Abstract

The formation of permanent periodic structural changes in fused silica induced by the multifilamentation process was investigated. A cylindrical lens was used to focus 800 nm 50 fs pulses with 0.5 - 3mJ energy down to a line, resulting in a quasi-periodic linear self-arrangement of multiple filaments (MF). The quasi-period of multiple filaments is shown to be uniquely defined by the critical power of the material and the peak intensity on the sample entrance surface. A novel technique to control this spatial self-arrangement of MF is demonstrated based on the use of a binary phase mask. This technique allowed us to decrease the relative variation of spacing between the adjacent tracks of refractive index modifications by a factor of 4 as compared with the case without the phase mask. 3D + time numerical simulations qualitatively reproduce the main features of multiple filament formation obtained in the experiment.

© 2010 OSA

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    [CrossRef] [PubMed]
  2. S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
    [CrossRef]
  3. S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
    [CrossRef]
  4. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996).
    [CrossRef] [PubMed]
  5. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
    [CrossRef]
  6. K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).
  7. A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
    [CrossRef]
  8. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
    [CrossRef]
  9. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
    [CrossRef] [PubMed]
  10. J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
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  11. V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
    [CrossRef]
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  15. T. Grow and A. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005).
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  16. V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
    [CrossRef] [PubMed]
  24. D. E. Roskey, M. Kolesik, J. V. Moloney, and E. M. Wright, “The role of linear power partitioning in beam filamentation,” Appl. Phys. B 86(2), 249–258 (2007).
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    [CrossRef]
  26. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
    [CrossRef]
  27. V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
    [CrossRef]
  28. H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
    [CrossRef] [PubMed]
  29. D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009).
    [CrossRef]
  30. Dependence of the refractive index on wavelength in fused silica, data of Melles Griot Inc.: www.mellesgriot.com .
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  32. Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
    [CrossRef] [PubMed]
  33. J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
    [CrossRef] [PubMed]
  34. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
    [CrossRef]
  35. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
    [CrossRef] [PubMed]

2009 (2)

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009).
[CrossRef]

2008 (1)

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

2007 (2)

D. E. Roskey, M. Kolesik, J. V. Moloney, and E. M. Wright, “The role of linear power partitioning in beam filamentation,” Appl. Phys. B 86(2), 249–258 (2007).
[CrossRef]

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

2006 (4)

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

2005 (5)

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005).
[CrossRef]

T. Grow and A. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005).
[CrossRef] [PubMed]

V. Kudriašov, E. Gaižaukas, and V. Sirutkaitis, “Beam transformation and permanent modification in fused silica induced by femtosecond filaments,” J. Opt. Soc. Am. B 22(12), 2619 (2005).
[CrossRef]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

2004 (6)

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004).
[CrossRef] [PubMed]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93(3), 035003 (2004).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

2003 (2)

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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

2002 (1)

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

2001 (2)

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26(11), 840–842 (2001).
[CrossRef]

1999 (5)

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
[CrossRef]

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
[CrossRef]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[CrossRef]

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[CrossRef]

1998 (1)

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef]

1996 (1)

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996).
[CrossRef] [PubMed]

1995 (1)

L. V. Keldysh, “Ionization in the field of strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1322 (1995).

1975 (1)

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[CrossRef]

Akozbek, N.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

Aközbek, N.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

André, Y.-B.

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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Azarm, A.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Barty, A.

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef]

Becker, A.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Bergé, L.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Bernhardt, J.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Biegert, J.

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Borrelli, N. F.

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Bourdon, P.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Brodeur, A.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
[CrossRef]

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
[CrossRef]

Châteauneuf, M.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Chen, X.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

Chin, S. L.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
[CrossRef]

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
[CrossRef]

Couairon, A.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93(3), 035003 (2004).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Dai, J.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

Daigle, J. F.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Davis, K. M.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996).
[CrossRef] [PubMed]

Dormidonov, A. E.

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

Dubietis, A.

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009).
[CrossRef]

Dubois, J.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Durécu, A.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Eisenmann, S.

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004).
[CrossRef] [PubMed]

Ferland, B.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

Fibich, G.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004).
[CrossRef] [PubMed]

G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26(11), 840–842 (2001).
[CrossRef]

Fleury, B.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Franco, M.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005).
[CrossRef]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93(3), 035003 (2004).
[CrossRef] [PubMed]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Gaeta, A.

T. Grow and A. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005).
[CrossRef] [PubMed]

Gaeta, A. L.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[CrossRef]

Gaižaukas, E.

