Abstract

We investigate theoretically the properties of spatial partially incoherent solitons in nematic liquid-crystal cells. Following the self-consistent multimode approach, we obtain nonlocal spatial incoherent soliton solutions in such noninstantaneous nonlinear media in closed form. The effect of nonlocality on the coherence properties of these self-trapped states is studied in detail. Pertinent examples are provided.

© 2005 Optical Society of America

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  1. M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
    [CrossRef] [PubMed]
  2. M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880-882 (1997).
    [CrossRef]
  3. M. Segev and D. N. Christodoulides, "Incoherent solitons," in Spatial Solitons, S.Trillo and W.Torruellas, eds. (Springer, Berlin, 2001), pp. 87-125.
    [CrossRef]
  4. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, "Incoherently coupled soliton pairs in biased photorefractive crystals," Appl. Phys. Lett. 68, 1763-1765 (1996).
    [CrossRef]
  5. Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Observation of incoherently coupled photorefractive spatial soliton pairs," Opt. Lett. 21, 1436-1438 (1996).
    [CrossRef] [PubMed]
  6. M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
    [CrossRef]
  7. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, "Composite multihump vector solitons carrying topological charge," Phys. Rev. Lett. 84, 1164-1167 (2000).
    [CrossRef] [PubMed]
  8. V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, "Cross-modulation coupling of incoherent soliton modes in photorefractive crystals," Phys. Rev. E 57, 6056-6065 (1998).
    [CrossRef]
  9. T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals," Opt. Lett. 23, 418-420 (1998).
    [CrossRef]
  10. Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
    [CrossRef] [PubMed]
  11. O. Katz, T. Carmon, M. Segev, and D. N. Christodouildes, "Observation of elliptic incoherent spatial solitons," Opt. Lett. 29, 1248-1251 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media," Phys. Rev. Lett. 80, 2310-2313 (1998).
    [CrossRef]
  14. T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
    [CrossRef] [PubMed]
  15. T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev, "Dark incoherent soliton splitting and phase-memory effects: theory and experiment," Phys. Rev. E 59, 4777-4780(R) (1999).
    [CrossRef]
  16. M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
    [CrossRef] [PubMed]
  17. D. Kip, M. Soljacic, M. Segev, E. D. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
    [CrossRef] [PubMed]
  18. C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
    [CrossRef] [PubMed]
  19. J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, "Transverse instabilities of incoherent solitons in Kerr media," Phys. Rev. E 65, 015601(R) (2001).
    [CrossRef]
  20. H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media," Phys. Rev. E 68, 036607 (2003).
    [CrossRef]
  21. H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21, 397-404 (2004).
    [CrossRef]
  22. D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601(R) (2001).
    [CrossRef]
  23. D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media," Phys. Rev. Lett. 78, 646-649 (1997).
    [CrossRef]
  24. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams," Phys. Rev. Lett. 79, 4990-4993 (1997).
    [CrossRef]
  25. G. A. Pasmanik, "Self-action of incoherent light-beams," Zh. Eksp. Teor. Fiz. 66, 490-500 (1974).
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    [CrossRef]
  28. L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, "Propagation of partially incoherent light in nonlinear media via the Wigner transform method," IEEE J. Sel. Top. Quantum Electron. 8, 408-412 (2002).
    [CrossRef]
  29. M. Lisak, L. Helczynski, and D. Anderson, "Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media," Opt. Commun. 220, 321-323 (2003).
    [CrossRef]
  30. M. Peccianti and G. Assanto, "Incoherent spatial solitary waves in nematic liquid crystals," Opt. Lett. 26, 1791-1793 (2001).
    [CrossRef]
  31. G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
    [CrossRef]
  32. M. Peccianti and G. Assanto, "Nematic liquid crystals: A suitable medium for self-confinement of coherent and incoherent light," Phys. Rev. E 65, 035603(R) (2002).
    [CrossRef]
  33. D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, "Self-focused optical structures in a nematic liquid crystal," Physica D 97, 471-497 (1996).
    [CrossRef]
  34. F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, "A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal," J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
    [CrossRef]
  35. C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  36. M. Peccianti, C. Conti, and G. Assanto, "Optical modulational instability in a nonlocal medium," Phys. Rev. E 68, 025602(R) (2003).
    [CrossRef]
  37. C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  38. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
    [CrossRef]
  39. G. Assanto, M. Peccianti, and C. Conti, "Nematicons: optical spatial solitons in nematic liquid crystals," Opt. Photonics News 14, 45-48 (2003).
    [CrossRef]
  40. N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel'dovich, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
    [CrossRef]
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    [CrossRef] [PubMed]
  44. A. W. Snyder and D. J. Mitchell, "Accessible solitons," Science 276, 1538-1541 (1997).
    [CrossRef]
  45. S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
    [CrossRef]
  46. D. J. Mitchell and A. W. Snyder, "Soliton dynamics in a nonlocal medium," J. Opt. Soc. Am. B 16, 236-239 (1999).
    [CrossRef]
  47. W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2001).
    [CrossRef]
  48. O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
    [CrossRef]
  49. N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
    [CrossRef]
  50. W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001).
    [CrossRef]
  51. N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical solitons," Opt. Lett. 29, 286-288 (2004).
    [CrossRef] [PubMed]
  52. W. Krolikowski, O. Bang, and J. Wyller, "Nonlocal incoherent solitons," Phys. Rev. E 70, 036617 (2004).
    [CrossRef]
  53. M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, "Coherence properties of multimode incoherent spatial solitons in noninstantaneous Kerr media," Phys. Rev. E 59, 1193-1199 (1999).
    [CrossRef]
  54. J. W. Goodman, Statistical Optics (Wiley Classics Library, New York, 2000).

