Abstract

We demonstrate energy exchange between two filament-forming femtosecond laser beams in liquid methanol. Our results are consistent with those of previous works documenting coupling between filaments in air; in addition, we identify an unreported phenomenon in which the direction of energy exchange oscillates at increments in the relative pulse delay equal to an optical period (2.6 fs). Energy transfer from one filament to another may be used in remote sensing and spectroscopic applications utilizing femtosecond laser filaments in water and air.

© 2012 Optical Society of America

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  1. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
    [CrossRef]
  2. P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
    [CrossRef]
  3. G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
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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]
  12. N. Akhmediev and A. Ankiewicz, Opt. Commun. 100, 186–192 (1993).
    [CrossRef]

2011

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

2010

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

2009

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, Phys. Rev. Lett. 102, 123902 (2009).
[CrossRef]

2006

2005

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

2004

H. Schroeder and S. L. Chin, Opt. Commun. 234, 399 (2004).
[CrossRef]

2003

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

1998

M. Segev and G. Stegeman, Phys. Today 51 (8), 42 (1998).
[CrossRef]

1993

N. Akhmediev and A. Ankiewicz, Opt. Commun. 100, 186–192 (1993).
[CrossRef]

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, Opt. Commun. 100, 186–192 (1993).
[CrossRef]

André, Y.-B.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, Opt. Commun. 100, 186–192 (1993).
[CrossRef]

Bernstein, A. C.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, Phys. Rev. Lett. 102, 123902 (2009).
[CrossRef]

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Châteauneuf, M.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

Chen, S.

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

Chin, S. L.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

H. Schroeder and S. L. Chin, Opt. Commun. 234, 399 (2004).
[CrossRef]

Couairon, A.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

D’Amico, C.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

Daigle, J.-F.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

Ditmire, T.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, Phys. Rev. Lett. 102, 123902 (2009).
[CrossRef]

Dubois, J.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

Durand, M.

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

Dyer, G. M.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, Phys. Rev. Lett. 102, 123902 (2009).
[CrossRef]

Eisenmann, S.

Erlich, Y.

Fibich, G.

Forestier, B.

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

Fraenkel, M.

Franco, M.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Goda, S. N.

Harris, S. E.

Hemmer, P.

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Houard, A.

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

Kamali, Y.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Katzir, Y.

Liu, W.

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

Louzon, E.

Lui, Y.

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

McCormick, M.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, Phys. Rev. Lett. 102, 123902 (2009).
[CrossRef]

Méchain, G.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

Méjean, G.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Miles, R. B.

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Mysyrowicz, A.

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Polynkin, P.

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Prade, B.

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Roy, G.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

Safiri, S. M.

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

Salmon, E.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Sanders, J. C.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, Phys. Rev. Lett. 102, 123902 (2009).
[CrossRef]

Sauerbrey, R.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Schroeder, H.

H. Schroeder and S. L. Chin, Opt. Commun. 234, 399 (2004).
[CrossRef]

Scully, M. O.

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Segev, M.

M. Segev and G. Stegeman, Phys. Today 51 (8), 42 (1998).
[CrossRef]

Shverdin, M. Y.

Siebert, T.

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Simard, P. T.

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

Sivan, Y.

Sokolov, A. V.

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Sprangle, P.

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Stegeman, G.

M. Segev and G. Stegeman, Phys. Today 51 (8), 42 (1998).
[CrossRef]

Theberge, F.

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

Théberge, F.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

Tremblay, G.

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

Tzortzakis, S.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Wolf, J.-P.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Wöste, L.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Xu, H. L.

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

Yin, G. Y.

Yu, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

Zigler, A.

Appl. Phys. B

W. Liu, F. Theberge, J.-F. Daigle, P. T. Simard, S. M. Safiri, Y. Kamali, H. L. Xu, and S. L. Chin, Appl. Phys. B 85, 55 (2006).
[CrossRef]

J.-F. Daigle, Y. Kamali, M. Châteauneuf, G. Tremblay, F. Théberge, J. Dubois, G. Roy, and S. L. Chin, Appl. Phys. B 97, 701 (2009).
[CrossRef]

Opt. Commun.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

H. Schroeder and S. L. Chin, Opt. Commun. 234, 399 (2004).
[CrossRef]

N. Akhmediev and A. Ankiewicz, Opt. Commun. 100, 186–192 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, Phys. Rev. Lett. 102, 123902 (2009).
[CrossRef]

Y. Lui, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, Phys. Rev. Lett. 105, 055003 (2010).
[CrossRef]

Phys. Today

M. Segev and G. Stegeman, Phys. Today 51 (8), 42 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. USA

P. Hemmer, R. B. Miles, P. Polynkin, T. Siebert, A. V. Sokolov, P. Sprangle, and M. O. Scully, Proc. Natl. Acad. Sci. USA 108, 3130 (2011).
[CrossRef]

Science

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Experimental schematic filter: ND, neutral density. The inset shows the intersection of two filaments involved in energy transfer.

Fig. 2.
Fig. 2.

(a) Fraction of energy transfer versus pulse delay for input energies of 1.20 and 1.52 μJ. (b) Difference between fraction of energy transfer curve extrema for several pulse energies.

Fig. 3.
Fig. 3.

(a) Typical raw spectral measurement of a filament involved in energy transfer in liquid methanol as a function of relative pulse delay. Such raw measurements are spectrally integrated to yield energy transfer curves of Fig. 2(a). (b) Typical FFT of an energy transfer curve for filament-forming, intersecting laser pulses. This FFT peak was completely absent for intersecting pulses that did not form filaments.

Fig. 4.
Fig. 4.

The fine-scale energy transfer between the fixed and translation-stage beams. The measured energies of each pulse are compared to two out-of-phase sine functions. The fixed and translation-stage pulse energies are shown by circles and triangles (displaced by 2*104 units), respectively.

Equations (1)

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S=(PfixedPtrans)/(Pfixed+Ptrans),

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