Abstract

Intense light propagating in a nonlinear medium can generate an ensemble of interacting filaments of light, or spatial solitons. Using nematic liquid crystals, we demonstrate that the filaments exhibit collective behavior typical of complex systems, including the formation of clusters and soundlike vibrations, as well as the reduction of the configurational entropy, controlled by the degree of nonlocality of the medium.

© 2006 Optical Society of America

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  1. M. Mezard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, 1986).
  2. R. Badii and A. Politi, Complexity: Hierarchical Structures and Scaling in Physics (Cambridge U. Press, 1999).
  3. F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
    [CrossRef]
  4. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  5. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
    [CrossRef] [PubMed]
  6. J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
    [CrossRef]
  7. Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
    [CrossRef]
  8. S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
    [CrossRef]
  9. F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
    [CrossRef]
  10. M. Kolesik and J. V. Moloney, Opt. Lett. 29, 590 (2004).
    [CrossRef] [PubMed]
  11. A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
    [CrossRef]
  12. C. N. Likos, Phys. Rep. 348, 267 (2001).
    [CrossRef]
  13. L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
    [CrossRef]
  14. K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
    [CrossRef]
  15. W. Kob, F. Sciortino, and P. Tartaglia, Europhys. Lett. 49, 590 (2000).
    [CrossRef]
  16. T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
    [CrossRef] [PubMed]
  17. C. Conti, Phys. Rev. E 72, 066620 (2005).
    [CrossRef]
  18. N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
    [CrossRef]
  19. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).
  20. M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
    [CrossRef] [PubMed]
  21. S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature 393, 554 (1998).
    [CrossRef]
  22. B. Rumpf and A. C. Newell, Phys. Rev. Lett. 87, 054102 (2001).
    [CrossRef] [PubMed]
  23. T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Phys. Rev. Lett. 87, 085502 (2001).
    [CrossRef] [PubMed]

2005 (2)

2004 (3)

M. Kolesik and J. V. Moloney, Opt. Lett. 29, 590 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
[CrossRef] [PubMed]

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

2003 (1)

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

2002 (3)

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
[CrossRef]

T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
[CrossRef] [PubMed]

2001 (3)

C. N. Likos, Phys. Rep. 348, 267 (2001).
[CrossRef]

B. Rumpf and A. C. Newell, Phys. Rev. Lett. 87, 054102 (2001).
[CrossRef] [PubMed]

T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Phys. Rev. Lett. 87, 085502 (2001).
[CrossRef] [PubMed]

2000 (3)

L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
[CrossRef]

K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
[CrossRef]

W. Kob, F. Sciortino, and P. Tartaglia, Europhys. Lett. 49, 590 (2000).
[CrossRef]

1999 (1)

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

1998 (1)

S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature 393, 554 (1998).
[CrossRef]

1996 (1)

A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
[CrossRef]

1986 (1)

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

Angelani, L.

L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

Assanto, G.

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Badii, R.

R. Badii and A. Politi, Complexity: Hierarchical Structures and Scaling in Physics (Cambridge U. Press, 1999).

Bang, O.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Bergè, L.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Bhattacharya, K. K.

K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
[CrossRef]

Boccaletti, S.

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

Bourayou, R.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Bourtou, V.

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

Broderix, K.

K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
[CrossRef]

Brodeur, A.

A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
[CrossRef]

Cavagna, A.

T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
[CrossRef] [PubMed]

K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
[CrossRef]

Chen, Z.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
[CrossRef]

Chin, S. L.

A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
[CrossRef]

Christodoulides, D. N.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
[CrossRef]

Conti, C.

C. Conti, Phys. Rev. E 72, 066620 (2005).
[CrossRef]

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Courvoisier, F.

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

De Luca, A.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Debenedetti, P. G.

S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature 393, 554 (1998).
[CrossRef]

DiLeonardo, R.

L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
[CrossRef]

Giardina, I.

T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
[CrossRef] [PubMed]

K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
[CrossRef]

Grigera, T. S.

T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
[CrossRef] [PubMed]

T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Phys. Rev. Lett. 87, 085502 (2001).
[CrossRef] [PubMed]

Ilkov, F. A.

A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
[CrossRef]

Kasparian, J.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

Khoo, I. C.

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

Kob, W.

W. Kob, F. Sciortino, and P. Tartaglia, Europhys. Lett. 49, 590 (2000).
[CrossRef]

Kolesik, M.

Krolikowski, W.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Lederer, F.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Likos, C. N.

C. N. Likos, Phys. Rep. 348, 267 (2001).
[CrossRef]

Martin, H.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
[CrossRef]

Martin-Mayor, V.

T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Phys. Rev. Lett. 87, 085502 (2001).
[CrossRef] [PubMed]

Mejean, G.

