Abstract

Self-similar propagation of linearly chirped hyperbolic-secant pulses in a comblike decreasing-dispersion fiber amplifier has been observed experimentally for the first time to our knowledge. The scheme takes advantage of an exact solution of the generalized nonlinear Schrödinger equation with distributed coefficients.

© 2006 Optical Society of America

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References

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  1. V. I. Kruglov, D. Méchin, and J. D. Harvey, Opt. Express 12, 6198 (2004).
    [CrossRef] [PubMed]
  2. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
    [CrossRef] [PubMed]
  3. V. N. Serkin and A. Hasegawa, IEEE J. Sel. Top. Quantum Electron. 8, 418 (2002).
    [CrossRef]
  4. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. Lett. 90, 113902 (2003).
    [CrossRef] [PubMed]
  5. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. E 71, 056619 (2005).
    [CrossRef]
  6. C. Finot, G. Millot, C. Billet, and J. M. Dudley, Opt. Express 11, 1547 (2003).
    [CrossRef] [PubMed]
  7. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
    [CrossRef] [PubMed]
  8. J. D. Moores, Opt. Lett. 21, 555 (1996).
    [CrossRef] [PubMed]
  9. T. E. Murphy, IEEE Photon. Technol. Lett. 14, 1424 (2002).
    [CrossRef]
  10. S. V. Chernikov, J. R. Taylor, and R. Kashyap, Opt. Lett. 19, 539 (1994).
    [CrossRef] [PubMed]

2005 (1)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. E 71, 056619 (2005).
[CrossRef]

2004 (2)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

V. I. Kruglov, D. Méchin, and J. D. Harvey, Opt. Express 12, 6198 (2004).
[CrossRef] [PubMed]

2003 (2)

C. Finot, G. Millot, C. Billet, and J. M. Dudley, Opt. Express 11, 1547 (2003).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

2002 (2)

V. N. Serkin and A. Hasegawa, IEEE J. Sel. Top. Quantum Electron. 8, 418 (2002).
[CrossRef]

T. E. Murphy, IEEE Photon. Technol. Lett. 14, 1424 (2002).
[CrossRef]

2000 (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

1996 (1)

1994 (1)

Billet, C.

Buckley, J. R.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Chernikov, S. V.

Clark, W. G.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Dudley, J. M.

C. Finot, G. Millot, C. Billet, and J. M. Dudley, Opt. Express 11, 1547 (2003).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Finot, C.

Harvey, J. D.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. E 71, 056619 (2005).
[CrossRef]

V. I. Kruglov, D. Méchin, and J. D. Harvey, Opt. Express 12, 6198 (2004).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Hasegawa, A.

V. N. Serkin and A. Hasegawa, IEEE J. Sel. Top. Quantum Electron. 8, 418 (2002).
[CrossRef]

Ilday, F. Ö.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Kashyap, R.

Kruglov, V. I.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. E 71, 056619 (2005).
[CrossRef]

V. I. Kruglov, D. Méchin, and J. D. Harvey, Opt. Express 12, 6198 (2004).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Méchin, D.

Millot, G.

Moores, J. D.

Murphy, T. E.

T. E. Murphy, IEEE Photon. Technol. Lett. 14, 1424 (2002).
[CrossRef]

Peacock, A. C.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. E 71, 056619 (2005).
[CrossRef]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

Serkin, V. N.

V. N. Serkin and A. Hasegawa, IEEE J. Sel. Top. Quantum Electron. 8, 418 (2002).
[CrossRef]

Taylor, J. R.

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Wise, F. W.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

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

V. N. Serkin and A. Hasegawa, IEEE J. Sel. Top. Quantum Electron. 8, 418 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. E. Murphy, IEEE Photon. Technol. Lett. 14, 1424 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (1)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. E 71, 056619 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Theoretical (dashed curve), experimental comblike (thin curve) and average (thick lines) β profiles of the DDF.

Fig. 3
Fig. 3

Top, experimental normalized intensity and, bottom, frequency chirp for the input pulse (thick curve, FWHM = 17.88 ps ), and the pulse after 280 m (dotted curve, FWHM = 7.38 ps ), 480 m (dashed curve, FWHM = 3.15 ps ), and 640 m (thin curve, FWHM = 1.47 ps ) of the comblike DDF.

Fig. 4
Fig. 4

Analytical X ( z ) profiles obtained by using the theoretical β profile (dashed curve) and the comblike β profile (solid curve); experimental X ( z ) profiles obtained from chirp measurement (crosses), from time width measurement (circles), and from peak power measurement (triangles).

Fig. 5
Fig. 5

Top, normalized intensity and, bottom, frequency chirp for the input pulse of the first DDF (crosses) and theoretical (dashed curve), experimental (solid curve), and simulated output pulses after the first DDF, from the theoretical input pulse plus the theoretical β profile (triangles), the experimental input pulse plus the theoretical β profile (stars), the theoretical input pulse plus the comblike β profile (circles), and the experimental input pulse plus the comblike β profile (squares).

Fig. 6
Fig. 6

Top, normalized intensity and, bottom, frequency chirp for input and output pulses of the second DDF. Symbols are as in Fig. 5.

Equations (10)

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i ψ z = β ( z ) 2 ψ r r γ ( z ) ψ 2 ψ + i g ( z ) 2 ψ .
ψ ( z , τ ) = U ( z , τ ) exp [ i Φ ( z , τ ) ] ,
U ( z , τ ) = ρ ( z ) τ 0 X ( z ) sech [ τ τ c τ 0 X ( z ) ] ,
Φ ( z , τ ) = a 0 1 X ( z ) 4 c 0 τ 0 2 X ( z ) + c 0 X ( z ) ( τ τ c ) 2 ,
X ( z ) = 1 2 c 0 0 z β ( z ) d z ,
g ( z ) = 1 ρ ( z ) d ρ ( z ) d z + 2 c 0 β ( z ) X ( z ) .
X ( z ) = c 0 c ( z ) = τ ( z ) τ 0 = [ P 0 β ( z ) P ( z ) β 0 ] 1 2 .
g ( z ) = g 0 exp [ 0 z α ( z ) d z ] α ( z ) ,
β ( z ) = β ( 0 ) exp [ G ( z ) 2 c 0 β ( 0 ) R ( z ) ] ,
G ( z ) = 0 z g ( z ) d z , R ( z ) = 0 z exp [ G ( z ) ] d z .

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