Abstract

In-line spatial holographic methods are used to image the optical diffraction patterns of ultrafast laser produced plasma filaments in air. Using femtosecond laser pump-probe methods the plasma filament is produced and subsequently probed by a time-delayed probe beam traversing the filament at a right angle. The resulting probe beam image is recorded as a holographic diffraction pattern on a charge coupled device camera as the probe beam is diffracted due to the optical index change caused by the plasma filament. Extraction of the electron density in the filament down to 1016cm3 is obtained by using the Helmholtz wave equation beam propagation model to simulate the data. By varying the pump-probe optical time delay, a plasma electron recombination time of approximately 250ps is measured and agrees with our rate equation population kinetics model.

© 2008 Optical Society of America

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  1. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
    [CrossRef]
  2. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47-189 (2007).
    [CrossRef]
  3. S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
    [CrossRef]
  4. A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
    [CrossRef]
  5. H. Schillinger and R. Sauerbrey, “Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses,” Appl. Phys. B 68, 753-756 (1999).
    [CrossRef]
  6. R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
    [CrossRef]
  7. B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
    [CrossRef]
  8. J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
    [CrossRef]
  9. C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
    [CrossRef]
  10. H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
    [CrossRef]
  11. J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
    [CrossRef]
  12. A. Talebpour, M. Abdel-Fattah, and S. L. Chin, “Focusing limits of intense laser pulses in a high pressure gas: road to new spectroscopic sources,” Opt. Commun. 183, 479-484 (2000).
    [CrossRef]
  13. A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
    [CrossRef]
  14. S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the tail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123-127 (2000).
    [CrossRef]
  15. M. Centurion, Y. Pu, Z. Liu, D. Psaltis, and T. W. Hänsch, “Holographic recording of laser-induced plasma,” Opt. Lett. 29, 772-774 (2004).
    [CrossRef] [PubMed]
  16. M. Centurion, Y. Pu, and D. Psaltis, “Holographic capture of femtosecond pulse propagation,” J. Appl. Phys. 100, 063104 (2006).
    [CrossRef]
  17. S. Minardi, A. Gopal, M. Tatarakis, A. Couairon, G. Tamosauskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Time-resolved refractive index and absorption mapping of light-plasma filaments in water,” Opt. Lett. 33, 86-88 (2008).
    [CrossRef]
  18. D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
    [CrossRef] [PubMed]
  19. Z. Henis, G. Milikh, K. Papadopoulos, and A. Zigler, “Generation of controlled radiation sources in the atmosphere using a dual femtosecond/nanosecond laser pulse,” J. Appl. Phys. 103, 103111 (2008).
    [CrossRef]
  20. Q. Luo, W. Lui, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337-340 (2003).
    [CrossRef]
  21. A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
    [CrossRef]
  22. A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
    [CrossRef]
  23. A. Ting, D. Gordon, E. Briscoe, J. Peñano, and P. Sprangle, “Direct characterization of self-guided femtosecond laser filaments in air,” Appl. Opt. 44, 1474-1479 (2005).
    [CrossRef] [PubMed]
  24. D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
    [CrossRef]
  25. J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
    [CrossRef]
  26. X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599-612 (1995).
    [CrossRef]
  27. I. A. Kossyi, A. Y. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the nonequilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1, 207-220 (1992).
    [CrossRef]
  28. A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924-934 (1966).
  29. A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N-2 and O-2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
    [CrossRef]
  30. M. J. Schmitt, “Mitigation of thermal blooming and diffraction effects with high power laser beams,” J. Opt. Soc. Am. B 20, 719-724 (2003).
    [CrossRef]
  31. I. V. Lisitsyn, S. Kohno, S. Katsuki, and H. Akiyama, “Effect of laser beam deflection on the accuracy of interferometer measurements,” Rev. Sci. Instrum. 69, 1584-1586 (1998).
    [CrossRef]
  32. J. Ruiz-Camacho, F. N. Beg, and P. Lee, “Comparison of sensitivities of moiré deflectometry and interferometry to measure electron densities in z-pinch plasmas,” J. Phys. D 40, 2026-2032 (2007).
    [CrossRef]

