Abstract

Multiple foci and a long filament are observed when we focus a femtosecond laser pulse into a fused-silica sample. The dependences of the intensity distribution of the plasma luminescence on the pulse energy and the numerical aperture (NA) of the focusing objective are investigated. Multiple foci are observed when NA of 0.65. A long filament tail is formed instead of multiple foci when the NA is 0.85. A physical image of femtoseond pulse propagation is given by a model based on the nonlinear Schrödinger equation.

© 2002 Optical Society of America

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References

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2001 (2)

2000 (1)

N. Akozbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
[CrossRef]

1999 (2)

A. A. Zozulya, Phys. Rev. Lett. 82, 1430 (1999).
[CrossRef]

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

1998 (2)

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998).
[CrossRef]

1997 (2)

1996 (2)

1995 (1)

1974 (1)

M. D. Feit and J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

1968 (1)

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Akozbek, N.

N. Akozbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
[CrossRef]

Bowden, C. M.

N. Akozbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
[CrossRef]

Braun, A.

Brodeur, A.

Callan, J. P.

Chien, C. Y.

Chin, S. L.

N. Akozbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
[CrossRef]

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

A. Brodeur, O. G. Kosareva, C. Y. Chien, F. A. Ilkov, V. P. Kandidov, and S. L. Chin, Opt. Lett. 22, 304 (1997).
[CrossRef] [PubMed]

Curley, P. F.

Du, D.

Feit, M. D.

M. D. Feit and J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

Finlay, R. J.

Fleck, J. A.

M. D. Feit and J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

France, M. A.

Garcia, J. F.

Glezer, E. N.

Grillon, G.

Haus, H. A.

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Her, T.-H.

Hirao, K.

E. Miura, J. Qiu, H. Inouge, T. Mitsayu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Huang, L.

Ilkov, F. A.

Inouge, H.

E. Miura, J. Qiu, H. Inouge, T. Mitsayu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Itoh, K.

Kandidov, V. P.

Korn, G.

Kosareva, O. G.

Liu, X.

Marburger, J. H.

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Mazur, E.

Milosavljevic, M.

Mitsayu, T.

E. Miura, J. Qiu, H. Inouge, T. Mitsayu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Miura, E.

E. Miura, J. Qiu, H. Inouge, T. Mitsayu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Mlejnek, M.

Moloney, J. V.

Mourou, G.

Mysyravicz, A.

Nibbering, E. T. J.

Nishii, J.

Petit, S.

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

Prade, B. S.

Qiu, J.

E. Miura, J. Qiu, H. Inouge, T. Mitsayu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

Salin, F.

Schaffer, C. B.

Squier, J.

Talebpour, A.

N. Akozbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
[CrossRef]

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

Toma, T.

Wagner, W. G.

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Watanabe, W.

Wright, E. M.

Yamada, K.

Zozulya, A. A.

A. A. Zozulya, Phys. Rev. Lett. 82, 1430 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

E. Miura, J. Qiu, H. Inouge, T. Mitsayu, and K. Hirao, Appl. Phys. Lett. 71, 3329 (1997).
[CrossRef]

M. D. Feit and J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

Opt. Commun. (1)

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. (1)

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Phys. Rev. E (1)

N. Akozbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

A. A. Zozulya, Phys. Rev. Lett. 82, 1430 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. CPA, chirped-pulse amplification.

Fig. 2
Fig. 2

Photomicrographs and on-axis relative intensities of the plasma luminescence at different pulse energies: (a) 0.80 µJ, (b) 140 µJ, (c) 1.61 µJ. The NA of the objective is 0.15.

Fig. 3
Fig. 3

Photomicrographs and on-axis relative intensities of the plasma luminescence at different pulse energies: (a) 0.27 µJ, (b) 0.35 µJ, (c) 0.55 µJ, (d) 0.95 µJ. The NA of the objective is 0.40.

Fig. 4
Fig. 4

Photomicrographs and on-axis relative intensities of the plasma luminescence at different pulse energies: (a) 0.24 µJ, (b) 0.64 µJ, (c) 0.92 µJ.

Fig. 5
Fig. 5

Profiles of the potential well in Eq. (4) with different focal lengths and single-pulse input energies: (a) f= (solid curve), f=3 cm (dashed curve), f=2 cm (dotted curve), and f=1 cm (dashed–dotted curve). Initial beam radius a0=0.01 cm, Pin=10Pcr. (b) Pin=8Pcr (dashed curve), Pin=3Pcr (dotted curve), and Pin=Pcr (dashed–dotted curve). Initial beam radius a0=0.01 cm, f=3 cm.

Equations (5)

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i2kz+2E=kk2Eξ2-ikσ1+iωτρE-ikβKE2K-2E-2kk0n2E2E,
ρξ=1nb2σEgρE2+βKE2KKω-aρ2.
k2dadz2+Ua,τ=0,
Ua,τ=Va,τ-Va0,τ-ka02/2f2,
Va,τ=2ka2+σωττ0βKgτ2PinK2KωπKa2K×exp-2Kτ2-2k0n2Pinπa2exp-2τ2, Va0,τ=2ka02+σωττ0βKgτ2PinK2KωπKa02K×exp-2Kτ2-2k0n2Pinπa02exp-2τ2,

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