Abstract

Nonlinear effects present fundamental obstacles to the propagation of femtosecond pulses of detectable energy in single-mode optical fibers, inducing severe distortion even after a very short (a few meters) propagation distance. We show here that adaptive pulse shaping can overcome these limitations by synthesizing pulses that are self-correcting for higher-order nonlinear effects when they are launched in the fiber. This approach would not only affect optical communications but also yield benefits in various disciplines requiring optimized fiber-based femtosecond pulse delivery, for example, nonlinear imaging techniques such as multiphoton microscopy, material processing, and medical diagnostics.

© 2001 Optical Society of America

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  1. D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
    [CrossRef] [PubMed]
  2. A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  3. F. G. Omenetto, B. P. Luce, and A. J. Taylor, Opt. Lett. 24, 1392 (1999).
    [CrossRef]
  4. R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
    [CrossRef] [PubMed]
  5. E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, Opt. Lett. 25, 587 (2000), and references therein.
    [CrossRef]
  6. S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 827 (1999).
    [CrossRef]
  7. F. Futami, K. Taira, K. Kikuchi, and A. Suzuki, Electron. Lett. 35, 2221 (1999).
    [CrossRef]
  8. F. G. Omenetto, J. W. Nicholson, and A. J. Taylor, Opt. Lett. 24, 1780 (1999).
    [CrossRef]
  9. R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
    [CrossRef]
  10. G. Agrawal, Nonlinear Fiber Optics (Academic, Orlando, Fla., 1989).
  11. F. G. Omenetto, B. P. Luce, and A. J. Taylor, J. Opt. Soc. Am. B 16, 2005 (1999).
    [CrossRef]

2000 (1)

1999 (6)

S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 827 (1999).
[CrossRef]

F. Futami, K. Taira, K. Kikuchi, and A. Suzuki, Electron. Lett. 35, 2221 (1999).
[CrossRef]

F. G. Omenetto, J. W. Nicholson, and A. J. Taylor, Opt. Lett. 24, 1780 (1999).
[CrossRef]

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

F. G. Omenetto, B. P. Luce, and A. J. Taylor, Opt. Lett. 24, 1392 (1999).
[CrossRef]

F. G. Omenetto, B. P. Luce, and A. J. Taylor, J. Opt. Soc. Am. B 16, 2005 (1999).
[CrossRef]

1997 (1)

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

1992 (1)

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

1973 (1)

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, Orlando, Fla., 1989).

Backus, S.

Bartels, R.

Blow, K. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Cotter, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Ellis, A. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Fittinghoff, D.

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Futami, F.

F. Futami, K. Taira, K. Kikuchi, and A. Suzuki, Electron. Lett. 35, 2221 (1999).
[CrossRef]

Hasegawa, A.

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Judson, R. S.

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

Kane, D.

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Kapteyn, H. C.

Kelly, A. E.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Kikuchi, K.

F. Futami, K. Taira, K. Kikuchi, and A. Suzuki, Electron. Lett. 35, 2221 (1999).
[CrossRef]

Krumbugel, M. A.

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Luce, B. P.

Manning, R. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Murnane, M. M.

Nesset, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Nicholson, J. W.

Omenetto, F. G.

Phillips, I. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Poustie, A. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Rabitz, H.

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

Rogers, D. C.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Shen, S.

S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 827 (1999).
[CrossRef]

Suzuki, A.

F. Futami, K. Taira, K. Kikuchi, and A. Suzuki, Electron. Lett. 35, 2221 (1999).
[CrossRef]

Sweetster, J.

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Taira, K.

F. Futami, K. Taira, K. Kikuchi, and A. Suzuki, Electron. Lett. 35, 2221 (1999).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Taylor, A. J.

Trebino, R.

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Vdovin, G.

Weiner, A. M.

S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 827 (1999).
[CrossRef]

Zeek, E.

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Electron. Lett. (1)

F. Futami, K. Taira, K. Kikuchi, and A. Suzuki, Electron. Lett. 35, 2221 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Shen and A. M. Weiner, IEEE Photon. Technol. Lett. 11, 827 (1999).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. Lett. (1)

R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. Fittinghoff, J. Sweetster, M. A. Krumbugel, and D. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Science (1)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, Science 286, 1523 (1999).
[CrossRef] [PubMed]

Other (1)

G. Agrawal, Nonlinear Fiber Optics (Academic, Orlando, Fla., 1989).

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Figures (4)

Fig. 1
Fig. 1

(a) Output after propagation through 10  m of single-mode fiber of an unshaped τ=204 fs pulse with P=25 mW. The pulse width is τ=352 fs FWHM, with features that extend to 1  ps and are asymmetrically distorted. The phase function ϕt, obtained from deconvolution of the frequency-resolved optical gating trace, exhibits a complex structure. A fit to ϕt=A+B1t+B2t2+B3t3+B4t4 indicates strong cubic and quartic contributions to the pulse distortion (B2=6.6×10-6 rad/fs2, B3=1×10-9 rad/fs3, B4=-3.5×10-11 rad/fs4). The dotted curve indicates the original input pulse. (b) Output owing to the propagation of an optimally shaped τ=204 fs pulse with P=25 mW. The output pulse has a duration of 214  fs and is very similar to the original input pulse (dotted curve). The phase function is considerably smoother despite the presence of nonlinear effects.

Fig. 2
Fig. 2

Comparison of the 25-mW output of Fig.  1(a) and the output after propagation through the same 10-m link of an unshaped pulse with the same initial pulse duration τ=204 fs but with lower average power P=5 mW. The lower-power pulse is broadened mostly because of linear contributions (chromatic dispersion) to τ=702 fs.

Fig. 3
Fig. 3

Comparison of the initial unshaped input pulse (dashed curve), output from the unshaped pulse (Unoptimized out), and output from the optimally shaped pulse propagation (Optimized out) plotted on a logarithmic scale covering the dynamic range of the measurement. Suppression of the wing structure is particularly evident in this case.

Fig. 4
Fig. 4

Temporal phase functions of the original input pulse, ϕint, and the optimized input pulse, ϕin,optt. The optimized-pulse phase function is asymmetric, indicating that compensation occurs on odd and higher-order phase terms. A fit to the temporal phase function, ϕt=A+B1t+B2t2+B3t3+B4t4 of ϕin,optt, confirms this B2=-1.7×10-5 rad/fs2,B3=-9.3×10-9 rad/fs3,B4=2.3×10-11 rad/fs4.

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