2008 (3)

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

S. Minardi, A. Gopal, M. Tatarakis, A. Couairon, G. Tamosauskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Time-resolved refractive index and absorption mapping of light-plasma filaments in water,” Opt. Lett. 33, 86-88 (2008).
[CrossRef]

Z. Henis, G. Milikh, K. Papadopoulos, and A. Zigler, “Generation of controlled radiation sources in the atmosphere using a dual femtosecond/nanosecond laser pulse,” J. Appl. Phys. 103, 103111 (2008).
[CrossRef]

2007 (3)

J. Ruiz-Camacho, F. N. Beg, and P. Lee, “Comparison of sensitivities of moiré deflectometry and interferometry to measure electron densities in z-pinch plasmas,” J. Phys. D 40, 2026-2032 (2007).
[CrossRef]

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

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
[CrossRef]

2006 (2)

M. Centurion, Y. Pu, and D. Psaltis, “Holographic capture of femtosecond pulse propagation,” J. Appl. Phys. 100, 063104 (2006).
[CrossRef]

D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
[CrossRef]

2005 (4)

A. Ting, D. Gordon, E. Briscoe, J. Peñano, and P. Sprangle, “Direct characterization of self-guided femtosecond laser filaments in air,” Appl. Opt. 44, 1474-1479 (2005).
[CrossRef] [PubMed]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

2004 (1)

2003 (4)

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

M. J. Schmitt, “Mitigation of thermal blooming and diffraction effects with high power laser beams,” J. Opt. Soc. Am. B 20, 719-724 (2003).
[CrossRef]

Q. Luo, W. Lui, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337-340 (2003).
[CrossRef]

2002 (1)

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

2001 (1)

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

2000 (4)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

A. Talebpour, M. Abdel-Fattah, and S. L. Chin, “Focusing limits of intense laser pulses in a high pressure gas: road to new spectroscopic sources,” Opt. Commun. 183, 479-484 (2000).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the tail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123-127 (2000).
[CrossRef]

C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
[CrossRef]

1999 (4)

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

H. Schillinger and R. Sauerbrey, “Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses,” Appl. Phys. B 68, 753-756 (1999).
[CrossRef]

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N-2 and O-2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
[CrossRef]

1998 (1)

I. V. Lisitsyn, S. Kohno, S. Katsuki, and H. Akiyama, “Effect of laser beam deflection on the accuracy of interferometer measurements,” Rev. Sci. Instrum. 69, 1584-1586 (1998).
[CrossRef]

1995 (1)

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599-612 (1995).
[CrossRef]

1992 (1)

I. A. Kossyi, A. Y. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the nonequilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1, 207-220 (1992).
[CrossRef]

1966 (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924-934 (1966).

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Abdel-Fattah, M.

A. Talebpour, M. Abdel-Fattah, and S. L. Chin, “Focusing limits of intense laser pulses in a high pressure gas: road to new spectroscopic sources,” Opt. Commun. 183, 479-484 (2000).
[CrossRef]

Akiyama, H.

I. V. Lisitsyn, S. Kohno, S. Katsuki, and H. Akiyama, “Effect of laser beam deflection on the accuracy of interferometer measurements,” Rev. Sci. Instrum. 69, 1584-1586 (1998).
[CrossRef]

Aközbek, N.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

Alexeev, I.

D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
[CrossRef]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

André, Y.-B.

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

Becker, A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

Beg, F. N.

J. Ruiz-Camacho, F. N. Beg, and P. Lee, “Comparison of sensitivities of moiré deflectometry and interferometry to measure electron densities in z-pinch plasmas,” J. Phys. D 40, 2026-2032 (2007).
[CrossRef]

Bernhardt, J.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

Bowden, C. M.

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

Briscoe, E.

