Abstract

We present a new technique based on genetic algorithms for retrieving the electric field and the phase of ultrashort pulses from frequency-resolved optical gating (FROG) traces. We have successfully applied a very basic genetic algorithm to the two most common beam geometries: polarization gate and second-harmonic generation (SHG). In the case of SHG FROG, the genetic algorithm returns a lower error than the standard iterative composite algorithm.

© 1999 Optical Society of America

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References

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  1. D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
    [CrossRef]
  2. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, J. Opt. Soc. Am. B 11, 2206 (1994).
    [CrossRef]
  3. K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, Opt. Lett. 19, 2152 (1994).
    [CrossRef] [PubMed]
  4. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
    [CrossRef]
  5. M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, Mass., 1996).
  6. K. Edwards, T. Edgar, and V. Manousiouthakis, Comput. Chem. Eng. 22, 239 (1998).
    [CrossRef]
  7. T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
    [CrossRef]
  8. R. Wehrens and L. M. Buydens, Trends Anal. Chem. 17, 193 (1998).
    [CrossRef]
  9. D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, J. Opt. Soc. Am. B 12, 1955 (1995).
    [CrossRef]
  10. C. W. Siders, A. J. Taylor, and C. M. Downer, Opt. Lett. 22, 624 (1997).
    [CrossRef] [PubMed]
  11. C. W. Siders, J. L. Siders, F. G. Omenetto, and A. J. Taylor, “Multi-pulse interferometric frequency resolved optical gating,” IEEE J. Quantum Electron. (to be published).

1998 (2)

K. Edwards, T. Edgar, and V. Manousiouthakis, Comput. Chem. Eng. 22, 239 (1998).
[CrossRef]

R. Wehrens and L. M. Buydens, Trends Anal. Chem. 17, 193 (1998).
[CrossRef]

1997 (3)

T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

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

C. W. Siders, A. J. Taylor, and C. M. Downer, Opt. Lett. 22, 624 (1997).
[CrossRef] [PubMed]

1995 (1)

1994 (2)

1993 (1)

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Baumert, T.

T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Brixner, T.

T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Buydens, L. M.

R. Wehrens and L. M. Buydens, Trends Anal. Chem. 17, 193 (1998).
[CrossRef]

DeLong, K. W.

Downer, C. M.

Edgar, T.

K. Edwards, T. Edgar, and V. Manousiouthakis, Comput. Chem. Eng. 22, 239 (1998).
[CrossRef]

Edwards, K.

K. Edwards, T. Edgar, and V. Manousiouthakis, Comput. Chem. Eng. 22, 239 (1998).
[CrossRef]

Fittinghoff, D. N.

Gerber, G.

T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Hunter, J.

Kane, D. J.

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

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Kohler, B.

Krumbugel, M. A.

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

Ladera, C. L.

Manousiouthakis, V.

K. Edwards, T. Edgar, and V. Manousiouthakis, Comput. Chem. Eng. 22, 239 (1998).
[CrossRef]

Mitchell, M.

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

Omenetto, F. G.

C. W. Siders, J. L. Siders, F. G. Omenetto, and A. J. Taylor, “Multi-pulse interferometric frequency resolved optical gating,” IEEE J. Quantum Electron. (to be published).

Richman, B. A.

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

Seyfried, V.

T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Siders, C. W.

C. W. Siders, A. J. Taylor, and C. M. Downer, Opt. Lett. 22, 624 (1997).
[CrossRef] [PubMed]

C. W. Siders, J. L. Siders, F. G. Omenetto, and A. J. Taylor, “Multi-pulse interferometric frequency resolved optical gating,” IEEE J. Quantum Electron. (to be published).

Siders, J. L.

C. W. Siders, J. L. Siders, F. G. Omenetto, and A. J. Taylor, “Multi-pulse interferometric frequency resolved optical gating,” IEEE J. Quantum Electron. (to be published).

Streehle, M.

T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Sweetser, J. N.

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

Taylor, A. J.

C. W. Siders, A. J. Taylor, and C. M. Downer, Opt. Lett. 22, 624 (1997).
[CrossRef] [PubMed]

C. W. Siders, J. L. Siders, F. G. Omenetto, and A. J. Taylor, “Multi-pulse interferometric frequency resolved optical gating,” IEEE J. Quantum Electron. (to be published).

Trebino, R.

Wehrens, R.

R. Wehrens and L. M. Buydens, Trends Anal. Chem. 17, 193 (1998).
[CrossRef]

White, W. E.

Wilson, K.

Appl. Phys. B (1)

T. Baumert, T. Brixner, V. Seyfried, M. Streehle, and G. Gerber, Appl. Phys. B 65, 779 (1997).
[CrossRef]

Comput. Chem. Eng. (1)

K. Edwards, T. Edgar, and V. Manousiouthakis, Comput. Chem. Eng. 22, 239 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

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

Trends Anal. Chem. (1)

R. Wehrens and L. M. Buydens, Trends Anal. Chem. 17, 193 (1998).
[CrossRef]

Other (2)

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

C. W. Siders, J. L. Siders, F. G. Omenetto, and A. J. Taylor, “Multi-pulse interferometric frequency resolved optical gating,” IEEE J. Quantum Electron. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a single generation in the GA, illustrating the selection, crossover, and mutation operators.

Fig. 2
Fig. 2

Target intensity and phase (solid curve), the intensity and phase retrieved from the GA (dashed curves), and the intensity and phase from the composite (Femtosoft) algorithm (dotted curves) in the SHG FROG case. The GA returned an error of 0.00175, and the composite algorithm returned an error of 0.00256. A generalized projection algorithm (result not shown) returned an error of 0.00270.

Fig. 3
Fig. 3

Typical experimentally measured SHG FROG trace from an optical parametric amplifier at λ=1.55 μm.

Fig. 4
Fig. 4

Retrieved intensity and phase from the FROG trace in Fig.  3. The GA returned a FROG error of 0.00193, the generalized projection algorithm returned an error of 0.00407, and the composite algorithm returned a FROG error of 0.00254.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

IFROGω,τ=-dt Esigt,τexpiωt2,
Esig=EtEt-τ,
G=1N2ω,τ=1NImω,τ-Irω,τ21/2,

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