Abstract

The standard explanation for multiple filamentation of laser pulses is that it is caused by noise in the input beam. We propose an alternative explanation that is based on deterministic vectorial (polarization) effects. We present numerical simulations in support of the vectorial-effects explanation and suggest a simple experiment for deciding whether multiple filamentation is due to vectorial effects.

© 2001 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  2. P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
    [CrossRef]
  3. For example, γ=0 (electrostriction), γ=0.5 (nonresonant electrons), and γ=3 (molecular orientation).1
  4. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  5. G. Fibich and A. Gaeta, Opt. Lett. 25, 335 (2000).
    [CrossRef]
  6. N. F. Pilipetskii and A. R. Rustamov, JETP Lett. 2, 55 (1965).
  7. V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).
  8. G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” www.math.tau.ac.il/~fibich .
  9. The vectorial effects in Eq.  (5) result only from coupling between A1 and A3, because the effect of coupling to A2 is Of4.8
  10. S. Chi and Q. Guo, Opt. Lett. 20, 1598 (1995).
    [CrossRef] [PubMed]
  11. B. Crosignani, P. D. Porto, and A. Yariv, Opt. Lett. 22, 778 (1997).
    [CrossRef] [PubMed]
  12. B. Crosignani, P. D. Porto, and A. Yariv, Opt. Lett. 22, 1820 (1997), erratum of Ref.  11.
    [CrossRef]
  13. R. de la Fuente, O. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
    [CrossRef]
  14. To the best of our knowledge, there has been no report of simulations in which noise in the input beam did lead to multiple filamentation in the unperturbed NLS (6).
  15. A. V. Nowak and D. O. Ham, Opt. Lett. 6, 185 (1981).
    [CrossRef] [PubMed]
  16. J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 45, 3168 (1992).
    [CrossRef] [PubMed]
  17. J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, 3170 (1994).
    [CrossRef]
  18. F. Vidal and T. W. Johnston, Phys. Rev. Lett. 7, 1282 (1996).
    [CrossRef]
  19. S. Gatz and J. Hermann, Opt. Lett. 23, 1176 (1998).
    [CrossRef]

2000 (2)

G. Fibich and A. Gaeta, Opt. Lett. 25, 335 (2000).
[CrossRef]

R. de la Fuente, O. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

1998 (1)

1997 (2)

1996 (1)

F. Vidal and T. W. Johnston, Phys. Rev. Lett. 7, 1282 (1996).
[CrossRef]

1995 (1)

1994 (1)

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, 3170 (1994).
[CrossRef]

1992 (1)

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

1981 (1)

1966 (1)

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

1965 (2)

N. F. Pilipetskii and A. R. Rustamov, JETP Lett. 2, 55 (1965).

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

1964 (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Akhmediev, N. N.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

Atai, J.

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, 3170 (1994).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

Chen, Y.

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, 3170 (1994).
[CrossRef]

Chi, S.

Crosignani, B.

de la Fuente, R.

R. de la Fuente, O. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

Fibich, G.

G. Fibich and A. Gaeta, Opt. Lett. 25, 335 (2000).
[CrossRef]

G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” www.math.tau.ac.il/~fibich .

Gaeta, A.

Gatz, S.

Guo, Q.

Ham, D. O.

Hermann, J.

Ilan, B.

G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” www.math.tau.ac.il/~fibich .

Johnston, T. W.

F. Vidal and T. W. Johnston, Phys. Rev. Lett. 7, 1282 (1996).
[CrossRef]

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Michinel, H.

R. de la Fuente, O. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

Nowak, A. V.

Pilipetskii, N. F.

N. F. Pilipetskii and A. R. Rustamov, JETP Lett. 2, 55 (1965).

Porto, P. D.

Rustamov, A. R.

N. F. Pilipetskii and A. R. Rustamov, JETP Lett. 2, 55 (1965).

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Soto-Crespo, J. M.

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, 3170 (1994).
[CrossRef]

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Terhune, R. W.

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Varela, O.

R. de la Fuente, O. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

Vidal, F.

F. Vidal and T. W. Johnston, Phys. Rev. Lett. 7, 1282 (1996).
[CrossRef]

Wright, E. M.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

Yariv, A.

JETP Lett. (2)

N. F. Pilipetskii and A. R. Rustamov, JETP Lett. 2, 55 (1965).

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Opt. Commun. (1)

R. de la Fuente, O. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (2)

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 45, 3168 (1992).
[CrossRef] [PubMed]

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, 3170 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

F. Vidal and T. W. Johnston, Phys. Rev. Lett. 7, 1282 (1996).
[CrossRef]

P. D. Maker, R. W. Terhune, and C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Other (5)

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

For example, γ=0 (electrostriction), γ=0.5 (nonresonant electrons), and γ=3 (molecular orientation).1

G. Fibich and B. Ilan, “Vectorial and random effects in self-focusing and in multiple filamentation,” www.math.tau.ac.il/~fibich .

The vectorial effects in Eq.  (5) result only from coupling between A1 and A3, because the effect of coupling to A2 is Of4.8

To the best of our knowledge, there has been no report of simulations in which noise in the input beam did lead to multiple filamentation in the unperturbed NLS (6).

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Figures (2)

Fig. 1
Fig. 1

Deterministic multiple filamentation of an axially symmetric input beam A1z=0,x,y=25Pcexp-x2+y2. Here f=0.025 and γ=0.5.

Fig. 2
Fig. 2

Isosurface A1228 of the data in Fig.  1.

Equations (6)

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ΔE-·E+k02E=-k02ϵ0n02PNL,·E=-1ϵ0n02·PNL.
PNLE=4ϵ0n0n¯21+γE2E+γE2E*,
2ik0A1,z+ΔA1+2k02n¯2n0A12A1=0,
iA,z+ΔA+14f2A,zz+N=-f+e^3i+12f2z×f·N+iN3+12f2N3,z,f·A+iA3+12f2A3,z=-4f2f·N+iN3+12f2N3,z,
iA1,z+ΔA1+A12A1=-f214A1,zz+4+6γ1+γA1,x2A1+A1,x2A1*+1+2γ1+γA12A1,xx+A12A1,xx*,
iA1,z+ΔA1+A12A1=0.

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