Abstract

Propagation-invariant, X waves with negative group velocity are reported. Beam aperturing allows for a comprehensive analysis concerning the causality of the optical signal and forerunner formation.

© 2006 Optical Society of America

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References

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  1. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  2. J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 438 (1990).
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  3. J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
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  4. M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
    [CrossRef]
  5. E. Recami, Physica A 252, 586 (1998).
    [CrossRef]
  6. M. A. Porras, S. Trillo, C. Conti, and P. Di Trapani, Opt. Lett. 28, 1090 (2003).
    [CrossRef] [PubMed]
  7. J. Salo and M. M. Salomaa, ARLO 2, 31 (2001).
    [CrossRef]
  8. C. G. B. Garrett and D. E. McCumber, Phys. Rev. A 1, 305 (1970).
    [CrossRef]
  9. S. Chu and S. Wong, Phys. Rev. Lett. 48, 738 (1982).
    [CrossRef]
  10. B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
    [CrossRef]
  11. M. W. Mitchel and R. Y. Chiao, Phys. Lett. A 230, 133 (1997).
    [CrossRef]
  12. L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
    [CrossRef] [PubMed]
  13. H. Sonajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
    [CrossRef] [PubMed]
  14. M. Zamboni-Rached, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, Opt. Commun. 226, 15 (2003).
    [CrossRef]
  15. Z. L. Horváth and Z. Bor, Phys. Rev. E 63, 026601 (2001).
    [CrossRef]

2003 (3)

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

M. Zamboni-Rached, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, Opt. Commun. 226, 15 (2003).
[CrossRef]

M. A. Porras, S. Trillo, C. Conti, and P. Di Trapani, Opt. Lett. 28, 1090 (2003).
[CrossRef] [PubMed]

2001 (2)

Z. L. Horváth and Z. Bor, Phys. Rev. E 63, 026601 (2001).
[CrossRef]

J. Salo and M. M. Salomaa, ARLO 2, 31 (2001).
[CrossRef]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

1998 (1)

E. Recami, Physica A 252, 586 (1998).
[CrossRef]

1997 (1)

M. W. Mitchel and R. Y. Chiao, Phys. Lett. A 230, 133 (1997).
[CrossRef]

1996 (2)

H. Sonajalg and P. Saari, Opt. Lett. 21, 1162 (1996).
[CrossRef] [PubMed]

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
[CrossRef]

1990 (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 438 (1990).
[CrossRef] [PubMed]

1987 (1)

1985 (1)

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

1982 (1)

S. Chu and S. Wong, Phys. Rev. Lett. 48, 738 (1982).
[CrossRef]

1970 (1)

C. G. B. Garrett and D. E. McCumber, Phys. Rev. A 1, 305 (1970).
[CrossRef]

Bor, Z.

Z. L. Horváth and Z. Bor, Phys. Rev. E 63, 026601 (2001).
[CrossRef]

Chiao, R. Y.

M. W. Mitchel and R. Y. Chiao, Phys. Lett. A 230, 133 (1997).
[CrossRef]

Chu, S.

S. Chu and S. Wong, Phys. Rev. Lett. 48, 738 (1982).
[CrossRef]

Conti, C.

Di Trapani, P.

M. A. Porras, S. Trillo, C. Conti, and P. Di Trapani, Opt. Lett. 28, 1090 (2003).
[CrossRef] [PubMed]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

Durnin, J.

Fagerholm, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
[CrossRef]

Friberg, A. T.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
[CrossRef]

Garrett, C. G. B.

C. G. B. Garrett and D. E. McCumber, Phys. Rev. A 1, 305 (1970).
[CrossRef]

Greenleaf, J. F.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 438 (1990).
[CrossRef] [PubMed]

Hernández-Figueroa, H. E.

M. Zamboni-Rached, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, Opt. Commun. 226, 15 (2003).
[CrossRef]

Horváth, Z. L.

Z. L. Horváth and Z. Bor, Phys. Rev. E 63, 026601 (2001).
[CrossRef]

Huttunen, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
[CrossRef]

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

Lu, J.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 438 (1990).
[CrossRef] [PubMed]

Macke, B.