V. Kudriašov, E. Gaižaukas, and V. Sirutkaitis, “Beam transformation and permanent modification in fused silica induced by femtosecond filaments,” J. Opt. Soc. Am. B 22(12), 2619 (2005).
[CrossRef]

Gaizauskas, E.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

Gavish, N.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Gong, Q.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

Grow, T.

T. Grow and A. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005).
[CrossRef] [PubMed]

Grow, T. D.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Hirao, K.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996).
[CrossRef] [PubMed]

Homoelle, D.

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[CrossRef]

Hosseini, S. A.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

Houard, A.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Ilan, B.

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004).
[CrossRef] [PubMed]

G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26(11), 840–842 (2001).
[CrossRef]

Ishaaya, A. A.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Itoh, K.

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).

Jarutis, V.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

Jiang, H.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

Jukna, V.

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009).
[CrossRef]

Juodkazis, S.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

Kamali, Y.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Kandidov, V. P.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
[CrossRef]

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
[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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1322 (1995).

Keller, U.

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Kolesik, M.

D. E. Roskey, M. Kolesik, J. V. Moloney, and E. M. Wright, “The role of linear power partitioning in beam filamentation,” Appl. Phys. B 86(2), 249–258 (2007).
[CrossRef]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[CrossRef]

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

Kosareva, O.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Kosareva, O. G.

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
[CrossRef]

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
[CrossRef]

Kudriašov, V.

V. Kudriašov, E. Gaižaukas, and V. Sirutkaitis, “Beam transformation and permanent modification in fused silica induced by femtosecond filaments,” J. Opt. Soc. Am. B 22(12), 2619 (2005).
[CrossRef]

Lamouroux, B.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Leng, Y.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

Li, R.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

Liu, J.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

Liu, W.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

Liu, Y.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

Lombard, L.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Luo, Q.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

Majus, D.

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009).
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J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
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S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Mathieu, P.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Méchain, G.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93(3), 035003 (2004).
[CrossRef] [PubMed]

Méjean, G.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Michau, V.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Misawa, H.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

Miura, K.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996).
[CrossRef] [PubMed]

Mizeikis, V.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

Mlejnek, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[CrossRef]

Moloney, J. V.

D. E. Roskey, M. Kolesik, J. V. Moloney, and E. M. Wright, “The role of linear power partitioning in beam filamentation,” Appl. Phys. B 86(2), 249–258 (2007).
[CrossRef]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[CrossRef]

Mysyrowicz, A.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005).
[CrossRef]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93(3), 035003 (2004).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Nadeau, M. C.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

Nguyen, N. T.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

Nguyen, T.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

Nishii, J.

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).

Nugent, K. A.

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef]

Nyakk, A. V.

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

Paganin, D.

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef]

Panov, N. A.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

Petit, S.

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
[CrossRef]

Prade, B.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93(3), 035003 (2004).
[CrossRef] [PubMed]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Robert, C.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Roberts, A.

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Roskey, D. E.

D. E. Roskey, M. Kolesik, J. V. Moloney, and E. M. Wright, “The role of linear power partitioning in beam filamentation,” Appl. Phys. B 86(2), 249–258 (2007).
[CrossRef]

Roy, G.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Saliminia, A.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

Salmon, E.

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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Sauerbrey, 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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Scalora, M.

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

Schroeder, H.

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

Sharifi, M.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Simard, J. R.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Simard, P. T.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Sirutkaitis, V.

V. Kudriašov, E. Gaižaukas, and V. Sirutkaitis, “Beam transformation and permanent modification in fused silica induced by femtosecond filaments,” J. Opt. Soc. Am. B 22(12), 2619 (2005).
[CrossRef]

Smith, C.

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[CrossRef]

Sudrie, L.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005).
[CrossRef]

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

Sugimoto, N.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996).
[CrossRef] [PubMed]

Sun, Q.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

Tamarov, M. P.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
[CrossRef]

Théberge, F.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Toma, T.

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).

Tzortzakis, S.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

Valiulis, G.

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009).
[CrossRef]

Vallée, R.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

Vanagas, E.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

Vasseur, O.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Vuong, L. T.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Watanabe, W.

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).

Wielandy, S.

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Wright, E. M.

D. E. Roskey, M. Kolesik, J. V. Moloney, and E. M. Wright, “The role of linear power partitioning in beam filamentation,” Appl. Phys. B 86(2), 249–258 (2007).
[CrossRef]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[CrossRef]

Wu, Z.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

Xu, H. L.

