Abstract

We analytically and numerically find families of polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium and analyze their coherence properties. We find that the polychromatic incoherent solitons exist when higher temporal frequency constituents of the light are less spatially coherent than smaller temporal frequency constituents.

© 2004 Optical Society of America

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  1. M. Mitchell, Z. Chen, M. 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.
  4. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
    [CrossRef]
  5. 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]
  6. V. V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
    [CrossRef]
  7. D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).
    [CrossRef]
  8. A. W. Snyder and D. J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
    [CrossRef]
  9. B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
    [CrossRef]
  10. D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (1998).
    [CrossRef]
  11. 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]
  12. N. Akhmediev, W. Krolikowski, and A. W. Snyder, “Partially coherent solitons of variable shape,” Phys. Rev. Lett. 81, 4632–4635 (1998).
    [CrossRef]
  13. A. Ankiewicz, W. Krolikowski, and N. N. Akhmediev, “Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions,” Phys. Rev. E 59, 6079–6087 (1999).
    [CrossRef]
  14. 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]
  15. A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83, 4736–4739 (1999).
    [CrossRef]
  16. T. H. Coskun, D. N. Christodoulides, Y.-R. 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]
  17. D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, “Incoherent spatial solitons in saturable nonlinear media,” Opt. Lett. 22, 1080–1082 (1997).
    [CrossRef] [PubMed]
  18. 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]
  19. W. Krolikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically nonlinear media,” Phys. Rev. E 61, 3122–3125 (2000).
    [CrossRef]
  20. 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 photorefractive crystals,” Opt. Lett. 23, 418–420 (1998).
    [CrossRef]
  21. S. A. Ponomarenko, “Linear superposition principle for partially coherent solitons,” Phys. Rev. E 65, 055601 (2002).
    [CrossRef]
  22. H. Buljan, M. Segev, M. Soljačić, N. K. Efremidis, and D. N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
    [CrossRef] [PubMed]
  23. H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
    [CrossRef]
  24. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
  25. H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601 (2002).
    [CrossRef]
  26. O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83, 5479–5482 (1999).
    [CrossRef]
  27. Such a representation of mutual spectral density as a superposition of coherent modes, that are mutually incoherent, is inherited from the linear theory for propagation of incoherent light (see Ref. 24, p. 214.)
  28. S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505–516 (1973).
  29. Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
    [CrossRef]
  30. T. H. Coskun, D. N. Christodoulides, Z. G. Chen, and M. Segev, “Dark incoherent soliton splitting and ‘phase-memory’ effects: theory and experiment,” Phys. Rev. E 59, R4777–R4780 (1999).
    [CrossRef]
  31. M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66.1–66.14 (2002).
    [CrossRef]

2003

H. Buljan, M. Segev, M. Soljačić, N. K. Efremidis, and D. N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[CrossRef] [PubMed]

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

2002

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601 (2002).
[CrossRef]

S. A. Ponomarenko, “Linear superposition principle for partially coherent solitons,” Phys. Rev. E 65, 055601 (2002).
[CrossRef]

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66.1–66.14 (2002).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[CrossRef]

2001

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

2000

T. H. Coskun, D. N. Christodoulides, Y.-R. 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]

W. Krolikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically nonlinear media,” Phys. Rev. E 61, 3122–3125 (2000).
[CrossRef]

1999

A. Ankiewicz, W. Krolikowski, and N. N. Akhmediev, “Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions,” Phys. Rev. E 59, 6079–6087 (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]

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83, 4736–4739 (1999).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Z. G. Chen, and M. Segev, “Dark incoherent soliton splitting and ‘phase-memory’ effects: theory and experiment,” Phys. Rev. E 59, R4777–R4780 (1999).
[CrossRef]

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83, 5479–5482 (1999).
[CrossRef]

1998

Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (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]

A. W. Snyder and D. J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (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 photorefractive crystals,” Opt. Lett. 23, 418–420 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (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]

N. Akhmediev, W. Krolikowski, and A. W. Snyder, “Partially coherent solitons of variable shape,” Phys. Rev. Lett. 81, 4632–4635 (1998).
[CrossRef]

V. V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[CrossRef]

1997

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, 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, T. H. Coskun, and R. I. Joseph, “Incoherent spatial solitons in saturable nonlinear media,” Opt. Lett. 22, 1080–1082 (1997).
[CrossRef] [PubMed]

1996

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

1973

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505–516 (1973).

