Abstract

We investigate azimuthal instabilities of intense rotationally symmetric pulsed beams propagating in air. Although the spatial–temporal evolution of the field is strongly influenced by the onset of plasma generation, the instabilities are caused chiefly by the Kerr effect. We conclude that calculations that assume rotational symmetry become unrealistic because of the fast growth of azimuthal instabilities shortly after the onset of plasma generation.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
    [CrossRef]
  2. L. Bergé and A. Couairon, Phys. Rev. Lett. 86, 1003 (2001).
    [CrossRef]
  3. A. Braun, G. Korn, K. Liu, D. Du, J. Squier, and G. Mourou, Opt. Lett. 20, 73 (1995).
    [CrossRef] [PubMed]
  4. A. Couairon and L. Bergé, Phys. Rev. Lett. 88, 135003 (2002).
    [CrossRef]
  5. S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
    [CrossRef]
  6. J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J.-P. Wolf, Y.-B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, Opt. Lett. 25, 1397 (2000).
    [CrossRef]
  7. J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).
    [CrossRef]
  8. M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 73, 382 (1998).
    [CrossRef]
  9. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
    [CrossRef]
  10. H. Schillinger and R. Sauerbrey, Appl. Phys. B 68, 753 (1999).
    [CrossRef]
  11. S. Tzortzakis, B. Lamouroux, A. Chiron, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Lett. 25, 1270 (2000).
    [CrossRef]
  12. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 86, 5470 (2001).
    [CrossRef] [PubMed]
  13. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
    [CrossRef]
  14. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 24, 178 (1974).
    [CrossRef]
  15. K. Konno and H. Suzuki, Phys. Scr. 20, 382 (1979).
    [CrossRef]
  16. N. E. Kosmatov, V. F. Shvets, and V. E. Zakharov, Physica D 52, 16 (1991).
    [CrossRef]

2002 (1)

A. Couairon and L. Bergé, Phys. Rev. Lett. 88, 135003 (2002).
[CrossRef]

2001 (3)

S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
[CrossRef]

L. Bergé and A. Couairon, Phys. Rev. Lett. 86, 1003 (2001).
[CrossRef]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 86, 5470 (2001).
[CrossRef] [PubMed]

2000 (4)

1999 (2)

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
[CrossRef]

H. Schillinger and R. Sauerbrey, Appl. Phys. B 68, 753 (1999).
[CrossRef]

1998 (1)

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 73, 382 (1998).
[CrossRef]

1995 (1)

1991 (1)

N. E. Kosmatov, V. F. Shvets, and V. E. Zakharov, Physica D 52, 16 (1991).
[CrossRef]

1979 (1)

K. Konno and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

1974 (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 24, 178 (1974).
[CrossRef]

1973 (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Aközbek, N.

S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
[CrossRef]

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

André, Y.-B.

Bergé, L.

A. Couairon and L. Bergé, Phys. Rev. Lett. 88, 135003 (2002).
[CrossRef]

L. Bergé and A. Couairon, Phys. Rev. Lett. 86, 1003 (2001).
[CrossRef]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 86, 5470 (2001).
[CrossRef] [PubMed]

Bowden, C. M.

S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
[CrossRef]

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

Braun, A.

Campillo, A. J.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 24, 178 (1974).
[CrossRef]

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Chin, S. L.

S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
[CrossRef]

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

J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).
[CrossRef]

Chiron, A.

Couairon, A.

A. Couairon and L. Bergé, Phys. Rev. Lett. 88, 135003 (2002).
[CrossRef]

L. Bergé and A. Couairon, Phys. Rev. Lett. 86, 1003 (2001).
[CrossRef]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 86, 5470 (2001).
[CrossRef] [PubMed]

Du, D.

Franco, M.

Kasparian, J.

Kolesik, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
[CrossRef]

Konno, K.

K. Konno and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

Korn, G.

Kosmatov, N. E.

N. E. Kosmatov, V. F. Shvets, and V. E. Zakharov, Physica D 52, 16 (1991).
[CrossRef]

Lamouroux, B.

Liu, K.