2004 (5)

2003 (8)

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

G. Assanto, M. Peccianti, and C. Conti, "Nematicons: optical spatial solitons in nematic liquid crystals," Opt. Photonics News 14, 45-48 (2003).
[CrossRef]

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, "Optical modulational instability in a nonlocal medium," Phys. Rev. E 68, 025602(R) (2003).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[CrossRef]

M. Lisak, L. Helczynski, and D. Anderson, "Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media," Opt. Commun. 220, 321-323 (2003).
[CrossRef]

H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media," Phys. Rev. E 68, 036607 (2003).
[CrossRef]

2002 (4)

M. Peccianti and G. Assanto, "Nematic liquid crystals: A suitable medium for self-confinement of coherent and incoherent light," Phys. Rev. E 65, 035603(R) (2002).
[CrossRef]

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, "Propagation of partially incoherent light in nonlinear media via the Wigner transform method," IEEE J. Sel. Top. Quantum Electron. 8, 408-412 (2002).
[CrossRef]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
[CrossRef]

2001 (5)

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2001).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

M. Peccianti and G. Assanto, "Incoherent spatial solitary waves in nematic liquid crystals," Opt. Lett. 26, 1791-1793 (2001).
[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601(R) (2001).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, "Transverse instabilities of incoherent solitons in Kerr media," Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

2000 (7)

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. D. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

E. D. Eugenieva, D. N. Christodouildes, and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media," Opt. Lett. 25, 972-975 (2000).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, "Composite multihump vector solitons carrying topological charge," Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, "A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal," J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

1999 (3)

T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev, "Dark incoherent soliton splitting and phase-memory effects: theory and experiment," Phys. Rev. E 59, 4777-4780(R) (1999).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, "Coherence properties of multimode incoherent spatial solitons in noninstantaneous Kerr media," Phys. Rev. E 59, 1193-1199 (1999).
[CrossRef]

D. J. Mitchell and A. W. Snyder, "Soliton dynamics in a nonlocal medium," J. Opt. Soc. Am. B 16, 236-239 (1999).
[CrossRef]

1998 (6)

S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media," Phys. Rev. Lett. 80, 2310-2313 (1998).
[CrossRef]

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, "Cross-modulation coupling of incoherent soliton modes in photorefractive crystals," Phys. Rev. E 57, 6056-6065 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals," Opt. Lett. 23, 418-420 (1998).
[CrossRef]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

1997 (5)

M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880-882 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media," Phys. Rev. Lett. 78, 646-649 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams," Phys. Rev. Lett. 79, 4990-4993 (1997).
[CrossRef]