A. Ting, D. Gordon, E. Briscoe, J. Peñano, and P. Sprangle, “Direct characterization of self-guided femtosecond laser filaments in air,” Appl. Opt. 44, 1474-1479 (2005).
[CrossRef] [PubMed]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Centurion, M.

M. Centurion, Y. Pu, and D. Psaltis, “Holographic capture of femtosecond pulse propagation,” J. Appl. Phys. 100, 063104 (2006).
[CrossRef]

M. Centurion, Y. Pu, Z. Liu, D. Psaltis, and T. W. Hänsch, “Holographic recording of laser-induced plasma,” Opt. Lett. 29, 772-774 (2004).
[CrossRef] [PubMed]

Chateâuneuf, M.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

Chen, Z.

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

Chien, C. Y.

C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Chin, S. L.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

Q. Luo, W. Lui, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337-340 (2003).
[CrossRef]

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

A. Talebpour, M. Abdel-Fattah, and S. L. Chin, “Focusing limits of intense laser pulses in a high pressure gas: road to new spectroscopic sources,” Opt. Commun. 183, 479-484 (2000).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N-2 and O-2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
[CrossRef]

Chiron, A.

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

Comtois, D.

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Couairon, A.

S. Minardi, A. Gopal, M. Tatarakis, A. Couairon, G. Tamosauskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Time-resolved refractive index and absorption mapping of light-plasma filaments in water,” Opt. Lett. 33, 86-88 (2008).
[CrossRef]

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

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

Daigle, J. F.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

Deng, Y.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
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C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

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DiComo, G. P.

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
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X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599-612 (1995).
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J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

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Dubois, J.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

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X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599-612 (1995).
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A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

Fernsler, R. F.

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
[CrossRef]

Fischer, R.

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
[CrossRef]

D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
[CrossRef]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Franco, M.

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the tail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123-127 (2000).
[CrossRef]

Franco, M. A.

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
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D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
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Gopal, A.

Gordon, D.

D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
[CrossRef]

A. Ting, D. Gordon, E. Briscoe, J. Peñano, and P. Sprangle, “Direct characterization of self-guided femtosecond laser filaments in air,” Appl. Opt. 44, 1474-1479 (2005).
[CrossRef] [PubMed]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Gordon, D. F.

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
[CrossRef]

Hänsch, T. W.

Henis, Z.

Z. Henis, G. Milikh, K. Papadopoulos, and A. Zigler, “Generation of controlled radiation sources in the atmosphere using a dual femtosecond/nanosecond laser pulse,” J. Appl. Phys. 103, 103111 (2008).
[CrossRef]

Hosseini, S. A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Hubbard, R.

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Iwasaki, A.

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

Jiang, Z.

C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Johnston, T. W.

C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Jones, T.

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Kaganovich, D.

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Kandidov, V. P.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Kasparian, J.

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

Katsuki, S.

I. V. Lisitsyn, S. Kohno, S. Katsuki, and H. Akiyama, “Effect of laser beam deflection on the accuracy of interferometer measurements,” Rev. Sci. Instrum. 69, 1584-1586 (1998).
[CrossRef]

Kieffer, J. C.

Kieffer, J.-C.

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Kohno, S.

I. V. Lisitsyn, S. Kohno, S. Katsuki, and H. Akiyama, “Effect of laser beam deflection on the accuracy of interferometer measurements,” Rev. Sci. Instrum. 69, 1584-1586 (1998).
[CrossRef]

Kosareva, O. G.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Kossyi, I. A.

I. A. Kossyi, A. Y. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the nonequilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1, 207-220 (1992).
[CrossRef]

Kostinsky, A. Y.

I. A. Kossyi, A. Y. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the nonequilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1, 207-220 (1992).
[CrossRef]

La Fontaine, B.

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

LaFontaine, B.

Lamouroux, B.

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

Lee, P.

J. Ruiz-Camacho, F. N. Beg, and P. Lee, “Comparison of sensitivities of moiré deflectometry and interferometry to measure electron densities in z-pinch plasmas,” J. Phys. D 40, 2026-2032 (2007).
[CrossRef]

Li, R.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

Li, Y.