Mlejnek, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 73, 382 (1998).
[CrossRef]

Moloney, J. V.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 73, 382 (1998).
[CrossRef]

Mondelain, D.

Mourou, G.

Mysyrowicz, A.

Niedermeier, S.

Petit, S.

S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
[CrossRef]

Prade, B.

Proulx, A.

S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
[CrossRef]

Rodriguez, M.

Sauerbrey, R.

Schillinger, H.

H. Schillinger and R. Sauerbrey, Appl. Phys. B 68, 753 (1999).
[CrossRef]

Shapiro, S. L.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 24, 178 (1974).
[CrossRef]

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Shvets, V. F.

N. E. Kosmatov, V. F. Shvets, and V. E. Zakharov, Physica D 52, 16 (1991).
[CrossRef]

Squier, J.

Suydam, B. R.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 24, 178 (1974).
[CrossRef]

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Suzuki, H.

K. Konno and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

Talebpour, A.

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

Tzortzakis, S.

Wille, H.

Wolf, J.-P.

Wöste, L.

Wright, E. M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 73, 382 (1998).
[CrossRef]

Yu, J.

Zakharov, V. E.

N. E. Kosmatov, V. F. Shvets, and V. E. Zakharov, Physica D 52, 16 (1991).
[CrossRef]

Appl. Phys. B (2)

J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).
[CrossRef]

H. Schillinger and R. Sauerbrey, Appl. Phys. B 68, 753 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 24, 178 (1974).
[CrossRef]

Opt. Commun. (1)

S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (1)

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

Phys. Rev. Lett. (4)

L. Bergé and A. Couairon, Phys. Rev. Lett. 86, 1003 (2001).
[CrossRef]

A. Couairon and L. Bergé, Phys. Rev. Lett. 88, 135003 (2002).
[CrossRef]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
[CrossRef]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 86, 5470 (2001).
[CrossRef] [PubMed]

Phys. Scr. (1)

K. Konno and H. Suzuki, Phys. Scr. 20, 382 (1979).
[CrossRef]

Physica D (1)

N. E. Kosmatov, V. F. Shvets, and V. E. Zakharov, Physica D 52, 16 (1991).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Amplitude of the rotationally symmetric solution ER and the corresponding plasma density ρ at several propagation distances Pin=9.9 GW, R=7 mm, T=85 fs, and f=66 cm. In addition, the evolution of the peak amplitude ERmax is shown; the region of considerable plasma generation is shaded (bottom right).

Fig. 2
Fig. 2

Evolution of the energy contained in azimuthal perturbations vm of several orders for various initial field distributions. All energies are scaled to the initial energies.

Fig. 3
Fig. 3

Energy fluence of the rotationally symmetric solution ER and the perturbed solutions ER+vm cos mφ, m=1,2 (for the parameters, see Fig. 1) after a propagation length of z=34 cm. The energy of the initial perturbation is 5% of the total energy.

Fig. 4
Fig. 4

Evolution of the energy contained in azimuthal perturbations vm of several orders for various nonlinearities (Pin=20 GW, R=7 mm, T=85 fs). All energies are scaled to the initial energies.

Fig. 5
Fig. 5

Amplitude of the rotationally symmetric solution ER and the perturbations v2 and v4 after a propagation length of 32 cm for the full model and for the saturable Kerr nonlinearity only (for input parameters, see Fig. 4).

Equations (5)

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

zE=i12k0Δ-k2t2+ω0n2cE2-σω0τ02ρE-σ2ρ+βK2E2K-2E,
tρ=βKKω0E2K,
ERr,z=0,t=2PinπR21/2exp-r2R2-t2T2,
δEmr,φ,z,t=vmr,z,tcos mφ+wmr,z,tsin mφ,    m>0,
zvm=i2k01rr+r2-m2r2-k0kt2vm+i2ω0n2cER2-KβK2ER2K-2vm+iω0n2c-K-1βK2ER2K-4ER2vm*-1+iω0τ0σβK2ω0vmK-tdtER2K+ER-tdtER2K-2ER*vm+ERvm*.

Metrics