Abstract

We investigate experimentally and theoretically the broadening of the optical spectrum of a multimode cw field propagating in the normal dispersion regime of a single-mode fiber. The width of the optical spectrum is not a monotonic function of propagation length. This behavior arising from the interplay between the Kerr effect and group-velocity dispersion contrasts with spectral broadening of mode-locked pulses.

© 2006 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  2. J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jorgensen, Appl. Phys. B 77, 211 (2003).
    [CrossRef]
  3. A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Express 12, 2838 (2004).
    [CrossRef] [PubMed]
  4. F. Vanholsbeeck, S. Martin-Lopez, M. González-Herráez, and S. Coen, Opt. Express 13, 6615 (2005).
    [CrossRef] [PubMed]
  5. A. Sauter, S. Pitois, G. Millot, and A. Picozzi, Opt. Lett. 30, 2143 (2005).
    [CrossRef] [PubMed]
  6. A. K. Abeeluck, C. Headley, and C. G. Jorgensen, Opt. Lett. 29, 2163 (2004).
    [CrossRef] [PubMed]
  7. G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, Opt. Fiber Technol. 7, 170 (2001).
    [CrossRef]
  8. A. K. Abeeluck and C. Headley, Opt. Lett. 30, 61 (2005).
    [CrossRef] [PubMed]
  9. P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004) and references therein.
    [CrossRef]
  10. J. T. Manassah, Opt. Lett. 15, 329 (1990).
    [CrossRef] [PubMed]
  11. D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
    [CrossRef]
  12. E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Vol. 8 of Springer Series in Computational Mathematics (Springer-Verlag, 1987).
  13. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 2.

2005 (3)

2004 (3)

2003 (1)

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jorgensen, Appl. Phys. B 77, 211 (2003).
[CrossRef]

2001 (1)

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, Opt. Fiber Technol. 7, 170 (2001).
[CrossRef]

1998 (1)

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

1990 (1)

Abeeluck, A. K.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Beletic, J. W.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Coen, S.

González-Herráez, M.

Hairer, E.

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Vol. 8 of Springer Series in Computational Mathematics (Springer-Verlag, 1987).

Hart, D. L.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Headley, C.

Jorgensen, C. G.

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, Opt. Lett. 29, 2163 (2004).
[CrossRef] [PubMed]

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jorgensen, Appl. Phys. B 77, 211 (2003).
[CrossRef]

Judy, A. F.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Lantz, E.

Maillotte, H.

Manassah, J. T.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 2.

Martin-Lopez, S.

Millot, G.

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, Opt. Lett. 30, 2143 (2005).
[CrossRef] [PubMed]

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, Opt. Fiber Technol. 7, 170 (2001).
[CrossRef]

Mussot, A.

Nicholson, J. W.

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jorgensen, Appl. Phys. B 77, 211 (2003).
[CrossRef]

Norsett, S. P.

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Vol. 8 of Springer Series in Computational Mathematics (Springer-Verlag, 1987).

Picozzi, A.

Pitois, S.

Randoux, S.

P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004) and references therein.
[CrossRef]

Roy, R.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Sauter, A.

Seve, E.

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, Opt. Fiber Technol. 7, 170 (2001).
[CrossRef]

Suret, P.

P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004) and references therein.
[CrossRef]

Sylvestre, T.

Tchofo Dinda, P.

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, Opt. Fiber Technol. 7, 170 (2001).
[CrossRef]

Vanholsbeeck, F.

Wabnitz, S.

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, Opt. Fiber Technol. 7, 170 (2001).
[CrossRef]

Wanner, G.

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Vol. 8 of Springer Series in Computational Mathematics (Springer-Verlag, 1987).

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 2.

Yan, M. F.

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jorgensen, Appl. Phys. B 77, 211 (2003).
[CrossRef]

Appl. Phys. B (1)

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jorgensen, Appl. Phys. B 77, 211 (2003).
[CrossRef]

Opt. Commun. (1)

P. Suret and S. Randoux, Opt. Commun. 237, 201 (2004) and references therein.
[CrossRef]

Opt. Express (2)

Opt. Fiber Technol. (1)

G. Millot, P. Tchofo Dinda, E. Seve, and S. Wabnitz, Opt. Fiber Technol. 7, 170 (2001).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (1)

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Other (3)

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Vol. 8 of Springer Series in Computational Mathematics (Springer-Verlag, 1987).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 2.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. HWP, half-wave plate; FC, fiber coupler; PC, polarization controller; OSA, optical spectrum analyzer.

Fig. 2
Fig. 2

(a) Optical power spectra for L = 0 m (thick curve), L = 50 m (dashed curve) and 500 m (thin curve) of fiber for P 0 = 2 W . (b) Same as (a) with L = 1000 m (thin curve) and L = 2500 m (thick curve). (c) Experimental and (d) theoretical evolution of Γ ( L ) for increasing values of P 0 ( P 0 = 0.5 , 1 , 1.5 , 2 W ) . The dashed curve in (d) represents the evolution of Γ for a mode-locked pulse with an initial spectrum plotted in Fig. 3a.

Fig. 3
Fig. 3

Numerical simulations. (a) Normalized power spectrum and (b) phase spectrum of the input field. (c) Normalized power spectrum of the light field for L = 1000 m ( P 0 = 1 W ) . (d) Normalized ensemble average over 200 realizations of the power spectrum of the output field L = 1000 m and P 0 = 1 W .

Equations (1)

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U ( Z , T ) Z = i B 2 U ( Z , T ) T 2 + i U ( Z , T ) 2 U ( Z , T ) ,

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