Akhmediev, N.

N. Akhmediev, W. Krolikowski, and A. W. Snyder, “Partially coherent solitons of variable shape,” Phys. Rev. Lett. 81, 4632–4635 (1998).
[CrossRef]

Akhmediev, N. N.

A. Ankiewicz, W. Krolikowski, and N. N. Akhmediev, “Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions,” Phys. Rev. E 59, 6079–6087 (1999).
[CrossRef]

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83, 4736–4739 (1999).
[CrossRef]

Anderson, D.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[CrossRef]

V. V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[CrossRef]

Ankiewicz, A.

A. Ankiewicz, W. Krolikowski, and N. N. Akhmediev, “Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions,” Phys. Rev. E 59, 6079–6087 (1999).
[CrossRef]

Bang, O.

W. Krolikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically nonlinear media,” Phys. Rev. E 61, 3122–3125 (2000).
[CrossRef]

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83, 5479–5482 (1999).
[CrossRef]

Berry, M. V.

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66.1–66.14 (2002).
[CrossRef]

Buljan, H.

H. Buljan, M. Segev, M. Soljačić, N. K. Efremidis, and D. N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[CrossRef] [PubMed]

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601 (2002).
[CrossRef]

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]

Chen, Z.

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

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (1998).
[CrossRef]

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

Chen, Z. G.

T. H. Coskun, D. N. Christodoulides, Z. G. Chen, and M. Segev, “Dark incoherent soliton splitting and ‘phase-memory’ effects: theory and experiment,” Phys. Rev. E 59, R4777–R4780 (1999).
[CrossRef]

Cher, Z. G.

Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[CrossRef]

Christodoulides, D. N.

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

H. Buljan, M. Segev, M. Soljačić, N. K. Efremidis, and D. N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[CrossRef] [PubMed]

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

T. H. Coskun, D. N. Christodoulides, Y.-R. 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. 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]

T. H. Coskun, D. N. Christodoulides, Z. G. Chen, and M. Segev, “Dark incoherent soliton splitting and ‘phase-memory’ effects: theory and experiment,” Phys. Rev. E 59, R4777–R4780 (1999).
[CrossRef]

Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (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 photorefractive crystals,” Opt. Lett. 23, 418–420 (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]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (1998).
[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, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, “Incoherent spatial solitons in saturable nonlinear media,” Opt. Lett. 22, 1080–1082 (1997).
[CrossRef] [PubMed]

Coskun, T. H.

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

T. H. Coskun, D. N. Christodoulides, Y.-R. 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. 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]

T. H. Coskun, D. N. Christodoulides, Z. G. Chen, and M. Segev, “Dark incoherent soliton splitting and ‘phase-memory’ effects: theory and experiment,” Phys. Rev. E 59, R4777–R4780 (1999).
[CrossRef]

Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (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]

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 photorefractive crystals,” Opt. Lett. 23, 418–420 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (1998).
[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, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, “Incoherent spatial solitons in saturable nonlinear media,” Opt. Lett. 22, 1080–1082 (1997).
[CrossRef] [PubMed]

Edmundson, D.

W. Krolikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically nonlinear media,” Phys. Rev. E 61, 3122–3125 (2000).
[CrossRef]

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83, 5479–5482 (1999).
[CrossRef]

Efremidis, N. K.

Eugenieva, E. D.

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

Fedele, R.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[CrossRef]

Hall, B.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[CrossRef]

Joseph, R. I.

Kim, Y.-R.

T. H. Coskun, D. N. Christodoulides, Y.-R. 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]

Krolikowski, W.

W. Krolikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically nonlinear media,” Phys. Rev. E 61, 3122–3125 (2000).
[CrossRef]

A. Ankiewicz, W. Krolikowski, and N. N. Akhmediev, “Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions,” Phys. Rev. E 59, 6079–6087 (1999).
[CrossRef]

N. Akhmediev, W. Krolikowski, and A. W. Snyder, “Partially coherent solitons of variable shape,” Phys. Rev. Lett. 81, 4632–4635 (1998).
[CrossRef]

Królikowski, W.

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83, 5479–5482 (1999).
[CrossRef]

Kutuzov, 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]

Lisak, M.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[CrossRef]

Manakov, S. V.

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505–516 (1973).

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
[CrossRef]

Mitchell, M.

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

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 photorefractive crystals,” Opt. Lett. 23, 418–420 (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]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (1998).
[CrossRef]

Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880–882 (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, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

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

Petnikova, V. M.

