Abstract

The population-split genetic algorithm (PSGA) was successfully applied to retrieve femtosecond optical fields from interferometric autocorrelation traces. PSGA strikes a balance between diversity and the size of population in the genetic algorithm. As a result, PSGA is less likely prematurely converging to sub-optimal solutions. Theoretical and experimental studies indicate that the PSGA can yield more accurate results in shorter time compared with conventional genetic algorithm and the iterative method.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. S. F. Shu, C. L. Pan, and C. T. Sun, "Population-split genetic algorithm for retrieval of ultrafast laser parameters," Int. J. Neural, Parallel, Sci. Comput. 11, 207-220 (2003).Q2
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2006 (2)

D. A. Bender, M. P. Hasselbeck, and M. S. Bahae, "Sensitive ultrashort pulse chirp measurement," Opt. Lett. 31, 122-124 (2006).
[CrossRef] [PubMed]

S. F. Shu, "Evolving ultrafast laser information by a learning genetic algorithm combined with a knowledge base," IEEE Photon. Technol. Lett. 18, 379-381 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (3)

S. F. Shu, C. L. Pan, and C. T. Sun, "Population-split genetic algorithm for retrieval of ultrafast laser parameters," Int. J. Neural, Parallel, Sci. Comput. 11, 207-220 (2003).Q2

R. Mizoguchi, K. Onda, S. S. Kano, A. Wada, " Thinning-out in optimized pulse shaping method using genetic algorithm," Rev. Sci. Instruments. 74, 2670-2674 (2003).
[CrossRef]

S. -F. Shu, Y. Lai, C. -L. Pan, "Learning evolution design of multiband-transmission fiber Bragg grating filters," Opt. Eng. 42, 2856-2860 (2003).
[CrossRef]

2002 (3)

2001 (3)

X. Chu and S. -I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403-1-021403-4 (2001).
[CrossRef]

D. Zeidler, S. Frey, K. -L. Kompa, and M. Motzkus, "Evolutionary algorithms and their application to optical control studies," Phys. Rev. A 64, 023420-1-023420-13 (2001).
[CrossRef]

J. Kunde, B. Baumann, S. Arlt, F. M. -Genoud, U. Siegner, U. Keller, "Optimization of adaptive feedback control for ultrafast semiconductor spectroscopy," J. Opt. Soc. Am. B 18, 872-881 (2001).
[CrossRef]

1999 (3)

1998 (3)

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

1994 (1)

1989 (1)

K. Naganuma, K. Mogi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225-1233 (1989).
[CrossRef]

1985 (1)

Arlt, S.

Bahae, M. S.

Baumann, B.

Bender, D. A.

Chen, M. C.

Chu, S. -I.

X. Chu and S. -I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403-1-021403-4 (2001).
[CrossRef]

Chu, X.

X. Chu and S. -I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403-1-021403-4 (2001).
[CrossRef]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

K. W. DeLong, R. Trebino, J. Hunter and W. E. White, "Frequency-resolved optical gating with the use of second-harmonic generation," J. Opt. Soc. Am. B 11, 2206-2215 (1994).
[CrossRef]

Diels, J. -C. M.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

Fontaine, J. J.

Frey, S.

D. Zeidler, S. Frey, K. -L. Kompa, and M. Motzkus, "Evolutionary algorithms and their application to optical control studies," Phys. Rev. A 64, 023420-1-023420-13 (2001).
[CrossRef]

Funk, D. J.

Garcia, M. E.

I. Grigorenko, O. Speer, and M. E. Garcia, "Coherent control of photon-assisted tunneling between quantum dots: A theoretical approach using genetic algorithms," Phys. Rev. B 65, 235309-1-235309-7 (2002).
[CrossRef]

Grigorenko, I.

I. Grigorenko, O. Speer, and M. E. Garcia, "Coherent control of photon-assisted tunneling between quantum dots: A theoretical approach using genetic algorithms," Phys. Rev. B 65, 235309-1-235309-7 (2002).
[CrossRef]

Hasselbeck, M. P.

Hirayama, T.

Honzatko, P.

Huang, J. Y.

Hunter, J.

Iaconis, C.

Jasapara, J.

Kane, D. J.

D. J. Kane, "Real-time measurement of ultrashort laser pulses using principal component generalized projections," IEEE J. Sel. Top. Quantum Electron. 4, 278-284 (1998).Q1
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

Kanka, J.

