Abstract

We demonstrate, through simulation, an optimization method based on genetic algorithms applied to propagation of ultrashort (femtosecond) pulses in single-mode optical fibers. The algorithm employs a feedback loop that acts on a pulse shaper (spectral amplitude filter) in response to a fitness function based on the output pulse. The system evolves toward an optimum filter configuration that, in contrast to unfiltered pulse propagation, when it is applied to shape the input pulse permits successful transmission of the pulse without loss of intensity or pulse width.

© 1999 Optical Society of America

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References

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  1. A. Weiner, “Femtosecond pulse processing,” Prog. Quantum Electron. 19, 161–237 (1995).
    [CrossRef]
  2. R. N. Zare, “Laser control of chemical reactions,” Science 279, 1875–1878 (1998); A. H. Zewail, “Femtochemistry: recent progress in studies of dynamics and control of reactions and their transition states,” J. Phys. Chem. 100, 12, 701–12, 724 (1996).
    [CrossRef] [PubMed]
  3. A. Efimov and D. H. Reitze, “Programmable dispersion compensation and pulse shaping in a 26-fs chirped pulse amplifier,” Opt. Lett. 23, 1612–1614 (1998).
    [CrossRef]
  4. D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
    [CrossRef]
  5. C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
    [CrossRef]
  6. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
    [CrossRef] [PubMed]
  7. J. W. Nicholson, F. G. Omenetto, D. Funk, and A. J. Taylor, “Evolving FROG’s: phase retrieval from frequency-resolved optical gating measurements by use of genetic algorithms,” Opt. Lett. 24, 490–492 (1999).
    [CrossRef]
  8. M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, Mass., 1996).
  9. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Orlando, Fla., 1989).
  10. K. C. Chan and H. F. Liu, “Short pulse generation by high-order soliton compression, effects of optical fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2231 (1995).
    [CrossRef]

1999

1998

A. Efimov and D. H. Reitze, “Programmable dispersion compensation and pulse shaping in a 26-fs chirped pulse amplifier,” Opt. Lett. 23, 1612–1614 (1998).
[CrossRef]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

1997

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
[CrossRef]

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

1995

A. Weiner, “Femtosecond pulse processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

K. C. Chan and H. F. Liu, “Short pulse generation by high-order soliton compression, effects of optical fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2231 (1995).
[CrossRef]

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Bardeen, C.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Baumert, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Bergt, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Brixner, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Carpenter, S. D.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Chan, K. C.

K. C. Chan and H. F. Liu, “Short pulse generation by high-order soliton compression, effects of optical fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2231 (1995).
[CrossRef]

Efimov, A.

Funk, D.

Gerber, G.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Kiefer, B.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Liu, H. F.

K. C. Chan and H. F. Liu, “Short pulse generation by high-order soliton compression, effects of optical fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2231 (1995).
[CrossRef]

Meshulach, D.

Nicholson, J. W.

Omenetto, F. G.

Reitze, D. H.

Seyfried, V.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Silberberg, Y.

Strehle, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Taylor, A. J.

Warren, W. S.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Weber, P. M.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Weiner, A.

A. Weiner, “Femtosecond pulse processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Wilson, K. R.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Yakovlev, V.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Yelin, D.

Chem. Phys. Lett.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

IEEE J. Quantum Electron.

K. C. Chan and H. F. Liu, “Short pulse generation by high-order soliton compression, effects of optical fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2231 (1995).
[CrossRef]

Opt. Lett.

Prog. Quantum Electron.

A. Weiner, “Femtosecond pulse processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Science

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Other

M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, Mass., 1996).

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

R. N. Zare, “Laser control of chemical reactions,” Science 279, 1875–1878 (1998); A. H. Zewail, “Femtochemistry: recent progress in studies of dynamics and control of reactions and their transition states,” J. Phys. Chem. 100, 12, 701–12, 724 (1996).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematic of GAPS. An initial filter population is used to shape the input pulse before propagating the pulse through the fiber. The output pulses are detected and evaluated for peak intensity. The GA acquires the peak intensity that corresponds to each filter configuration and selects the best filters according to the fitness criterion (maximum peak intensity at the output). A new population of filters is generated with the best filters through the crossover and mutation operators (illustrated schematically above), and the process is iterated. For more details on the operation of the GA refer to the text.

Fig. 2
Fig. 2

Evolution of the filter population, plotted as the output pulse peak amplitude for each filter (with respect to the initial pulse amplitude) versus generation number. The peak amplitude became fully recovered after approximately 40 generations. There are 16 filters (=one population) associated with each abscissa point.

Fig. 3
Fig. 3

Propagation of (a) an unfiltered and (b) an optimally filtered pulse through 100 m of fiber. The unfiltered pulse is severely dispersed and broadened temporally, whereas the optimally filtered pulse shape recovers (and actually exceeds) its original peak intensity. (c) Profiles of the optimally filtered pulse (solid curves) at the input and the output of the fiber. The unfiltered pulse profile is drawn (dashed curves) for comparison in both plots to illustrate the filtering at the input and the combined shortening–intensity increase at the output.

Fig. 4
Fig. 4

Representation of the best amplitude filter superimposed upon the original input pulse spectrum. Black areas represent complete transmission; white areas represent no transmission of the spectral component.

Fig. 5
Fig. 5

Variation of optimized output pulses in the presence of ±10% energy fluctuations on the input pulse (E0). The output pulses correspond to input energies (a) E=E0-0.1E0, (b) E=E0, and (c) E=E0+0.1E0.

Fig. 6
Fig. 6

(a) Unoptimized and (b) optimized propagation of 176-fs pulses through 2 km of fiber. The energy of these pulses is 30% less than in the 100-m case. (c) Comparison of input and output pulses for these two cases.

Fig. 7
Fig. 7

Propagation of (a) unfiltered and (b) optimally filtered pulse trains through 100 m of fiber. See text for a description.

Equations (2)

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qZ=i22qτ2+i|q|2q-12δq-α |q|2qτ-iβq |q|2τ+γ 163qτ3,
α=1/(ω0t0),β=tR/t0,γ=-β3/(t0β2),

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