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]

Ponomarenko, S. A.

S. A. Ponomarenko, “Linear superposition principle for partially coherent solitons,” Phys. Rev. E 65, 055601 (2002).
[CrossRef]

Schwartz, T.

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

Segev, M.

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

H. Buljan, M. Segev, M. Soljačić, N. K. Efremidis, and D. N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[CrossRef] [PubMed]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601 (2002).
[CrossRef]

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

T. H. Coskun, D. N. Christodoulides, Y.-R. 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. 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]

T. H. Coskun, D. N. Christodoulides, Z. G. Chen, and M. Segev, “Dark incoherent soliton splitting and ‘phase-memory’ effects: theory and experiment,” Phys. Rev. E 59, R4777–R4780 (1999).
[CrossRef]

Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (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 photorefractive crystals,” Opt. Lett. 23, 418–420 (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]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, 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 and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880–882 (1997).
[CrossRef]

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

Semenov, V. E.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[CrossRef]

Shih, M.

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

Shkunov, V. V.

V. V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[CrossRef]

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]

Šiber, A.

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601 (2002).
[CrossRef]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
[CrossRef]

N. Akhmediev, W. Krolikowski, and A. W. Snyder, “Partially coherent solitons of variable shape,” Phys. Rev. Lett. 81, 4632–4635 (1998).
[CrossRef]

Soljacic, M.

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

H. Buljan, M. Segev, M. Soljačić, N. K. Efremidis, and D. N. Christodoulides, “White-light solitons,” Opt. Lett. 28, 1239–1241 (2003).
[CrossRef] [PubMed]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601 (2002).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Y.-R. 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]

Sukhorukov, A. A.

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83, 4736–4739 (1999).
[CrossRef]

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]

Nature (London)

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

New J. Phys.

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66.1–66.14 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. E

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]

A. Ankiewicz, W. Krolikowski, and N. N. Akhmediev, “Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions,” Phys. Rev. E 59, 6079–6087 (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, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).
[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear medium,” Phys. Rev. E 68, 036607 (2003).
[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent white light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601 (2002).
[CrossRef]

S. A. Ponomarenko, “Linear superposition principle for partially coherent solitons,” Phys. Rev. E 65, 055601 (2002).
[CrossRef]

W. Krolikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically nonlinear media,” Phys. Rev. E 61, 3122–3125 (2000).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Z. G. Chen, and M. Segev, “Dark incoherent soliton splitting and ‘phase-memory’ effects: theory and experiment,” Phys. Rev. E 59, R4777–R4780 (1999).
[CrossRef]

Phys. Rev. Lett.

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

O. Bang, D. Edmundson, and W. Królikowski, “Collapse of incoherent light beams in inertial bulk Kerr media,” Phys. Rev. Lett. 83, 5479–5482 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of incoherent dark solitons,” Phys. Rev. Lett. 80, 5113–5116 (1998).
[CrossRef]

A. W. Snyder and D. J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422–1425 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, 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. V. Shkunov and D. Anderson, “Radiation transfer model of self-trapping spatially incoherent radiation by nonlinear media,” Phys. Rev. Lett. 81, 2683–2686 (1998).
[CrossRef]

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83, 4736–4739 (1999).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Y.-R. 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]

N. Akhmediev, W. Krolikowski, and A. W. Snyder, “Partially coherent solitons of variable shape,” Phys. Rev. Lett. 81, 4632–4635 (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]

Science

Z. G. Cher, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889–892 (1998).
[CrossRef]

Zh. Eksp. Teor. Fiz.

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505–516 (1973).

Other

Such a representation of mutual spectral density as a superposition of coherent modes, that are mutually incoherent, is inherited from the linear theory for propagation of incoherent light (see Ref. 24, p. 214.)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).

M. Segev and D. N. Christodoulides, “Incoherent solitons,” in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, Berlin, 2001), pp. 87–125.

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Figures (6)

Fig. 1
Fig. 1

Complex coherence factors μω(x, 0) of the spatially incoherent soliton with the discrete temporal power spectrum. The function μω is plotted for frequencies ωj, where j=2, 3, 4, 5 [see Eq. (12)]. The characteristic width of μω(x, 0) is evidently smaller at larger frequencies (ω2<ω3<ω4<ω5).