Kano, S. S.

R. Mizoguchi, K. Onda, S. S. Kano, A. Wada, " Thinning-out in optimized pulse shaping method using genetic algorithm," Rev. Sci. Instruments. 74, 2670-2674 (2003).
[CrossRef]

Kompa, K. -L.

D. Zeidler, S. Frey, K. -L. Kompa, and M. Motzkus, "Evolutionary algorithms and their application to optical control studies," Phys. Rev. A 64, 023420-1-023420-13 (2001).
[CrossRef]

Krumbugel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

Kunde, J.

Lai, Y.

S. -F. Shu, Y. Lai, C. -L. Pan, "Learning evolution design of multiband-transmission fiber Bragg grating filters," Opt. Eng. 42, 2856-2860 (2003).
[CrossRef]

Luce, B. P.

McMichael, I. C.

Mizoguchi, R.

R. Mizoguchi, K. Onda, S. S. Kano, A. Wada, " Thinning-out in optimized pulse shaping method using genetic algorithm," Rev. Sci. Instruments. 74, 2670-2674 (2003).
[CrossRef]

Mogi, K.

K. Naganuma, K. Mogi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225-1233 (1989).
[CrossRef]

Motzkus, M.

D. Zeidler, S. Frey, K. -L. Kompa, and M. Motzkus, "Evolutionary algorithms and their application to optical control studies," Phys. Rev. A 64, 023420-1-023420-13 (2001).
[CrossRef]

Naganuma, K.

K. Naganuma, K. Mogi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225-1233 (1989).
[CrossRef]

Nicholson, J. W.

Omenetto, F. G.

Onda, K.

R. Mizoguchi, K. Onda, S. S. Kano, A. Wada, " Thinning-out in optimized pulse shaping method using genetic algorithm," Rev. Sci. Instruments. 74, 2670-2674 (2003).
[CrossRef]

Pan, C. L.

Pan, C. -L.

S. -F. Shu, Y. Lai, C. -L. Pan, "Learning evolution design of multiband-transmission fiber Bragg grating filters," Opt. Eng. 42, 2856-2860 (2003).
[CrossRef]

Peatross, J.

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

Rudolph, W.

Rundquist, A.

Shu, S. F.

S. F. Shu, "Evolving ultrafast laser information by a learning genetic algorithm combined with a knowledge base," IEEE Photon. Technol. Lett. 18, 379-381 (2006).
[CrossRef]

S. F. Shu, C. L. Pan, and C. T. Sun, "Population-split genetic algorithm for retrieval of ultrafast laser parameters," Int. J. Neural, Parallel, Sci. Comput. 11, 207-220 (2003).Q2

Shu, S. -F.

S. -F. Shu, Y. Lai, C. -L. Pan, "Learning evolution design of multiband-transmission fiber Bragg grating filters," Opt. Eng. 42, 2856-2860 (2003).
[CrossRef]

Simoni, F.

Speer, O.

I. Grigorenko, O. Speer, and M. E. Garcia, "Coherent control of photon-assisted tunneling between quantum dots: A theoretical approach using genetic algorithms," Phys. Rev. B 65, 235309-1-235309-7 (2002).
[CrossRef]

Sun, C. T.

S. F. Shu, C. L. Pan, and C. T. Sun, "Population-split genetic algorithm for retrieval of ultrafast laser parameters," Int. J. Neural, Parallel, Sci. Comput. 11, 207-220 (2003).Q2

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

Taylor, A. J.

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

K. W. DeLong, R. Trebino, J. Hunter and W. E. White, "Frequency-resolved optical gating with the use of second-harmonic generation," J. Opt. Soc. Am. B 11, 2206-2215 (1994).
[CrossRef]

Vrany, B.

Wada, A.

R. Mizoguchi, K. Onda, S. S. Kano, A. Wada, " Thinning-out in optimized pulse shaping method using genetic algorithm," Rev. Sci. Instruments. 74, 2670-2674 (2003).
[CrossRef]

Walmsley, I. A.

White, W. E.

Yamada, H.

K. Naganuma, K. Mogi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225-1233 (1989).
[CrossRef]

Yang, Q. T.

Zeidler, D.