V. P. Nayyar, "Propagation of partially coherent Gaussian Schell-model sources in nonlinear media," J. Opt. Soc. Am. B 14, 2248-2253 (1997).
[CrossRef]

A. W. Snyder and D. J. Mitchell, "Accessible solitons," Science 276, 1538-1541 (1997).
[CrossRef]

1996 (4)

D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, "Self-focused optical structures in a nematic liquid crystal," Physica D 97, 471-497 (1996).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, "Incoherently coupled soliton pairs in biased photorefractive crystals," Appl. Phys. Lett. 68, 1763-1765 (1996).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Observation of incoherently coupled photorefractive spatial soliton pairs," Opt. Lett. 21, 1436-1438 (1996).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

1986 (1)

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel'dovich, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

1981 (1)

V. A. Aleshkevich, S. S. Lebedev, and A. N. Matveev, "Self-action of an incoherent-light beam," Kvantovaya Elektron. (Kiev) 8, 1090-1094 (1981).

1974 (1)

G. A. Pasmanik, "Self-action of incoherent light-beams," Zh. Eksp. Teor. Fiz. 66, 490-500 (1974).

Abbate, G.

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, "A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal," J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

Abe, S.

S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
[CrossRef]

Aleshkevich, V. A.

V. A. Aleshkevich, S. S. Lebedev, and A. N. Matveev, "Self-action of an incoherent-light beam," Kvantovaya Elektron. (Kiev) 8, 1090-1094 (1981).

Anastassiou, C.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, "Transverse instabilities of incoherent solitons in Kerr media," Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Anderson, D.

M. Lisak, L. Helczynski, and D. Anderson, "Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media," Opt. Commun. 220, 321-323 (2003).
[CrossRef]

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, "Propagation of partially incoherent light in nonlinear media via the Wigner transform method," IEEE J. Sel. Top. Quantum Electron. 8, 408-412 (2002).
[CrossRef]

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, "Optical modulational instability in a nonlocal medium," Phys. Rev. E 68, 025602(R) (2003).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[CrossRef]

G. Assanto, M. Peccianti, and C. Conti, "Nematicons: optical spatial solitons in nematic liquid crystals," Opt. Photonics News 14, 45-48 (2003).
[CrossRef]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[CrossRef]

M. Peccianti and G. Assanto, "Nematic liquid crystals: A suitable medium for self-confinement of coherent and incoherent light," Phys. Rev. E 65, 035603(R) (2002).
[CrossRef]

M. Peccianti and G. Assanto, "Incoherent spatial solitary waves in nematic liquid crystals," Opt. Lett. 26, 1791-1793 (2001).
[CrossRef]

Bang, O.

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical solitons," Opt. Lett. 29, 286-288 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, and J. Wyller, "Nonlocal incoherent solitons," Phys. Rev. E 70, 036617 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2001).
[CrossRef]

Brzdakiewicz, K. A.

Buljan, H.

H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21, 397-404 (2004).
[CrossRef]

H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media," Phys. Rev. E 68, 036607 (2003).
[CrossRef]

Carmon, T.

Carvalho, M. I.

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, "Coherence properties of multimode incoherent spatial solitons in noninstantaneous Kerr media," Phys. Rev. E 59, 1193-1199 (1999).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, "Incoherently coupled soliton pairs in biased photorefractive crystals," Appl. Phys. Lett. 68, 1763-1765 (1996).
[CrossRef]

Chen, Z.

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
[CrossRef] [PubMed]

T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev, "Dark incoherent soliton splitting and phase-memory effects: theory and experiment," Phys. Rev. E 59, 4777-4780(R) (1999).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals," Opt. Lett. 23, 418-420 (1998).
[CrossRef]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media," Phys. Rev. Lett. 78, 646-649 (1997).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Observation of incoherently coupled photorefractive spatial soliton pairs," Opt. Lett. 21, 1436-1438 (1996).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

Christiansen, P. L.

Christodouildes, D. N.

Christodoulides, D. N.