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

Xu, Zh.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

Yamada, K.

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).

Yang, H.

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Zhu, Y.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

Zigler, A.

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004).
[CrossRef] [PubMed]

Appl. Phys. B (4)

S. L. Chin, H. L. Xu, Q. Luo, F. Théberge, W. Liu, J. F. Daigle, Y. Kamali, P. T. Simard, J. Bernhardt, S. A. Hosseini, M. Sharifi, G. Méjean, A. Azarm, C. Marceau, O. Kosareva, V. P. Kandidov, N. Aközbek, A. Becker, G. Roy, P. Mathieu, J. R. Simard, M. Châteauneuf, and J. Dubois, ““Filamentation “remote” sensing of chemical and biological agents/pollutants using only one femtosecond laser source,” Appl. Phys. B 95(1), 1–12 (2009).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).
[CrossRef]

D. E. Roskey, M. Kolesik, J. V. Moloney, and E. M. Wright, “The role of linear power partitioning in beam filamentation,” Appl. Phys. B 86(2), 249–258 (2007).
[CrossRef]

V. P. Kandidov, A. E. Dormidonov, O. G. Kosareva, N. Aközbek, M. Scalora, and S. L. Chin, “Optimum small-scale management of random beam perturbations in a femtosecond laser pulse,” Appl. Phys. B 87(1), 29–36 (2007).
[CrossRef]

J. Appl. Phys. (1)

A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in bulk fused silica using 1kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, “Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser),” J. Nonlinear Opt. Phys. Mater. 8(1), 121 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

V. Kudriašov, E. Gaižaukas, and V. Sirutkaitis, “Beam transformation and permanent modification in fused silica induced by femtosecond filaments,” J. Opt. Soc. Am. B 22(12), 2619 (2005).
[CrossRef]

Opt. Commun. (1)

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallée, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006).
[CrossRef]

Opt. Express (4)

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[CrossRef] [PubMed]

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Zh. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006).
[CrossRef] [PubMed]

T. Grow and A. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005).
[CrossRef] [PubMed]

Opt. Lett. (9)

G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26(11), 840–842 (2001).
[CrossRef]

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004).
[CrossRef] [PubMed]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729 (1996).
[CrossRef] [PubMed]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999).
[CrossRef]

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 8, 19 (1999).

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef]

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31(1), 80–82 (2006).
[CrossRef] [PubMed]

Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005).
[CrossRef] [PubMed]

Phys. Rev. A (3)

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70(3), 033802 (2004).
[CrossRef]

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009).
[CrossRef]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[CrossRef]

Phys. Rev. B (1)

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002).
[CrossRef] [PubMed]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically Turbulent Femtosecond Light Guide in Air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[CrossRef]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86(24), 5470–5473 (2001).
[CrossRef] [PubMed]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93(3), 035003 (2004).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[CrossRef]

Quantum Electron. (2)

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911 (1999).
[CrossRef]

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “A method for spatial regularisation of a bunch of filaments in a femtosecond laser pulse,” Quantum Electron. 34(10), 879–880 (2004).
[CrossRef]

Science (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, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

L. V. Keldysh, “Ionization in the field of strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1322 (1995).

Other (1)

Dependence of the refractive index on wavelength in fused silica, data of Melles Griot Inc.: www.mellesgriot.com .

Supplementary Material (5)

» Media 1: MOV (1079 KB)     
» Media 2: MOV (521 KB)     
» Media 3: MOV (253 KB)     
» Media 4: MOV (181 KB)     
» Media 5: MOV (213 KB)     

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Figures (14)

Fig. 1
Fig. 1

Schematic representation of the set-up used for the investigation of the formation of multiple filaments in bulk glass. The inset on the right side of the figure shows an actual image of the interference zone measured using a CCD camera 3.5mm in front of the focal plane along the z axis.

Fig. 2
Fig. 2

Coordinate system and a typical modified zone.

Fig. 3
Fig. 3

Images (in the x-y plane) of the modified zone inscribed for two different values of the geometrical focus of the Ti:Sapphire femtosecond pulse zgf = 0 mm (a-c) and 3.8 mm (d-f) and different values of the pulse energy ranging from 1mJ to 3.75 mJ. The microscope image (observation plane) was set at the z position indicated in the upper right corner.