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

Lisitsyn, I. V.

I. V. Lisitsyn, S. Kohno, S. Katsuki, and H. Akiyama, “Effect of laser beam deflection on the accuracy of interferometer measurements,” Rev. Sci. Instrum. 69, 1584-1586 (1998).
[CrossRef]

Liu, J.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

Liu, W.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Liu, Z.

Lui, W.

Q. Luo, W. Lui, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337-340 (2003).
[CrossRef]

Luo, Q.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Q. Luo, W. Lui, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337-340 (2003).
[CrossRef]

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

Matveyev, A. A.

I. A. Kossyi, A. Y. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the nonequilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1, 207-220 (1992).
[CrossRef]

Méchain, G.

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

Mecure, H. P.

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Mercure, H. P.

Milikh, G.

Z. Henis, G. Milikh, K. Papadopoulos, and A. Zigler, “Generation of controlled radiation sources in the atmosphere using a dual femtosecond/nanosecond laser pulse,” J. Appl. Phys. 103, 103111 (2008).
[CrossRef]

Minardi, S.

Mysyrowicz, A.

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

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the tail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123-127 (2000).
[CrossRef]

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

Orel, E.

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

Papadopoulos, K.

Z. Henis, G. Milikh, K. Papadopoulos, and A. Zigler, “Generation of controlled radiation sources in the atmosphere using a dual femtosecond/nanosecond laser pulse,” J. Appl. Phys. 103, 103111 (2008).
[CrossRef]

Peñano, J.

A. Ting, D. Gordon, E. Briscoe, J. Peñano, and P. Sprangle, “Direct characterization of self-guided femtosecond laser filaments in air,” Appl. Opt. 44, 1474-1479 (2005).
[CrossRef] [PubMed]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Pépin, H.

C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924-934 (1966).

Piskarskas, R.

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924-934 (1966).

Prade, B.

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the tail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123-127 (2000).
[CrossRef]

Prade, B. S.

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

Psaltis, D.

M. Centurion, Y. Pu, and D. Psaltis, “Holographic capture of femtosecond pulse propagation,” J. Appl. Phys. 100, 063104 (2006).
[CrossRef]

M. Centurion, Y. Pu, Z. Liu, D. Psaltis, and T. W. Hänsch, “Holographic recording of laser-induced plasma,” Opt. Lett. 29, 772-774 (2004).
[CrossRef] [PubMed]

Pu, Y.

M. Centurion, Y. Pu, and D. Psaltis, “Holographic capture of femtosecond pulse propagation,” J. Appl. Phys. 100, 063104 (2006).
[CrossRef]

M. Centurion, Y. Pu, Z. Liu, D. Psaltis, and T. W. Hänsch, “Holographic recording of laser-induced plasma,” Opt. Lett. 29, 772-774 (2004).
[CrossRef] [PubMed]

Roy, G.

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

Ruiz-Camacho, J.

J. Ruiz-Camacho, F. N. Beg, and P. Lee, “Comparison of sensitivities of moiré deflectometry and interferometry to measure electron densities in z-pinch plasmas,” J. Phys. D 40, 2026-2032 (2007).
[CrossRef]

Sauerbrey, R.

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

H. Schillinger and R. Sauerbrey, “Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses,” Appl. Phys. B 68, 753-756 (1999).
[CrossRef]

Schillinger, H.

H. Schillinger and R. Sauerbrey, “Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses,” Appl. Phys. B 68, 753-756 (1999).
[CrossRef]

Schmitt, M. J.

Schroeder, H.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Sheng, Z.

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

Silakov, V. P.

I. A. Kossyi, A. Y. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the nonequilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1, 207-220 (1992).
[CrossRef]

Sprangle, P.

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
[CrossRef]

D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
[CrossRef]

A. Ting, D. Gordon, E. Briscoe, J. Peñano, and P. Sprangle, “Direct characterization of self-guided femtosecond laser filaments in air,” Appl. Opt. 44, 1474-1479 (2005).
[CrossRef] [PubMed]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Talebpour, A.