H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21, 397-404 (2004).
[CrossRef]

H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media," Phys. Rev. E 68, 036607 (2003).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, "Transverse instabilities of incoherent solitons in Kerr media," Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601(R) (2001).
[CrossRef]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. D. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, "Composite multihump vector solitons carrying topological charge," Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev, "Dark incoherent soliton splitting and phase-memory effects: theory and experiment," Phys. Rev. E 59, 4777-4780(R) (1999).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, "Coherence properties of multimode incoherent spatial solitons in noninstantaneous Kerr media," Phys. Rev. E 59, 1193-1199 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media," Phys. Rev. Lett. 80, 2310-2313 (1998).
[CrossRef]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals," Opt. Lett. 23, 418-420 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media," Phys. Rev. Lett. 78, 646-649 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams," Phys. Rev. Lett. 79, 4990-4993 (1997).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, "Incoherently coupled soliton pairs in biased photorefractive crystals," Appl. Phys. Lett. 68, 1763-1765 (1996).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Observation of incoherently coupled photorefractive spatial soliton pairs," Opt. Lett. 21, 1436-1438 (1996).
[CrossRef] [PubMed]

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[CrossRef]

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C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, "Optical modulational instability in a nonlocal medium," Phys. Rev. E 68, 025602(R) (2003).
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G. Assanto, M. Peccianti, and C. Conti, "Nematicons: optical spatial solitons in nematic liquid crystals," Opt. Photonics News 14, 45-48 (2003).
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D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601(R) (2001).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev, "Dark incoherent soliton splitting and phase-memory effects: theory and experiment," Phys. Rev. E 59, 4777-4780(R) (1999).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, "Coherence properties of multimode incoherent spatial solitons in noninstantaneous Kerr media," Phys. Rev. E 59, 1193-1199 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media," Phys. Rev. Lett. 80, 2310-2313 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals," Opt. Lett. 23, 418-420 (1998).
[CrossRef]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media," Phys. Rev. Lett. 78, 646-649 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams," Phys. Rev. Lett. 79, 4990-4993 (1997).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Observation of incoherently coupled photorefractive spatial soliton pairs," Opt. Lett. 21, 1436-1438 (1996).
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D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601(R) (2001).
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D. Kip, M. Soljacic, M. Segev, E. D. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
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N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical solitons," Opt. Lett. 29, 286-288 (2004).
[CrossRef] [PubMed]

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H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21, 397-404 (2004).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. D. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, "Composite multihump vector solitons carrying topological charge," Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev, "Dark incoherent soliton splitting and phase-memory effects: theory and experiment," Phys. Rev. E 59, 4777-4780(R) (1999).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, "Coherence properties of multimode incoherent spatial solitons in noninstantaneous Kerr media," Phys. Rev. E 59, 1193-1199 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media," Phys. Rev. Lett. 80, 2310-2313 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, "Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefracrive crystals," Opt. Lett. 23, 418-420 (1998).
[CrossRef]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880-882 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media," Phys. Rev. Lett. 78, 646-649 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams," Phys. Rev. Lett. 79, 4990-4993 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Observation of incoherently coupled photorefractive spatial soliton pairs," Opt. Lett. 21, 1436-1438 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, "Incoherently coupled soliton pairs in biased photorefractive crystals," Appl. Phys. Lett. 68, 1763-1765 (1996).
[CrossRef]

M. Segev and D. N. Christodoulides, "Incoherent solitons," in Spatial Solitons, S.Trillo and W.Torruellas, eds. (Springer, Berlin, 2001), pp. 87-125.
[CrossRef]

Shelley, M. J.

D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, "Self-focused optical structures in a nematic liquid crystal," Physica D 97, 471-497 (1996).
[CrossRef]

Shih, M. F.

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

Shuvalov, V. V.

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, "Cross-modulation coupling of incoherent soliton modes in photorefractive crystals," Phys. Rev. E 57, 6056-6065 (1998).
[CrossRef]

Siber, A.

H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media," Phys. Rev. E 68, 036607 (2003).
[CrossRef]

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, "Incoherently coupled soliton pairs in biased photorefractive crystals," Appl. Phys. Lett. 68, 1763-1765 (1996).
[CrossRef]

Snyder, A. W.

Soljacic, M.

H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21, 397-404 (2004).
[CrossRef]

H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media," Phys. Rev. E 68, 036607 (2003).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, "Transverse instabilities of incoherent solitons in Kerr media," Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, "Composite multihump vector solitons carrying topological charge," Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. D. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

Stegeman, G. I.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Sukhov, A. V.