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

Méjean, G.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Mezard, M.

M. Mezard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, 1986).

Moloney, J. V.

Newell, A. C.

B. Rumpf and A. C. Newell, Phys. Rev. Lett. 87, 054102 (2001).
[CrossRef] [PubMed]

Parisi, G.

T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
[CrossRef] [PubMed]

T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Phys. Rev. Lett. 87, 085502 (2001).
[CrossRef] [PubMed]

M. Mezard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, 1986).

Peccianti, M.

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Peschel, U.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Politi, A.

R. Badii and A. Politi, Complexity: Hierarchical Structures and Scaling in Physics (Cambridge U. Press, 1999).

Ramazza, P.

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

Rasmussen, J. J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Rodriguez, M.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Rumpf, B.

B. Rumpf and A. C. Newell, Phys. Rev. Lett. 87, 054102 (2001).
[CrossRef] [PubMed]

Ruocco, G.

L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
[CrossRef]

Salmon, E.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

Sastry, S.

S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature 393, 554 (1998).
[CrossRef]

Sauerbrey, R.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Scala, A.

L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
[CrossRef]

Sciortino, F.

L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
[CrossRef]

W. Kob, F. Sciortino, and P. Tartaglia, Europhys. Lett. 49, 590 (2000).
[CrossRef]

Sears, S. M.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
[CrossRef]

Segev, M.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
[CrossRef]

Skupin, S.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Stillinger, F. H.

S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature 393, 554 (1998).
[CrossRef]

Sukhov, A. V.

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Tabiryan, N. V.

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Tartaglia, P.

W. Kob, F. Sciortino, and P. Tartaglia, Europhys. Lett. 49, 590 (2000).
[CrossRef]

Umetom, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Verrocchio, P.

T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Phys. Rev. Lett. 87, 085502 (2001).
[CrossRef] [PubMed]

Virasoro, M.

M. Mezard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, 1986).

Wolf, J. P.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Wolf, J.-P.

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

Woste, L.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

Wyller, J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Yu, J.

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

Zel'dovich, B. Y.

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Zippelius, A.

K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

F. Courvoisier, V. Bourtou, J. Kasparian, E. Salmon, G. Mejean, J. Yu, and J.-P. Wolf, Appl. Phys. Lett. 83, 213 (2003).
[CrossRef]

Europhys. Lett. (1)

W. Kob, F. Sciortino, and P. Tartaglia, Europhys. Lett. 49, 590 (2000).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Nature (2)

S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature 393, 554 (1998).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umetom, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (2)

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

C. N. Likos, Phys. Rep. 348, 267 (2001).
[CrossRef]

Phys. Rev. E (3)

S. Skupin, L. Bergè, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J.P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
[CrossRef]

C. Conti, Phys. Rev. E 72, 066620 (2005).
[CrossRef]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
[CrossRef] [PubMed]

L. Angelani, R. DiLeonardo, G. Ruocco, A. Scala, and F. Sciortino, Phys. Rev. Lett. 85, 5356 (2000).
[CrossRef]

K. Broderix, K. K. Bhattacharya, A. Cavagna, A. Zippelius, and I. Giardina, Phys. Rev. Lett. 85, 5360 (2000).
[CrossRef]

B. Rumpf and A. C. Newell, Phys. Rev. Lett. 87, 054102 (2001).
[CrossRef] [PubMed]

T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Phys. Rev. Lett. 87, 085502 (2001).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, Proc. Natl. Acad. Sci. U.S.A. 99, 5223 (2002).
[CrossRef]

Other (4)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

M. Mezard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, 1986).

R. Badii and A. Politi, Complexity: Hierarchical Structures and Scaling in Physics (Cambridge U. Press, 1999).

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995).

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Figures (4)

Fig. 1
Fig. 1

Filament evolution in plane x z at various biases V for a 260 mW input beam ( 1064 nm ) of waist 500 μ m along x and 5 μ m along y injected into a NLC cell kept at 26 ° C . The filaments appear slanted because of walk-off, which also depends on applied voltage.

Fig. 2
Fig. 2

Intensity distribution versus bias: time-averaged intensity distribution (over 50 snapshots separated by 100 ms ) at Z = 3 mm for various biases V (see also Fig. 18 in Ref. [17]).

Fig. 3
Fig. 3

A–C, Landscape (PEL) sections as the probability of finding a filament at a given position, obtained from 50 snapshots for three voltages. D, Shannon entropy of the strings versus voltage, determined in Z = 2 mm and Z = 3 mm .

Fig. 4
Fig. 4

Vibrational spectra: time-averaged spatial spectra of the intensity for various biases, with the formation of soundlike spectra (oblique bright stripes in C and D) following the DPT.

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