Abstract

The monomode guided propagation of a short (500-fs) laser pulse is studied for an incident intensity in the range 10133×1018 W/cm2 inside a glass-walled capillary tube (length, ≈1 cm; inner radius, 15 µm). The measured transmission is constant over a large range of incident intensities (10131016 W/cm2) and corresponds, except for a coupling constant, to the value predicted by an analytical model for monomode guiding. For incident intensities larger than 1017 W/cm2, a drop in transmission is observed, which is attributed to plasma creation at the entrance plane of the capillary tube.

© 2000 Optical Society of America

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  1. F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
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1999 (1)

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

1998 (3)

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

M. Borghesi, A. J. Mackinnon, R. Gaillard, O. Willi, and A. Offenberger, “Guiding of a 10-TW picosecond laser pulse through hollow capillary tubes,” Phys. Rev. E 57, 4899–4902 (1998).
[CrossRef]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

1995 (1)

1994 (2)

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

1993 (1)

C. G. Durfee III and H. M. Milcherg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
[CrossRef] [PubMed]

1972 (1)

R. L. Abrams, “Coupling losses in hollow waveguide laser resonators,” IEEE J. Quantum Electron. 8, 838–843 (1972).
[CrossRef]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Abrams, R. L.

R. L. Abrams, “Coupling losses in hollow waveguide laser resonators,” IEEE J. Quantum Electron. 8, 838–843 (1972).
[CrossRef]

Amiranoff, F.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Audebert, P.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

Baton, S.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Bernard, D.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Borghesi, M.

M. Borghesi, A. J. Mackinnon, R. Gaillard, O. Willi, and A. Offenberger, “Guiding of a 10-TW picosecond laser pulse through hollow capillary tubes,” Phys. Rev. E 57, 4899–4902 (1998).
[CrossRef]

Burris, R.

Campbell, E. M.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Cheng, Z.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

Courtois, C.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

Cros, B.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Descamps, D.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Dorchies, F.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Du, D.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Durfee III, C. G.

C. G. Durfee III and H. M. Milcherg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
[CrossRef] [PubMed]

Evans, K.

Gaillard, R.

M. Borghesi, A. J. Mackinnon, R. Gaillard, O. Willi, and A. Offenberger, “Guiding of a 10-TW picosecond laser pulse through hollow capillary tubes,” Phys. Rev. E 57, 4899–4902 (1998).
[CrossRef]

Geindre, J. P.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

Glinsky, M. E.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Grun, J.

Hammer, J.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Hamoniaux, G.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

Jackel, S.

Jacquet, F.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Kautek, W.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

Korn, G.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Kosakowskii, J.

Krausz, F.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

Kruer, W. L.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Krüger, J.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

Lenzner, M.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

Liu, X.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Mackinnon, A. J.

M. Borghesi, A. J. Mackinnon, R. Gaillard, O. Willi, and A. Offenberger, “Guiding of a 10-TW picosecond laser pulse through hollow capillary tubes,” Phys. Rev. E 57, 4899–4902 (1998).
[CrossRef]

Malka, V.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Manka, C.

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Marquès, J. R.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Mason, R. J.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Matthieussent, G.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Milcherg, H. M.

C. G. Durfee III and H. M. Milcherg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409–2412 (1993).
[CrossRef] [PubMed]

Miné, P.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Modena, A.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Mora, P.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Morillo, J.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Mourou, G.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Najmudin, Z.

F. Amiranoff, S. Baton, D. Bernard, B. Cros, D. Descamps, F. Dorchies, F. Jacquet, V. Malka, J. R. Marquès, G. Matthieussent, P. Miné, A. Modena, P. Mora, J. Morillo, and Z. Najmudin, “Observation of laser Wakefield acceleration of electrons,” Phys. Rev. Lett. 81, 995–998 (1998).
[CrossRef]

Offenberger, A.

M. Borghesi, A. J. Mackinnon, R. Gaillard, O. Willi, and A. Offenberger, “Guiding of a 10-TW picosecond laser pulse through hollow capillary tubes,” Phys. Rev. E 57, 4899–4902 (1998).
[CrossRef]

Perry, M. D.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Rebibo, S.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

Sartania, S.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Spielmann, Ch.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80, 4076–4079 (1998).
[CrossRef]

Squier, J.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994).
[CrossRef]

Tabak, M.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Ting, A.

Vélikoroussov, T.

F. Dorchies, J. R. Marquès, B. Cros, G. Matthieussent, C. Courtois, T. Vélikoroussov, P. Audebert, J. P. Geindre, S. Rebibo, G. Hamoniaux, and F. Amiranoff, “Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes,” Phys. Rev. Lett. 82, 4655–4658 (1999).
[CrossRef]

Wilks, S. C.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, “Ignition and high gain with ultrapowerful lasers,” Phys. Plasmas 1, 1626–1634 (1994).
[CrossRef]

Willi, O.

M. Borghesi, A. J. Mackinnon, R. Gaillard, O. Willi, and A. Offenberger, “Guiding of a 10-TW picosecond laser pulse through hollow capillary tubes,” Phys. Rev. E 57, 4899–4902 (1998).
[CrossRef]

Woodworth, J.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: E is the incident energy, τ is the pulse duration at FWHM, λ is the wavelength, and D is the diameter of the incident beam.

Fig. 2
Fig. 2

Transmission through glass capillary tubes (15-µm inner radius, length 1 cm) as a function of the maximum on-axis intensity at the entrance plane. Experimental (squares) and theoretical (triangles) transmission.

Fig. 3
Fig. 3

Transmission through glass capillary tubes (15-µm inner radius) as a function of length l for I<1016 W/cm2. Experimental (squares) and theoretical (triangles) transmission. C exp(-2l/Ld) with (a) C=1, (b) C=0.4, and (c) C=0.1.

Fig. 4
Fig. 4

Spatial intensity distribution at (a) the entrance and (b) the output planes of the capillary tube for typical shots (I<1016 W/cm2).

Equations (1)

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Ld-1=Im2.40522a3λ2π2 1+21-2,

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