Abstract

Energy exchange between two filament-forming pulses with initially free chirp in air was experimentally studied. It occurs because of the change of delayed nonlinear refractive index, which slightly chirps the incident filament-forming laser pulses. Accompanying energy exchange process, spectral characteristics of output laser pulses shows dramatic blueshift and supercontinuum generation. Nonlinear absorptive effect introduces an inbalance between energy exchange at the negative delays and that at the positive delays, and affects the energy exchange efficiency. These results may provide a more comprehensive understanding of energy exchange process between filament-forming laser pulses.

© 2013 OSA

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2013 (2)

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

2012 (3)

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

B. D. Strycker, M. Springer, C. Trendafilova, X. Hua, M. Zhi, A. A. Kolomenskii, H. Schroeder, J. Strohaber, H. A. Schuessier, G. W. Kattawar, and A. V. Sokolov, “Energy transfer between laser filaments in liquid methanol,” Opt. Lett.37, 16–18 (2012).

2011 (4)

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

M. Durand, Y. Liu, B. Forestier, A. Houard, and A. Mysyrowicz, “Experimental observation of a traveling plasma grating formed by two crossing filaments in gases,” Appl. Phys. Lett.98, 121110 (2011).

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

2010 (2)

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

2009 (2)

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett.102, 123902 (2009).

Y. B. Zhao, T. E. Witt, and J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett.103, 173903 (2009).

2007 (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441, 47–189 (2007).

2000 (1)

1997 (3)

1995 (1)

Azarm, A.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Bernstein, A. C.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett.102, 123902 (2009).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Braun, A.

Bukin, O. A.

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

Bykova, E. E.

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

Chen, S.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

Chen, Y. P.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Cheng, G.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Cheng, Y.-H.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

Chin, S.L.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Couairon, A.

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441, 47–189 (2007).

Daigle, J.–F.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Ding, L.’en

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

Ding, P. J.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Ditmire, T.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett.102, 123902 (2009).

Dogariu, A.

Du, D.

Durand, M.

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

M. Durand, Y. Liu, B. Forestier, A. Houard, and A. Mysyrowicz, “Experimental observation of a traveling plasma grating formed by two crossing filaments in gases,” Appl. Phys. Lett.98, 121110 (2011).

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

Dyer, G. M.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett.102, 123902 (2009).

Forestier, B.

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

M. Durand, Y. Liu, B. Forestier, A. Houard, and A. Mysyrowicz, “Experimental observation of a traveling plasma grating formed by two crossing filaments in gases,” Appl. Phys. Lett.98, 121110 (2011).

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

Franco, M. A.

Ge, X. C.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Geints, Y. E.

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

Golik, S. S.

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

Gordon, J.

Y. B. Zhao, T. E. Witt, and J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett.103, 173903 (2009).

Grillon, G.

Guo, Z. Q.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Hagan, D. J.

Houard, A.

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

M. Durand, Y. Liu, B. Forestier, A. Houard, and A. Mysyrowicz, “Experimental observation of a traveling plasma grating formed by two crossing filaments in gases,” Appl. Phys. Lett.98, 121110 (2011).

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

Hu, B. T.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Hua, X.

Jarnac, A.

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

Kabanov, A. M.

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

Kattawar, G. W.

Kolomenskii, A. A.

Korn, G.

Kosareva, O.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Levis, R. J.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

Li, C.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Li, R. X.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Li, Y. H.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Lic, R.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Liu, J. S.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Liu, Q. C.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Liu, W. W.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Liu, X.

Liu, X. L.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Liu, Y.

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

M. Durand, Y. Liu, B. Forestier, A. Houard, and A. Mysyrowicz, “Experimental observation of a traveling plasma grating formed by two crossing filaments in gases,” Appl. Phys. Lett.98, 121110 (2011).

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

Liu, Z. Y.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Marceau, C.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

McCole, E. T.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

McCormick, M.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett.102, 123902 (2009).

Milchberg, H. M.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

Mourou, G.

Mysyrowicz, A.

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

M. Durand, Y. Liu, B. Forestier, A. Houard, and A. Mysyrowicz, “Experimental observation of a traveling plasma grating formed by two crossing filaments in gases,” Appl. Phys. Lett.98, 121110 (2011).

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441, 47–189 (2007).

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B14, 650–660 (1997).

Nibbering, E. T. J.

Odhner, J. H.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

Palastro, J. P.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

Panov, N.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Prade, B.

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

Prade, B. S.

Richardson, M.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Said, A. A.

Sanders, J. C.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett.102, 123902 (2009).

Schroeder, H.

Schuessier, H. A.

Seideman, T.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Sh. Wang, X.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Shi, Y. C.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Smolorz, S.

Sokolov, A. V.

Springer, M.

Squier, J.

Strohaber, J.

Strycker, B. D.

Sun, S. H.

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

Sutherland, R. L.

Tang, N.

Tikhonchuk, V.

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

Tong, Y.

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

Trendafilova, C.

Van Stryland, E. W.

Wahlstrand, J. K.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

Wang, T.–J.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Wise, F.

Witt, T. E.