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel'dovich, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Tabiryan, N. V.

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel'dovich, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Torres, J. P.

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, "Transverse instabilities of incoherent solitons in Kerr media," Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Ultanir, E. A.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Vishwanath, A.

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Vysloukh, V. A.

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, "Cross-modulation coupling of incoherent soliton modes in photorefractive crystals," Phys. Rev. E 57, 6056-6065 (1998).
[CrossRef]

Warenghem, M.

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, "A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal," J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

Wyller, J.

W. Krolikowski, O. Bang, and J. Wyller, "Nonlocal incoherent solitons," Phys. Rev. E 70, 036617 (2004).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Zel'dovich, B. Ya.

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel'dovich, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, "Incoherently coupled soliton pairs in biased photorefractive crystals," Appl. Phys. Lett. 68, 1763-1765 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13-21 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, "Propagation of partially incoherent light in nonlinear media via the Wigner transform method," IEEE J. Sel. Top. Quantum Electron. 8, 408-412 (2002).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, "A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal," J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

J. Opt. Soc. Am. B (3)

Kvantovaya Elektron. (Kiev) (1)

V. A. Aleshkevich, S. S. Lebedev, and A. N. Matveev, "Self-action of an incoherent-light beam," Kvantovaya Elektron. (Kiev) 8, 1090-1094 (1981).

Mol. Cryst. Liq. Cryst. (1)

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel'dovich, "The orientational optical nonlinearity of liquid crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Nature (London) (1)

M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880-882 (1997).
[CrossRef]

Opt. Commun. (1)

M. Lisak, L. Helczynski, and D. Anderson, "Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media," Opt. Commun. 220, 321-323 (2003).
[CrossRef]

Opt. Lett. (7)

Opt. Photonics News (1)

G. Assanto, M. Peccianti, and C. Conti, "Nematicons: optical spatial solitons in nematic liquid crystals," Opt. Photonics News 14, 45-48 (2003).
[CrossRef]

Phys. Rev. E (14)

S. Abe and A. Ogura, "Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response," Phys. Rev. E 57, 6066-6070 (1998).
[CrossRef]

W. Krolikowski, O. Bang, and J. Wyller, "Nonlocal incoherent solitons," Phys. Rev. E 70, 036617 (2004).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, "Coherence properties of multimode incoherent spatial solitons in noninstantaneous Kerr media," Phys. Rev. E 59, 1193-1199 (1999).
[CrossRef]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: exact solutions," Phys. Rev. E 63, 016610 (2001).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev, "Dark incoherent soliton splitting and phase-memory effects: theory and experiment," Phys. Rev. E 59, 4777-4780(R) (1999).
[CrossRef]

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, "Cross-modulation coupling of incoherent soliton modes in photorefractive crystals," Phys. Rev. E 57, 6056-6065 (1998).
[CrossRef]

M. Peccianti and G. Assanto, "Nematic liquid crystals: A suitable medium for self-confinement of coherent and incoherent light," Phys. Rev. E 65, 035603(R) (2002).
[CrossRef]

M. Peccianti, C. Conti, and G. Assanto, "Optical modulational instability in a nonlocal medium," Phys. Rev. E 68, 025602(R) (2003).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Soljacic, and D. N. Christodoulides, "Transverse instabilities of incoherent solitons in Kerr media," Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

H. Buljan, A. Siber, M. Soljacic, T. Schwartz, M. Segev, and D. N. Christodoulides, "Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media," Phys. Rev. E 68, 036607 (2003).
[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601(R) (2001).
[CrossRef]

Phys. Rev. Lett. (12)

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media," Phys. Rev. Lett. 78, 646-649 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams," Phys. Rev. Lett. 79, 4990-4993 (1997).
[CrossRef]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, "Composite multihump vector solitons carrying topological charge," Phys. Rev. Lett. 84, 1164-1167 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Multimode incoherent spatial solitons in logarithmically saturable nonlinear media," Phys. Rev. Lett. 80, 2310-2313 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, "Bright spatial solitons on a partially incoherent background," Phys. Rev. Lett. 84, 2374-2377 (2000).
[CrossRef] [PubMed]