A. Talebpour, M. Abdel-Fattah, and S. L. Chin, “Focusing limits of intense laser pulses in a high pressure gas: road to new spectroscopic sources,” Opt. Commun. 183, 479-484 (2000).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N-2 and O-2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
[CrossRef]

Tamosauskas, G.

Tatarakis, M.

Teng, H.

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

Terent'ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924-934 (1966).

Théberge, F.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Ting, A.

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
[CrossRef]

D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
[CrossRef]

A. Ting, D. Gordon, E. Briscoe, J. Peñano, and P. Sprangle, “Direct characterization of self-guided femtosecond laser filaments in air,” Appl. Opt. 44, 1474-1479 (2005).
[CrossRef] [PubMed]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Tzortzakis, S.

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the tail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123-127 (2000).
[CrossRef]

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

Vidal, F.

C. Y. Chien, B. LaFontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure femtosecond ionization dynamics in air,” Opt. Lett. 25, 578-580 (2000).
[CrossRef]

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

Vijayalakshmi, N.

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

Wang, C. Y.

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599-612 (1995).
[CrossRef]

Weim, Z.

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

Xie, X.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

Xu, H. L.

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

Yang, H.

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

Yang, J.

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N-2 and O-2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
[CrossRef]

Zeng, Z.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

Zhang, J.

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

Zhao, X. M.

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599-612 (1995).
[CrossRef]

Zigler, A.

Z. Henis, G. Milikh, K. Papadopoulos, and A. Zigler, “Generation of controlled radiation sources in the atmosphere using a dual femtosecond/nanosecond laser pulse,” J. Appl. Phys. 103, 103111 (2008).
[CrossRef]

Zu, Z.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (5)

Q. Luo, W. Lui, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76, 337-340 (2003).
[CrossRef]

A. Becker, N. Aközbek, N. Vijayalakshmi, E. Orel, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287-290 (2001).
[CrossRef]

A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C. M. Bowden, and S. L. Chin, “A LIDAR technique to measure the filament length generated by a high-peak power femtosecond laser pulse in air,” Appl. Phys. B 76, 231-236 (2003).
[CrossRef]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877-879 (2000).
[CrossRef]

H. Schillinger and R. Sauerbrey, “Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses,” Appl. Phys. B 68, 753-756 (1999).
[CrossRef]

Can. J. Phys. (1)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

X. M. Zhao, J. C. Diels, C. Y. Wang, and J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599-612 (1995).
[CrossRef]

IEEE Trans. Plasma Sci. (2)

D. Gordon, A. Ting, I. Alexeev, R. Fischer, and P. Sprangle, “Direct measurements of the dynamics of self-guided femtosecond laser filaments in air,” IEEE Trans. Plasma Sci. 34, 249-253 (2006).
[CrossRef]

R. Fischer, A. Ting, D. F. Gordon, R. F. Fernsler, G. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laser-plasma filaments,” IEEE Trans. Plasma Sci. 35, 1430-1436 (2007).
[CrossRef]

J. Appl. Phys. (2)

M. Centurion, Y. Pu, and D. Psaltis, “Holographic capture of femtosecond pulse propagation,” J. Appl. Phys. 100, 063104 (2006).
[CrossRef]

Z. Henis, G. Milikh, K. Papadopoulos, and A. Zigler, “Generation of controlled radiation sources in the atmosphere using a dual femtosecond/nanosecond laser pulse,” J. Appl. Phys. 103, 103111 (2008).
[CrossRef]

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

J. Phys. D (1)

J. Ruiz-Camacho, F. N. Beg, and P. Lee, “Comparison of sensitivities of moiré deflectometry and interferometry to measure electron densities in z-pinch plasmas,” J. Phys. D 40, 2026-2032 (2007).
[CrossRef]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Opt. Commun. (5)