Y. B. Zhao, T. E. Witt, and J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett.103, 173903 (2009).

Wu, J.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

Xia, T.

Xu, Z.

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

Xu, Z. Z.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Yang, X.

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

Yuan, S.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Zemlyanov, A. A.

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

Zeng, H.

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

Zeng, H. P.

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Zeng, Z. N.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Zhao, Y. B.

Y. B. Zhao, T. E. Witt, and J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett.103, 173903 (2009).

Zheng, Y. H.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Zhi, M.

Zhong, Y.

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Appl. Phys. Lett. (4)

X. Yang, J. Wu, Y. Tong, L.’en Ding, Z. Xu, and H. Zeng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett.97, 071108 (2010).

M. Durand, Y. Liu, B. Forestier, A. Houard, and A. Mysyrowicz, “Experimental observation of a traveling plasma grating formed by two crossing filaments in gases,” Appl. Phys. Lett.98, 121110 (2011).

G. Cheng, Y. H. Zheng, Y. Zhong, Z. N. Zeng, C. Li, X. C. Ge, R. X. Li, and Z. Z. Xu, “Energy transfer between few-cycle laser filaments in air,” Appl. Phys. Lett.101, 251111 (2012).

Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, and S. S. Golik, “Kerr-driven nonlinear refractive index of air at 800 and 400nm measured through femtosecond laser pulse filamentation,” Appl. Phys. Lett.99, 181114 (2011).

J. Opt. Soc. Am. B (4)

Laser Phys. (1)

S.L. Chin, T.–J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.–F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Lic, and Z. Z. Xu, “Advances in intense femtosecond laser filamentation in air,” Laser Phys.22, 1–53 (2011).

Opt. Commun. (1)

Y. Liu, M. Durand, A. Houard, B. Forestier, A. Couairon, and A. Mysyrowicz, “Efficient generation of third harmonic radiation in air filaments: A revisit,” Opt. Commun.284, 4706–4713 (2011).

Opt. Lett. (2)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441, 47–189 (2007).

Phys. Rev. A (2)

P. J. Ding, Z. Y. Liu, Y. C. Shi, S. H. Sun, X. L. Liu, X. Sh. Wang, Z. Q. Guo, Q. C. Liu, Y. H. Li, and B. T. Hu, “Spectral characterization of third-order harmonic generation assisted by a two-dimensional plasma grating in air,” Phys. Rev. A87, 043828 (2013).

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experiments,” Phys. Rev. A87, 053801 (2013).

Phys. Rev. E (1)

M. Durand, A. Jarnac, Y. Liu, B. Prade, A. Houard, V. Tikhonchuk, and A. Mysyrowicz, ”Dynamics of plasma gratings in atomic and molecular gases,” Phys. Rev. E86, 036405 (2012).

Phys. Rev. Lett. (3)

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett.102, 123902 (2009).

Y. B. Zhao, T. E. Witt, and J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett.103, 173903 (2009).

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett.105, 055003 (2010).

Other (1)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of experimental setup (a) and images of the filament produced by the intersecting filament-forming laser pulses at the crossing angle of 17 degree, with (b) 0.15 ps and (c) zero time delay between the pulses. Apparatus components include two focusing lenses (L1, L2), a beam splitters (BS1), a delay line (DL), a neutral density filter (ND), a spectrograph (SM) and an energy monitor.

Fig. 2
Fig. 2

(a) The energy of two laser pulses versus the relative time delay with initial laser power of 0.7Pcr. (b)–(c) The transmission of Beam-1 as a function of the relative time delay when the initial laser powers are 3.0Pcr (b) and 6.6Pcr (c) respectively. The red solid (green dashed, blue dash-doted) line represents the best fit by using the formula T(τ) (T1(τ), T2(τ) + T3(τ)).

Fig. 3
Fig. 3

The spectra of the delay-tuned Beam-1 (a) and delay-fixed Beam-2 (b) verse the relative time delay when the initial total energy was 0.52 mJ.

Fig. 4
Fig. 4

The spectra of the delay-tuned Beam-1 verse the relative time delay when the initial total energy was 1.04 mJ.

Fig. 5
Fig. 5

The energy exchange efficiency (a) and the corresponding time duration (b) as a function of the incident laser power.

Equations (5)

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T ( τ ) = 1 + T 1 ( τ ) + T 2 ( τ ) + T 3 ( τ ) ,
T 1 ( τ ) = κ π τ p I 0 2 B x x x x { Im [ + d t u * ( t τ ) u ( t ) × t d t R ( t t ) u ( t τ ) u * ( t ) ] } ,
T 2 ( τ ) = κ π τ p I 0 2 B x x x x { Re + d t u * ( t τ ) u * ( t ) × t d t R ( t t ) u ( t τ ) u ( t ) ] } ,
T 3 ( τ ) = κ π τ p I 0 2 B x x x x { Re [ + d t u * ( t τ ) u ( t ) × t d t R ( t t ) u ( t τ ) u * ( t ) ] } ,
S = ( E 1 E 2 ) ( E 10 E 20 ) E 1 + E 2 ,

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