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Physica D (1)

D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, "Self-focused optical structures in a nematic liquid crystal," Physica D 97, 471-497 (1996).
[CrossRef]

Science (3)

D. Kip, M. Soljacic, M. Segev, E. D. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

A. W. Snyder and D. J. Mitchell, "Accessible solitons," Science 276, 1538-1541 (1997).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

G. A. Pasmanik, "Self-action of incoherent light-beams," Zh. Eksp. Teor. Fiz. 66, 490-500 (1974).

Other (4)

M. Segev and D. N. Christodoulides, "Incoherent solitons," in Spatial Solitons, S.Trillo and W.Torruellas, eds. (Springer, Berlin, 2001), pp. 87-125.
[CrossRef]

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

P. G. de Gennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, UK, 1972).

J. W. Goodman, Statistical Optics (Wiley Classics Library, New York, 2000).

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Figures (4)

Fig. 1
Fig. 1

(a) Nematic liquid-crystal cell in a planar configuration; (b) θ ̂ ( x ) is the pretilted angle distribution along the x axis as a result of the applied quasi-static field, and Ψ ( x ) is the angular perturbation caused by the incident optical beam.

Fig. 2
Fig. 2

Spatial coherence factor μ 12 as a function of η and δ for a (a) two-mode, (b) three-mode, (c) four-mode, (d) five-mode incoherent soliton. In all cases e = 6 .

Fig. 3
Fig. 3

Cuts of the spatial coherence factor μ 12 at η = 0 corresponding to a three-mode nematicon when (a) e = 20 (solid curve), (b) 4.8 (dotted curve), (c) 4.01 (dashed–dotted curve).

Fig. 4
Fig. 4

Cuts of the spatial coherence factor μ 12 in the η = 5 plane for three modes and e values of (a) 20 (solid curve), (b) 6 (dotted curve), (c) 4.01 (dashed–dotted curve).

Equations (34)