Fig. 4
Fig. 4

Movies of track arrays inscribed with a pulse energy of 2.5mJ and with the geometrical focus positioned in the middle of the bulk sample (z = 3.8mm) a) In the x-y plane; b) In the z-y plane. In (a) the image plane is moved along z (i.e. along the tracks) (Media 1). In (b) the view is moved along the y-axis (Media 2).

Fig. 5
Fig. 5

Sample image of movies of the evolution of the refractive index changes tracks along the z direction. The tracks are induced under the following conditions: (Media 3) (a) Pulse energy of 1mJ. (Media 4) (b) Pulses energy of 1.5mJ. (Media 5) (c) Pulse energy of 2mJ.

Fig. 11
Fig. 11

The relative variation δ Δ y (Eq. (2) of the track spacing along the y-axis after the inscription made with the initial pulse energy of 3mJ a) without the phase mask and b) with the binary phase mask.

Fig. 6
Fig. 6

Close-up images of closely spaced tracks induced by pulse energy of over 2mJ and inscribed with the phase mask.

Fig. 7
Fig. 7

Refractive index change of tracks inscribed with and without the phase mask as a function of the pulse energy. Error bars actually correspond to standard deviation of Δn computed for 15 tracks.

Fig. 8
Fig. 8

Relative refractive index amplitude of adjacent tracks inscribed with a binary phase mask and a fixed pulse energy of 3mJ. The spacing between tracks is 24μm.

Fig. 9
Fig. 9

(a)Position of adjacent tracks along the y-axis of a given line of modification inscribed without the phase mask for different pulse energies. (b) Analysis of the measured quasiperiodicity of tracks shown in panel (a). Squares – the average and the standard deviation of a quasiperiod d for the given initial pulse energy. Solid line – the fit to the quasi period d according to the Eq. (9). Circles show the ratio Ppeak/Pcr and its standard deviation per a cell with a side equal to the corresponding quasiperiod d.

Fig. 10
Fig. 10

(a)Position of adjacent tracks along the y-axis of a given line of modification inscribed with the phase mask for different pulse energies. (b) The average and the standard deviation of a track period d for the given initial pulse energy. Solid line corresponds to the full and a half of the phase mask period 47.4 μm.

Fig. 12
Fig. 12

(b)The simulated plasma distribution along the fused silica sample in (y,z) plane and (a) in the successive transverse sections shown by the vertical dashed lines in panel (b). The sample entrance surface corresponds to z = 0.

Fig. 13
Fig. 13

(a,b)The distribution of the simulated plasma hot spots in the (x,y) plane at the distance z = 2325 μm without (a) and with (b) a phase mask. White squares show the natural quasiperiod (a) or phase mask period (b). The energy flowing through several particular rectangular reservoirs surrounding the filaments is shown near the corresponding rectangles in microjoules. (c) Energy and amount of critical powers in the rectangular reservoirs, which surround the hot spots indicated by black numbers in panels (a) and (b).

Fig. 14
Fig. 14

(a,b) Positions of all the simulated local plasma maxima in the (y,z) plane of the sample without (a) and with (b) the phase mask. Vertical solid lines in panels (a),(b) indicate the propagation positions z = 2063 and 1887 μm, at which the plasma maximum transverse position is plotted as the function of the hot spot number in panel (c).

Equations (10)

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

Δ n = λ Δ φ 2 π d .
δ Δ y i = Δ y i Δ y ¯ Δ y ¯ × 100 % ,
2 i k ( z + 1 v g t ) E = Δ E kk ω 2 E t 2 + k 2 n 0 ( n 2 | E | 2 ω p 2 n 0 ( ω 2 + ν c 2 ) ( 1 + i ν c ω ) ) E i k α E ,
N e t = R ( | E | 2 ) ( N 0 N e ) + ν i N e N e τ r ,
E ( x , y , z = 0 , τ ) = E 0 exp ( x 2 + y 2 2 a 0 2 τ 2 2 τ 0 2 + i k x 2 2 R f + i ϕ ( y ) ) ,
ϕ ( y ) = k = N N 1 exp { ( y k d m a s k _ s i m ( d m a s k _ s i m h ) / 2 ) 2 s } ,
W c e l l = τ s t a r t τ e n d d τ ( d x d ) I ( x , y , τ ) d x d y ,
P p e a k _ c e l l = d 2 × I s ,
I s ( W ) = W π π τ 0 a 0 _ exp b 0 _ exp = W π τ 0 S ,
d ( W ) = P p e a k _ c e l l I s = P p e a k _ c e l l W S π τ 0

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