J. Bernhardt, W. Liu, F. Théberge, H. L. Xu, J. F. Daigle, M. Chateâuneuf, J. Dubois, and S. L. Chin, “Spectroscopic analysis of femtosecond laser plasma filament in air,” Opt. Commun. 281, 1268-1274 (2008).
[CrossRef]

A. Talebpour, M. Abdel-Fattah, and S. L. Chin, “Focusing limits of intense laser pulses in a high pressure gas: road to new spectroscopic sources,” Opt. Commun. 183, 479-484 (2000).
[CrossRef]

A. Couairon, G. Méchain, S. Tzortzakis, M. Franco, B. Lamouroux, B. Prade, and A. Mysyrowicz, “Propagation of twin pulses in air and concatenation of plasma strings produced by femtosecond infrared filaments,” Opt. Commun. 225, 177-192 (2003).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the tail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123-127 (2000).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N-2 and O-2 molecules in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29-32 (1999).
[CrossRef]

Opt. Lett. (3)

Phys. Plasmas (2)

B. La Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J.-C. Kieffer, H. Pépin, and H. P. Mecure, “Filamentation of ultrashort laser beams resulting from their propagation over long distance in air,” Phys. Plasmas 6, 1615-1621 (1999).
[CrossRef]

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005).
[CrossRef]

Phys. Rep. (1)

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

Phys. Rev. E (3)

S. Tzortzakis, M. A. Franco, Y.-B. André, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, “Formation of a conducting channel in air by self-guided femtosecond laser pulses,” Phys. Rev. E 60, R3505-R3507 (1999).
[CrossRef]

H. Yang, J. Zhang, Y. Li, J. Zhang, Y. Li, Z. Chen, H. Teng, Z. Weim, and Z. Sheng,“Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406 (2002).
[CrossRef]

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Zu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[CrossRef]

Plasma Sources Sci. Technol. (1)

I. A. Kossyi, A. Y. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the nonequilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1, 207-220 (1992).
[CrossRef]

Rev. Sci. Instrum. (1)

I. V. Lisitsyn, S. Kohno, S. Katsuki, and H. Akiyama, “Effect of laser beam deflection on the accuracy of interferometer measurements,” Rev. Sci. Instrum. 69, 1584-1586 (1998).
[CrossRef]

Sov. Phys. JETP (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924-934 (1966).

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Figures (11)

Fig. 1
Fig. 1

Experimental layout for side-on holographic imaging of ultrafast laser generated filaments. The distances d and L are adjusted to provide optimal diffraction contrast and CCD field of view coverage. In side-on filament imaging mode (dashed box), no probe beam is used and single-shot fluorescence images are captured by the CCD.

Fig. 2
Fig. 2

Example probe beam CCD images captured under (a) hard pump beam focusing, f 1 = 25 cm and (b) soft pump beam focusing, f 1 = 1 m . In each case the probe beam with no filament and with filament are shown, in addition to the probe beam difference images.

Fig. 3
Fig. 3

Example probe beam line out plots for the data in Fig. 2: (a) hard pump focus, f 1 = 25 cm and (b) soft pump beam focus, f 1 = 1 m . The solid gray traces are the probe beam line outs with no filament, and the dashed black traces are the probe beam line outs with the filament present. The inset figures are the intensity normalized difference line outs for each case.

Fig. 4
Fig. 4

(a) Side-on fluorescence image of 2 mm segment of filament. (b) Calibrated line out plot of (a). (c) Microscopic optical image of burn spot pattern on a piece of fused silica glass at the filament position (at pump focus).

Fig. 5
Fig. 5

(a) Plot of the peak-to-peak modulation (squares) versus pump energy. (b) Plot of the filament side-on fluorescence imaging diameter (solid circles) versus pump energy.

Fig. 6
Fig. 6

Plot of the peak-to-peak modulation versus pump-probe time delay for two pump energy settings: 15.2 mJ (squares) and 8.2 mJ (solid circles). Exponential fit to the data indicates a 224 ps (solid curve fit to squares) and 257 ps (solid curve fit to solid circles) plasma recombination time.