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

McCumber, D. E.

C. G. B. Garrett and D. E. McCumber, Phys. Rev. A 1, 305 (1970).
[CrossRef]

Mitchel, M. W.

M. W. Mitchel and R. Y. Chiao, Phys. Lett. A 230, 133 (1997).
[CrossRef]

Morgan, D. P.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
[CrossRef]

Nóbrega, K. Z.

M. Zamboni-Rached, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, Opt. Commun. 226, 15 (2003).
[CrossRef]

Porras, M. A.

M. A. Porras, S. Trillo, C. Conti, and P. Di Trapani, Opt. Lett. 28, 1090 (2003).
[CrossRef] [PubMed]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

Recami, E.

M. Zamboni-Rached, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, Opt. Commun. 226, 15 (2003).
[CrossRef]

E. Recami, Physica A 252, 586 (1998).
[CrossRef]

Saari, P.

Salo, J.

J. Salo and M. M. Salomaa, ARLO 2, 31 (2001).
[CrossRef]

Salomaa, M. M.

J. Salo and M. M. Salomaa, ARLO 2, 31 (2001).
[CrossRef]

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
[CrossRef]

Segard, B.

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

Sonajalg, H.

Trillo, S.

Valiulis, G.

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

Wong, S.

S. Chu and S. Wong, Phys. Rev. Lett. 48, 738 (1982).
[CrossRef]

Zamboni-Rached, M.

M. Zamboni-Rached, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, Opt. Commun. 226, 15 (2003).
[CrossRef]

ARLO (1)

J. Salo and M. M. Salomaa, ARLO 2, 31 (2001).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 438 (1990).
[CrossRef] [PubMed]

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

Nature (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Zamboni-Rached, K. Z. Nóbrega, H. E. Hernández-Figueroa, and E. Recami, Opt. Commun. 226, 15 (2003).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (2)

B. Segard and B. Macke, Phys. Lett. A 109, 213 (1985).
[CrossRef]

M. W. Mitchel and R. Y. Chiao, Phys. Lett. A 230, 133 (1997).
[CrossRef]

Phys. Rev. A (1)

C. G. B. Garrett and D. E. McCumber, Phys. Rev. A 1, 305 (1970).
[CrossRef]

Phys. Rev. E (3)

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, Phys. Rev. E 54, 4347 (1996).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

Z. L. Horváth and Z. Bor, Phys. Rev. E 63, 026601 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

S. Chu and S. Wong, Phys. Rev. Lett. 48, 738 (1982).
[CrossRef]

Physica A (1)

E. Recami, Physica A 252, 586 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Understanding (a) positive and (b) negative GV in X waves.

Fig. 2
Fig. 2

Gray-scale plots of E 2 at increasing times in frames with a width of 1.97 mm (z direction) and a height of 32.8 μ m (x direction). Insets, E 1 5 in the same instants to visualize the low intensity X tails.

Fig. 3
Fig. 3

Illustration of the spatiotemporal evolution of a truncated X wave of negative GV ( t i < t i + 1 ) . Boundary waves: forerunner pulse at t 2 and trailing pulse at t 5 .

Fig. 4
Fig. 4

Time evolution of E 2 at several axial points z.

Equations (7)

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

U ( r , z , ω ) = J 0 [ k ( ω ) sin θ ( ω ) r ] exp [ i k ( ω ) cos θ ( ω ) z ] ,
v g = v p ( 1 ω 0 θ 0 tan θ 0 ) 1 ,
θ 0 > ( ω 0 θ 0 ) 1 .
θ 0 = θ 0 ω 0 ( 2 + ω 0 θ 0 tan θ 0 ) ,
E ( r , z , t ) = S ( ω ) U ( r , z , ω ) exp ( i ω t ) d ω ,
Δ t X ( z ) = a 2 + f 2 c + f z v g ,
Δ t T ( z ) = 2 ( a 2 + f 2 c + f v g ) + a 2 + z 2 c .

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