D. Zeidler, S. Frey, K. -L. Kompa, and M. Motzkus, "Evolutionary algorithms and their application to optical control studies," Phys. Rev. A 64, 023420-1-023420-13 (2001).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

K. Naganuma, K. Mogi, and H. Yamada, "General method for ultrashort light pulse chirp measurement," IEEE J. Quantum Electron. 25, 1225-1233 (1989).
[CrossRef]

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

D. J. Kane, "Real-time measurement of ultrashort laser pulses using principal component generalized projections," IEEE J. Sel. Top. Quantum Electron. 4, 278-284 (1998).Q1
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. F. Shu, "Evolving ultrafast laser information by a learning genetic algorithm combined with a knowledge base," IEEE Photon. Technol. Lett. 18, 379-381 (2006).
[CrossRef]

J. Opt. Soc. Am. B (6)

Opt. Eng. (1)

S. -F. Shu, Y. Lai, C. -L. Pan, "Learning evolution design of multiband-transmission fiber Bragg grating filters," Opt. Eng. 42, 2856-2860 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. A (2)

X. Chu and S. -I. Chu, "Optimization of high-order harmonic generation by genetic algorithm and wavelet time-frequency analysis of quantum dipole emission," Phys. Rev. A 64, 021403-1-021403-4 (2001).
[CrossRef]

D. Zeidler, S. Frey, K. -L. Kompa, and M. Motzkus, "Evolutionary algorithms and their application to optical control studies," Phys. Rev. A 64, 023420-1-023420-13 (2001).
[CrossRef]

Phys. Rev. B (1)

I. Grigorenko, O. Speer, and M. E. Garcia, "Coherent control of photon-assisted tunneling between quantum dots: A theoretical approach using genetic algorithms," Phys. Rev. B 65, 235309-1-235309-7 (2002).
[CrossRef]

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, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3296 (1997).
[CrossRef]

Rev. Sci. Instruments. (1)

R. Mizoguchi, K. Onda, S. S. Kano, A. Wada, " Thinning-out in optimized pulse shaping method using genetic algorithm," Rev. Sci. Instruments. 74, 2670-2674 (2003).
[CrossRef]

Sci. Comput. (1)

S. F. Shu, C. L. Pan, and C. T. Sun, "Population-split genetic algorithm for retrieval of ultrafast laser parameters," Int. J. Neural, Parallel, Sci. Comput. 11, 207-220 (2003).Q2

Other (2)

N. A. Campbell and J. B. Reece, Biology (Benjamin Cummings, San Francisco, 2002).

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, Berlin Heidelberg, 1996), Chap. 9.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the structure of the PSGA algorithm

Fig. 2.
Fig. 2.

Flowchart for phase retrieval of ultrafast pulses from IAC using PSGA.

Fig. 3.
Fig. 3.

(a) The target and the retrieved pulse intensities (log plot) and phases of a double-peaked pulse with complicated phase. (b) Error as a function of generation number for PSGA, conventional GA and iterative algorithms.

Fig. 4.
Fig. 4.

Dynamic distributions of Genes at generation #3 for (a) PSGA and (b) conventional GA. The red line in Fig. 3(a), which marks the population splitting boundary, separates a region with much regular genetic organization from that with disordered genetic arrangement.

Fig. 5.
Fig. 5.

Measured (a) linear (b) second-order interferometric autocorrelation traces of a 25-fs pulse train at 90 MHz.

Fig. 6.
Fig. 6.

(a) Intensity and phase of a 25-fs pulse train at 90 MHz retrieved by three different algorithms from target interferometric traces shown in Fig. 5. (b) Errors in the retrieved interferometric traces are plotted as a function of generation number for PSGA, conventional GA and iterative algorithm.

Fig. 7.
Fig. 7.

Comparison between the experimental and theoretical second-order interferometric autocorrelation traces.

Equations (5)

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Z = Z I 2 + Z U 2
Z I 2 = ( I try ( ω ) 2 I ( ω ) M 2 ) 2 I ( ω ) M 4
Z U 2 = ( U try ( ω ) 2 U ( ω ) M 2 ) 2 U ( ω ) M 4 .
E ( t ) = exp [ i Ψ ( t ) ] * ( A . exp [ ( t t 1 T ) 2 ] + B · exp [ ( t t 2 T ) 2 ] )
Ψ ( t ) = a ( t T ) 2 + b ( t T ) 3 + c ( t T ) 4

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