Fig. 7
Fig. 7

Experimental results showing our background-free dark-field imaging capability (a) without and (b) with a filament. (c) shows a subregion where we extract the difference image showing the plasma filament induced modulation. (d) shows the intensity normalized difference line out for this case as below 0.2% peak-to-peak modulation. The pump pulse energy in this case is 2.75 mJ .

Fig. 8
Fig. 8

(a) Diagram showing relevant distances used in the two-dimensional beam propagation and image reconstruction model. Shown in (b) is the finite-sized diameter, L p , of the filament.

Fig. 9
Fig. 9

(a) Plot showing the fringe contrast as a function of L and d. By choosing L and d appropriately the contrast can be maximized. (b) Plot showing the fringe contrast as a function of L p and d. As the spatial resolution (or filament diameter) is decreased to 20 μ m the contrast decreases to 0.17% at d = 8 cm , close to the limit of experimental sensitivity.

Fig. 10
Fig. 10

Graphs of the intensity normalized difference line outs from Fig. 3. The solid curve plots are the experimental results and the dotted plots are the results extracted from the simulation fits for the (a) hard pump focus case, n e o = 2 × 10 18 cm 3 , and (b) the soft pump focus case, n e o = 7 × 10 16 cm 3 .

Fig. 11
Fig. 11

Symbols represent the analysis extracted electron densities n e o versus pump-probe time delay for the 8.2 mJ (dots solid circle) and 15.2 mJ (squares) pump energy cases, respectively. The inset is a graph of the radial electron density profile used to extract the experimentally measured electron densities from the analysis at each pump energy setting. The solid curves in the main plot are the best simulation fits to each data set using the rate equation based model for the electron population dynamics.

Equations (25)

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

n ( r ) = ( 1 ω p 2 ω o 2 ) 1 2 ,
ω o = 2 π c λ ,
ω p = ( n e ( r ) e 2 m e ϵ o ) 1 2 ,
Δ ϕ ( x , y ) = 2 π λ 0 L p n ( r ) d z ,
2 A z 2 + 2 A + k 2 A = 0 ,
I CCD = A 0 ( x , y ) [ 1 + S 0 ( x , y ) ] h 0 CCD 2 ,
I CCD = A 1 2 [ 1 + m 1 * A 1 + m 1 A 1 * A 1 2 ] ,
h 0 CCD = exp ( j k z z ) j λ z exp [ j k z 2 z ( x 2 + y 2 ) ] .
A ̃ ( k x , k y , z ) = A ̃ ( k x , k y , 0 ) e j ( z 2 k z ) ( k x 2 + k y 2 ) .
h ̃ z = e j [ ( k x 2 + k y 2 ) z 2 k z ] ,
T f = e j [ k z ( x 2 + y 2 ) 2 f ] ,
T p = e j Δ ϕ ( x , y ) .
Δ ϕ ( x , y ) = 2 π w k z Δ N ( x ) ,
w = L p 2 2 ln 2 ,
Δ N ( x ) = n e o e 2 m e ϵ o ω o 2 e ( x 2 2 w 2 ) .
Δ n ( r ) = n ( r ) 1 1 2 ( ω p 2 ω o 2 ) n e ( r ) ,
n e ( r ) = n e o e ( r 2 2 w 2 ) .
d n e d t = Z + α n e η n e β e + n e n + ,
d n + d t = Z + α n e β e + n e n + β + n + n ,
d n d t = η n e β + n + n ,
d n d t = Z α n e η n e + β e + n e n + + β + n + n ,
β e + [ cm 3 s ] = β e + [ O 2 + ] + β e + [ N 2 + ] ,
β e + [ O 2 + ] = 2 × 10 7 ( 300 T e ) ,
β e + [ N 2 + ] = 2.8 × 10 7 ( 300 T e ) 1 2 ,
β + = 2 × 10 7 ( 300 T e ) 1 2 ,

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