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

2 i k A z + 2 A + k 0 2 n a 2 sin ( θ + θ 0 ) sin ( θ θ 0 ) A = 0 ,
k k 0 n o [ 1 + ( n a 2 2 n e 2 ) sin 2 θ ] ,
K e 2 θ + ( Δ ϵ RF 2 E 2 + ϵ 0 4 n a 2 A 2 ) sin 2 θ = 0 ,
2 i k A z + 2 A + k 0 2 n a 2 Ψ A = 0 ,
K e 2 Ψ ( 2 Δ ϵ RF π E 2 ) Ψ + ϵ 0 4 n a 2 A 2 = 0 ,
θ ( x , y , z ) = θ ̂ ( x ) + θ ̂ ( x ) θ 0 Ψ ( x , y , z ) .
i A ξ + 2 A η 2 + k 0 2 n a 2 x 0 2 Ψ A = 0 ,
K e d 2 Ψ d η 2 2 Δ ϵ RF π x 0 2 E 2 Ψ + ϵ 0 4 n a 2 x 0 2 A 2 = 0 ,
A = m = 1 n c m a m ( η ) exp ( i β m ξ ) ,
d 2 a m d η 2 + ( k 0 2 x 0 2 n a 2 Ψ β m ) a m = 0 ,
d 2 Ψ d η 2 + ( 2 Δ ϵ RF π K e x 0 2 E 2 ) Ψ + ( ϵ 0 4 K e n a 2 x 0 2 ) m = 1 n c m 2 ( a m ) 2 = 0 ,
a ̃ m a m ( c m 2 A 2 max ) 1 2 ,
d 2 a ̃ m d η 2 + ( k 0 2 x 0 2 n a 2 Ψ β m ) a ̃ m = 0 ,
d 2 Ψ d η 2 + e Ψ + b m = 1 n ( a ̃ m ) 2 = 0 ,
Ψ = Ψ 0 sech 2 η .
a ̃ m ( η ) = D m P n m ( tanh η ) .
A 2 A 2 max = 6 2 e sech 4 η 4 + e 2 e sech 2 η .
e 4 .
a ̃ = S 2 , Ψ = Ψ 0 S 2 ,
For n = 2 , a ̃ 2 = D 2 S 2 , a ̃ 1 = D 1 S T ,
where D 1 2 = 4 + e 2 e , D 2 2 = 1 .
For n = 3 , a ̃ 3 = D 3 S 3 , a ̃ 2 = D 2 S 2 T , a ̃ 1 = D 1 S ( 4 5 S 2 ) ,
where D 1 2 = 4 + e 16 ( 2 e ) ,
D 2 2 = 8 + 5 e 2 ( 2 e ) , D 3 2 = 36 15 e 16 ( 2 e ) .
For n = 4 , a ̃ 4 = D 4 S 4 , a ̃ 3 = D 3 S 3 T , a ̃ 2 = D 2 S 2 ( 6 7 S 2 ) , a ̃ 1 = D 1 S T ( 4 7 S 2 ) ,
where D 1 2 = e + 4 16 ( 2 e ) , D 2 2 = 8 + 3 e 24 ( 2 e ) , D 3 2 = 7 ( 4 + 9 e ) 16 ( 2 e ) , D 4 2 = 7 ( 8 3 e ) 24 ( 2 e ) .
For n = 5 , a ̃ 5 = D 5 S 5 , a ̃ 4 = D 4 S 4 T , a ̃ 3 = D 3 S 3 ( 8 9 S 2 ) , a ̃ 2 = D 2 S 2 T ( 2 3 S 2 ) ,
a ̃ 1 = D 1 S ( 8 28 S 2 + 21 S 4 ) , where D 1 2 = ( 4 + e ) 64 ( 2 e ) , D 2 2 = 22 + 7 e 4 ( 2 e ) , D 3 2 = 3 ( 12 + 7 e ) 128 ( 2 e ) , D 4 2 = 3 ( 2 7 e ) 4 ( 2 e ) , D 5 2 = 15 ( 20 7 e ) 128 ( 2 e ) .
μ 12 ( η , η + δ ) = 1 N ( η , η + δ ) m = 1 n a ̃ m ( η ) a ̃ m ( η + δ ) sech ( η ) sech ( η + δ ) ,
N ( η , η + δ ) { ( 6 2 e sech 2 η 4 + e 2 e ) [ 6 2 e sech 2 ( η + δ ) 4 + e 2 e ] } 1 2 .
For n = 2 , μ 12 = N 1 [ D 2 2 S ( η ) S ( η + δ ) + D 1 2 T ( η ) T ( η + δ ) ] .
For n = 3 , μ 12 = N 1 { 16 D 1 2 20 D 1 2 [ S 2 ( η ) + S 2 ( η + δ ) ] + S ( η ) S ( η + δ ) [ ( D 3 2 + 25 D 1 2 ) S ( η ) S ( η + δ ) + D 2 2 T ( η ) T ( η + δ ) ] } .
For n = 4 , μ 12 = N 1 ( T ( η ) T ( η + δ ) { 16 D 1 2 28 D 1 2 [ S 2 ( η ) + S 2 ( η + δ ) ] + ( 49 D 1 2 + D 3 2 ) S 2 ( η ) S 2 ( η + δ ) } + S ( η ) S ( η + δ ) { 36 D 2 2 42 D 2 2 [ S 2 ( η ) + S 2 ( η + δ ) ] + ( 49 D 2 2 + D 4 2 ) S 2 ( η ) S 2 ( η + δ ) } ) .
For n = 5 , μ 12 = N 1 ( 64 D 1 2 + S ( η ) S ( η + δ ) T ( η ) T ( η + δ ) × { 4 D 2 2 6 D 2 2 [ S 2 ( η ) + S 2 ( η + δ ) ] + ( 9 D 2 2 + D 4 2 ) S 2 ( η ) S 2 ( η + δ ) } + 168 D 1 2 [ S 4 ( η ) + S 4 ( η + δ ) ] 224 D 1 2 [ S 2 ( η ) + S 2 ( η + δ ) ] + S 2 ( η ) S 2 ( η + δ ) { 784 D 1 2 + 64 D 3 2 + ( D 5 2 + 81 D 3 2 + 441 D 1 2 ) S 2 ( η ) S 2 ( η + δ ) ( 72 D 3 2 + 588 D 1 2 ) [ S 2 ( η ) + S 2 ( η + δ ) ] } ) ,

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