Fig. 2
Fig. 2

Frequencies ωj [see Eq. (12)] versus the characteristic width x0. Two horizontal dashed lines show the frequencies Ωmin and Ωmax. Four thin horizontal lines represent the frequency values corresponding to 400, 500, 600, and 700 nm. Two vertical dotted lines are placed at x0=10 and 70 µm. We can see that the number of ωj values within the interval [Ωmin,Ωmax] increases with the increase of x0. The separation between adjacent frequencies decreases with an increase of x0.

Fig. 3
Fig. 3

Normalized intensity profile I(x)/I0 of the incoherent white-light soliton in a noninstantaneous Kerr medium.

Fig. 4
Fig. 4

Complex coherence factors μω(x, 0) of the incoherent white-light soliton for three representative frequencies Ωmin (solid curve), ωc (dotted–dashed curve), and Ωmax (dotted curve). The functions μω(x, 0) are narrower at larger frequencies.

Fig. 5
Fig. 5

Intensity profiles Iω(x) of the incoherent white-light soliton at three representative frequencies Ωmin (solid curve), ωc (dotted–dashed curve), and Ωmax (dotted curve). The functions Iω(x) are more narrow with higher peaks at larger frequencies.

Fig. 6
Fig. 6

Two excited modes ν2ω(x) and ν1ω(x) at three frequencies Ωmin (solid curve), ωc (dotted–dashed curves), and Ωmax (dotted curves). The modal structure is similar at every frequency ω[Ωmin,Ωmax]. The only difference is that the modes at lower-frequency constituents are more stretched than the modes at higher frequencies.

Equations (39)

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Γ(x1, z1, x2, z2; τ)=E˜*(x2, z2, t2)E˜(x1, z1, t1),
Γ(x1, z1, x2, z2; τ)
=12π0dωΓω(x1, z1, x2, z2)exp(-iωτ).
Bωz-i2kω2x12-2x22Bω
=ikωn0{δn[I(x1, z)]-δn[I(x2, z)]}Bω(x1, x2, z),
μω(x1, x2, z)=Bω(x1, x2, z)[Bω(x1, x1, z)Bω(x2, x2, z)]1/2.
Bω(x1, x2, z)=m=1Nωλmωumω(x1, z)umω*(x2, z).
2umω(x, z)x2+2ikωumωz+2δn(I)kω2n0umω=0.
2umj(x, z)x2+2ikjumjz+n2kj2n02I(x, z)umj=0,
I(x, z)=j=1Nfm=1Njλmj|umj(x, z)|2.
d2νmj(x)dx2-2kjκmjνmj+n2kj2n02I(x)νmj=0,
I(x)=j=1Nfm=1Njλmj|νmj(x)|2.
I(x)=I0 sech2(x/x0).
ωj=cx0j(j+1)n2I01/2,j=1, 2, ,Nf.
κmj=m221kjx02=m22n2I0j(j+1)1/21n0x0,
m=1, 2,, j,
d2νmjd(x/x0)2+[j(j+1)sech2(x/x0)-m2]νmj=0.
νmj(x)Pjmtanhxx0.
m=1Njλmj|νmj(x)|2=Ij sech2(x/x0),
I(x)=j=1Nfm=1Njλmj|νmj(x)|2=j=1NfIj sech2(x/x0).
j=1NfIj=I0.
ν˜mj(x)=λmjIj1/2νmj(x)
For j=2,ν˜22(x)=S2,ν˜12(x)=ST;
forj=3,ν˜33(x)=1516 S3,
ν˜23(x)=52 S2T,
ν˜13(x)=14S(4-5S2).
For j=4,ν˜44(x)=78 S4,ν˜34(x)=34 7S3T,
ν˜24(x)=24S2(6-7S2),ν˜14(x)=14ST(4-7S2).
For j=5,ν˜55(x)=21016S5,ν˜45(x)=12 21S4T,
ν˜35(x)=4216S3(8-9S2),ν˜25(x)=72S2T(2-3S2),
ν˜15(x)=18S(8-28S2+21S4).
I(x)=j=25m=1jλmj|νmj(x)|2
=j=25m=1jIj|ν˜mj(x)|2
=(I2+I3+I4+I5)sech2(x/x0)
=I0 sech2(x/x0),
ωj+1-ωjcx0n2I0.
ωj=j-12Δω,j=1, 2,, Nf,
Δω=(Ωmax-Ωmin)/Nf.
Iω(x)=(2π)-1m=1Nfλmω|umω|2,

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