Abstract

Optical spatial solitons made from incoherent white light were experimentally observed in 1997 by Mitchell and Segev [Nature (London) 387, 880 (1997)]. We present what is believed to be the first theory describing these solitons and find the characteristic features of their spatiotemporal coherence properties and their temporal power spectrum.

© 2003 Optical Society of America

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References

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  1. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  2. M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef] [PubMed]
  3. M. Mitchell and M. Segev, Nature 387, 880 (1997).
    [CrossRef]
  4. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  5. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
    [CrossRef]
  6. V. V. Shkunov and D. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
    [CrossRef]
  7. A. W. Synder and D. J. Mitchell, Phys. Rev. Lett. 80, 1422 (1998).
    [CrossRef]
  8. B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
    [CrossRef]
  9. M. Segev and D. N. Christodoulides, in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, Berlin, 2001), pp. 87–125.
    [CrossRef]
  10. M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
    [CrossRef]
  11. H. Buljan, A. Šiber, M. Soljačić, and M. Segev, Phys. Rev. E 66, 035601 (2002).
    [CrossRef]
  12. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
    [CrossRef]
  13. D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
    [CrossRef]
  14. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  15. O. Bang, D. Edmundson, and W. Królikowski, Phys. Rev. Lett. 83, 5479 (1999).
    [CrossRef]

2002 (2)

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, Phys. Rev. E 66, 035601 (2002).
[CrossRef]

2001 (1)

D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

1999 (3)

O. Bang, D. Edmundson, and W. Królikowski, Phys. Rev. Lett. 83, 5479 (1999).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
[CrossRef]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1998 (2)

V. V. Shkunov and D. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

A. W. Synder and D. J. Mitchell, Phys. Rev. Lett. 80, 1422 (1998).
[CrossRef]

1997 (3)

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

1996 (1)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

1994 (1)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Anderson, D.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
[CrossRef]

V. V. Shkunov and D. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

Bang, O.

O. Bang, D. Edmundson, and W. Królikowski, Phys. Rev. Lett. 83, 5479 (1999).
[CrossRef]

Buljan, H.

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, Phys. Rev. E 66, 035601 (2002).
[CrossRef]

Carvalho, M. I.

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
[CrossRef]

Chen, Z.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

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

Coscun, T. H.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

Coskun, T. H.

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Crosignani, B.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Edmundson, D.

O. Bang, D. Edmundson, and W. Królikowski, Phys. Rev. Lett. 83, 5479 (1999).
[CrossRef]

Eugenieva, E. D.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

Fedele, R.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
[CrossRef]

Hall, B.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
[CrossRef]

Królikowski, W.

O. Bang, D. Edmundson, and W. Królikowski, Phys. Rev. Lett. 83, 5479 (1999).
[CrossRef]

Lisak, M.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

Mitchell, D. J.

A. W. Synder and D. J. Mitchell, Phys. Rev. Lett. 80, 1422 (1998).
[CrossRef]

Mitchell, M.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
[CrossRef]

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Segev, M.

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, Phys. Rev. E 66, 035601 (2002).
[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
[CrossRef]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

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

Semenov, V. E.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
[CrossRef]

Shih, M.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Shkunov, V. V.

V. V. Shkunov and D. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

Šiber, A.

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, Phys. Rev. E 66, 035601 (2002).
[CrossRef]

Soljacic, M.

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, Phys. Rev. E 66, 035601 (2002).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Synder, A. W.

A. W. Synder and D. J. Mitchell, Phys. Rev. Lett. 80, 1422 (1998).
[CrossRef]

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Nature (1)

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

Phys. Rev. E (4)

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 5602 (2002).
[CrossRef]

M. I. Carvalho, T. H. Coskun, D. N. Christodoulides, M. Mitchell, and M. Segev, Phys. Rev. E 59, 1193 (1999).
[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, Phys. Rev. E 66, 035601 (2002).
[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coscun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

Phys. Rev. Lett. (7)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

O. Bang, D. Edmundson, and W. Królikowski, Phys. Rev. Lett. 83, 5479 (1999).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

V. V. Shkunov and D. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

A. W. Synder and D. J. Mitchell, Phys. Rev. Lett. 80, 1422 (1998).
[CrossRef]

Science (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Other (2)

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Evolution of the intensity structure of white-light solitons in (a) saturable and (b) Kerr nonlinearity. The propagation distance, z, is expressed in diffraction length units, and spatial coordinate x is in characteristic width units. In the saturable case, the parameters are taken from Ref. 3.

Fig. 2
Fig. 2

Complex coherence factor μωx,0 and the intensity profile Iωx of a white-light soliton at three representative frequencies: ωmin (solid curve), ω0 (dotted–dashed curve), and ωmax (dotted curve).

Equations (2)

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ifωz+θfωx+12kω2fωx2+kωn0δnIfωx,z,θ=0.
2umωx2+2ikωumωz+2δnIkω2n0umωx,z=0.

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