Abstract

Optical pulse propagation in water is experimentally investigated using an evolutionary algorithm (EA) to control the shape of an optical pulse. The transmission efficiency (ratio of output to input optical power) is maximized by searching the combined amplitude and phase space governing an optical pulse shaper. The transmission efficiency of each tested pulse is physically determined by experiment during the course of the optimization. Combining the EA with an experiment in this manner is a powerful means of improving some figure of merit because no analytical or computational model is required–we optimize directly given the physics of the experiment. In addition, the EA is capable of efficiently searching a large parameter space. Here, we demonstrate improved linear optical pulse propagation near 800nm. Our results demonstrate a pulse with a dramatically narrower bandwidth that coincides with a local absorption minimum (near 800 nm) implying that the transmission efficiency is dominated by water’s absorption spectrum.

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. D. Segelstein, “The complex refractive index of water,” Master’s thesis, Department of Physics, University of Missouri-Kansas City (1981).

2010

2009

2007

2006

2000

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).

1997

R. Storn and R. Price, “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimization 11, 341–359 (1997).
[CrossRef]

C. J. Bardeen, V. 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]

1981

D. Segelstein, “The complex refractive index of water,” Master’s thesis, Department of Physics, University of Missouri-Kansas City (1981).

Aeschlimann, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Agha, I. H.

Alexander, D. R.

Ariunbold, G. O.

Bardeen, C. J.

C. J. Bardeen, V. 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]

Bauer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Bayer, D.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Brixner, T.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).

Bruce, J. C.

Buck, W. C.

Carpenter, S. D.

C. J. Bardeen, V. 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]

Doerr, D. W.

Fox, A. E.

Gaeta, A. L.

Garca De Abajo, F. J.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Geraghty, D. F.

Gerber, G.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).

Jieyu, W.

Kattawar, G. W.

Kolomenskii, A.

Li, J.

Naveira, L. M.

Oehrlein, A.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).

Okawachi, Y.

Österberg, U.

Parali, U.

Pfeiffer, W.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Poudel, M. P.

Price, R.

R. Storn and R. Price, “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimization 11, 341–359 (1997).
[CrossRef]

Rohmer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Schuessler, H.

Segelstein, D.

D. Segelstein, “The complex refractive index of water,” Master’s thesis, Department of Physics, University of Missouri-Kansas City (1981).

Slepkov, A. D.

Sokolov, A. V.

Spindler, C.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Steeb, F.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Storn, R.

R. Storn and R. Price, “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimization 11, 341–359 (1997).
[CrossRef]

Strehle, M.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).

Strohaber, J.

Strycker, B. D.

Trendafilova, C. S.

Wang, C.

Wang, H.

Wang, J.

Warren, W. S.

C. J. Bardeen, V. 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. J. Bardeen, V. 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]

Wilson, K. R.

C. J. Bardeen, V. 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. V.

C. J. Bardeen, V. 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]

Zhang, H.

Appl. Opt.

Appl. Phys. B

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).

Chem. Phys. Lett.

C. J. Bardeen, V. 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]

J. Global Optimization

R. Storn and R. Price, “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimization 11, 341–359 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Nature

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Opt. Express

Other

D. Segelstein, “The complex refractive index of water,” Master’s thesis, Department of Physics, University of Missouri-Kansas City (1981).

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Figures (5)

Fig. 1
Fig. 1

Experimental water propagation setup using a femtosecond laser followed by an optical pulse shaper, neutral density (ND) filters, spatial filter (SF), 4-pass water cell, and two photodiodes measuring laser reference power (P ref ) and transmitted power (P out ) which are fed into an evolutionary algorithm (EA) to control the pulse shaper.

Fig. 2
Fig. 2

Maximum and average population fitness versus generation for a typical optimization experiment with no constraints on the amplitude or phase.

Fig. 3
Fig. 3

Waterfall plot of shaped laser spectra as a function of generation in the EA. The spectrum labeled SLMoff is that of the laser with the pulse shaper turned off.

Fig. 4
Fig. 4

Spatial light modulator masks (amplitude and phase) for the pulse shaper’s optimal solution superimposed with the shaped laser spectrum.

Fig. 5
Fig. 5

Water absorption coefficient from Segelstein [10], superimposed with the shaped spectrum of EA’s optimal solution.

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