
[CrossRef] [PubMed]

Paré, C.

Smith, N. J.

N. J. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Tamura, K.

H. A. Haus, E. P. Ippen, K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

Taylor, J. R.

N. Pandit, D. U. Noske, S. M. J. Kelly, J. R. Taylor, Electron. Lett. 28, 455 (1992).
[CrossRef]

D. U. Noske, N. Pandit, J. R. Taylor, Opt. Lett. 17, 1515 (1992).
[CrossRef] [PubMed]

Electron. Lett. (2)

N. Pandit, D. U. Noske, S. M. J. Kelly, J. R. Taylor, Electron. Lett. 28, 455 (1992).
[CrossRef]

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

IEEE J. Quantum Electron. (3)

M. L. Dennis, I. N. Duling, IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

H. A. Haus, E. P. Ippen, K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

M. Hofer, M. H. Ober, F. Haberl, M. E. Fermann, IEEE J. Quantum Electron. 28, 720 (1992).
[CrossRef]

J. Lightwave Technol. (1)

N. J. Smith, K. J. Blow, I. Andonovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. E (1)

G. P. Agrawal, Phys. Rev. E 48, 2316 (1993).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

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Figures (3)

Fig. 1
Fig. 1

(a) Chirp parameter q and (b) the FWHM of the chirped soliton pulse as a function of the amplifier gain for the anomalous (solid curves) and normal (dashed curves) dispersion regimes.

Fig. 2
Fig. 2

Positions of the first three sidebands plotted as the product δνmTFWHM for the chirped soliton in the anomalous dispersion region as a function of the amplifier gain for cavity lengths of (a) 100 m and (b) 10 m.

Fig. 3
Fig. 3

Positions of the first two sidebands plotted as the product δνmTFWHM for a chirped soliton in the normal dispersion region as a function of the amplifier gain for cavity lengths of 100 and 10 m.

Equations (9)

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A ξ + i 2 ( s + i d ) 2 A τ 2 - i ( 1 - i δ ) A 2 A = 1 2 μ A ,
s = sgn ( β 2 ) ,             d = g 0 L D ,             μ = ( g 0 - α 0 ) L D ,
A ( ξ , τ ) = N [ sech ( p τ ) ] ( 1 + i q ) exp ( i Γ ξ ) ,
N 2 = p 2 2 [ s ( q 2 - 2 ) + 3 q d ] ,
p 2 = - μ [ d ( 1 - q 2 ) + 2 s q ] - 1 ,
Γ = p 3 2 [ 2 q d - s ( 1 - q 2 ) ]
( d + s δ ) q 2 - 3 ( s - d δ ) q - 2 ( d + s δ ) = 0.
δ ω 2 = p 2 β 2 L D [ - 4 π s m L D p 2 L - ( 1 - q 2 - 2 s q d ) ] ,
δ ν m = ± 0.28 T FWHM [ - s 8 m z 0 L - ( 1 - q 2 - 2 s q d ) ] 1 / 2 ,

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