Abstract

We present a simple and straightforward approach to investigate coupled spatial-soliton pairs of two copropagating mutually incoherent (i.e., both beams are fully spatially and temporally coherent, but are incoherent with respect to one another) light beams in saturable nonlinear media. The approach provides a deeper understanding of coupled spatial-soliton pairs and reveals many interesting features, including the entire existence curve of such solitons.

© 2006 Optical Society of America

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  1. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  2. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  3. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
    [CrossRef] [PubMed]
  4. M. Segev, M. Shih, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef]
  5. Y. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
    [CrossRef]
  6. A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
    [CrossRef]
  7. S. Lan, M. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, Opt. Lett. 24, 1145 (1999).
    [CrossRef]
  8. R. De La Fuente and A. Barthelemy, Opt. Commun. 88, 419 (1992).
    [CrossRef]
  9. Zhigang Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. Kivshar, J. Opt. Soc. Am. B 14, 3066 (1997).
    [CrossRef]
  10. M. S. Sodha, D. P. Tiwari, J. Kamal, and V. K. Tripathi, Radio Sci. 8, 559 (1973).
    [CrossRef]
  11. S. Medhekar and R. K. Sarkar, Opt. Lett. 30, 887 (2005).
    [CrossRef] [PubMed]
  12. M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, in Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974), pp. 25.
  13. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  14. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
    [CrossRef] [PubMed]

2005 (1)

2000 (1)

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

1999 (2)

1997 (1)

1996 (2)

M. Segev, M. Shih, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

1995 (2)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
[CrossRef]

1993 (1)

Y. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

1992 (2)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

R. De La Fuente and A. Barthelemy, Opt. Commun. 88, 419 (1992).
[CrossRef]

1973 (1)

M. S. Sodha, D. P. Tiwari, J. Kamal, and V. K. Tripathi, Radio Sci. 8, 559 (1973).
[CrossRef]

Anastassiou, C.

Barthelemy, A.

R. De La Fuente and A. Barthelemy, Opt. Commun. 88, 419 (1992).
[CrossRef]

Chen, Z.

Chen, Zhigang

Christodoulides, D. N.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

Zhigang Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. Kivshar, J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef]

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Coskun, T. H.

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

De La Fuente, R.

R. De La Fuente and A. Barthelemy, Opt. Commun. 88, 419 (1992).
[CrossRef]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Ghatak, A. K.

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, in Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974), pp. 25.

Giordmaine, J. A.

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Kamal, J.

M. S. Sodha, D. P. Tiwari, J. Kamal, and V. K. Tripathi, Radio Sci. 8, 559 (1973).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
[CrossRef]

Lan, S.

Luther-Davies, B.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Martin, J.

Medhekar, S.

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Mitchell, D. J.

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
[CrossRef]

Mizell, G.

Musslimani, Z. H.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

Sarkar, R. K.

Segev, M.

Shih, M.

Snyder, A. W.

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
[CrossRef]

Sodha, M. S.

M. S. Sodha, D. P. Tiwari, J. Kamal, and V. K. Tripathi, Radio Sci. 8, 559 (1973).
[CrossRef]

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, in Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974), pp. 25.

Soljacic, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

Stegeman, G. I.

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

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Tiwari, D. P.

M. S. Sodha, D. P. Tiwari, J. Kamal, and V. K. Tripathi, Radio Sci. 8, 559 (1973).
[CrossRef]

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Tripathi, V. K.

M. S. Sodha, D. P. Tiwari, J. Kamal, and V. K. Tripathi, Radio Sci. 8, 559 (1973).
[CrossRef]

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, in Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974), pp. 25.

Valley, G.

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Yariv, A.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

Y. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

J. Opt. Soc. Am. B (2)

Mod. Phys. Lett. B (1)

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
[CrossRef]

Opt. Commun. (1)

R. De La Fuente and A. Barthelemy, Opt. Commun. 88, 419 (1992).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (4)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

Radio Sci. (1)

M. S. Sodha, D. P. Tiwari, J. Kamal, and V. K. Tripathi, Radio Sci. 8, 559 (1973).
[CrossRef]

Science (1)

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

Other (1)

M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, in Self-Focusing of Laser Beams in Dielectrics, Plasmas and Semiconductors (Tata McGraw-Hill, 1974), pp. 25.

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Figures (4)

Fig. 1
Fig. 1

Plot of D 2 with D 1 and C 2 with C 1 obtained from Eqs. (3) and (4) and using parameters as given in the text.

Fig. 2
Fig. 2

Lowest line in Fig. 1 represents two very closely spaced (parallel) lines corresponding to the lower values of C 2 and D 2 and not passing through the origin. On modifying r 2 = 1.221 r 1 the two parallel lines merge as shown by the thick line.

Fig. 3
Fig. 3

As one example of mutual self-trapping, variation of b 1 ( = r 1 f 1 ) and b 2 ( = r 2 f 2 ) with the propagation distance using Eqs. (1, 2) are shown by solid lines. The strong beam could be greatly manipulated by slightly changing the weak beam as shown using the dashed curves.

Fig. 4
Fig. 4

Existence curve (thick curve) of the soliton of two copropagating beams obtained for r 2 = 1.221 r 1 . Two curves E 1 and E 2 are obtained instead of one if r 2 is chosen other than what is provided by Eq. (5) ( = 1.121 r 1 ) .

Equations (7)

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2 f 1 z 2 = 1 k 1 2 r 1 4 f 1 3 ϵ s 1 C 1 2 ϵ 10 r 1 2 f 1 3 Ω 2 f 1 ϵ s 1 C 2 2 ϵ 10 r 2 2 f 2 4 Ω 2 ,
Ω = 1 + C 1 2 f 1 2 + C 2 2 f 2 2 ,
2 f 2 z 2 = 1 k 2 2 r 2 4 f 2 3 ϵ s 2 D 2 2 ϵ 20 r 2 2 f 2 3 Λ 2 f 2 ϵ s 2 D 1 2 ϵ 20 r 1 2 f 1 4 Λ 2 ,
Λ = 1 + D 1 2 f 1 2 + D 2 2 f 2 2 ,
C 2 = 2 ( 1 + C 1 2 K 1 r 2 2 ) ± 2 ( K 1 r 2 2 ) 2 + K 1 ( C 1 r 1 2 C 1 + 2 r 2 2 ) ,
D 2 = 2 ( 1 + D 1 2 K 2 r 2 2 ) ± 2 ( K 2 r 2 2 ) 2 + K 2 ( D 1 r 1 2 D 1 + 2 r 2 2 ) ,
r 2 = r 1 ( ϵ s 1 ω 1 2 ϵ s 2 ω 2 2 ) 1 4 .

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