Abstract

We identify elliptic incoherent spatial solitons in isotropic saturable nonlinear media. These solitary states are possible, provided that their correlation function is anisotropic. The propagation dynamics of this new class of solitons are investigated by use of numerical simulations. We find that, during a collision event of two such elliptic solitons, their intensity ellipse rotates, and at the same time their centers of gravity tend to revolve around each other.

© 2000 Optical Society of America

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  1. M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef] [PubMed]
  2. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  3. D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1998).
    [CrossRef]
  4. T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
    [CrossRef]
  5. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
    [CrossRef]
  6. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 80, 2310 (1998).
    [CrossRef]
  7. N. Akhmediev, W. Krolikowski, and A. W. Snyder, Phys. Rev. Lett. 81, 4632 (1998); W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Phys. Rev. E 59, 4654 (1999).
    [CrossRef]
  8. G. A. Pasmanik, Sov. Phys. JETP 39, 234 (1974); V. A. Aleshkevich, S. S. Lebedev, and A. N. Matveev, Sov. J. Quantum Electron. 11, 647 (1981).
    [CrossRef]
  9. A. Hasegawa, Phys. Fluids 18, 77 (1975).
    [CrossRef]
  10. A. W. Snyder and D. J. Mitchell, Phys. Rev. Lett. 80, 1422 (1998).
    [CrossRef]
  11. V. V. Shkunov and D. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
    [CrossRef]
  12. O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. Lett. 83, 5479 (1999).
    [CrossRef]
  13. M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef] [PubMed]
  14. B. Crosignani and P. Di Porto, Opt. Lett. 18, 1394 (1993); A. W. Snyder and D. J. Mitchell, Opt. Lett. 22, 16 (1997); V. Tichonenko, Opt. Lett. 23, 594 (1998).
    [CrossRef] [PubMed]
  15. H. Kressel, M. Ettenberg, J. P. Wittke, and I. Ladany, in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 2.
  16. W. Krolikowski, D. Edmundson, and O. Bang, Phys. Rev. E 61, 3122 (2000).
    [CrossRef]
  17. M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999); A. Stepken, M. R. Belic, F. Keiser, W. Krolikowski, and B. Luther-Davies, Phys. Rev. Lett. 82, 540 (1999).
    [CrossRef]

2000 (2)

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

W. Krolikowski, D. Edmundson, and O. Bang, Phys. Rev. E 61, 3122 (2000).
[CrossRef]

1999 (1)

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

1998 (6)

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 80, 2310 (1998).
[CrossRef]

N. Akhmediev, W. Krolikowski, and A. W. Snyder, Phys. Rev. Lett. 81, 4632 (1998); W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Phys. Rev. E 59, 4654 (1999).
[CrossRef]

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

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

1997 (3)

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

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

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999); A. Stepken, M. R. Belic, F. Keiser, W. Krolikowski, and B. Luther-Davies, Phys. Rev. Lett. 82, 540 (1999).
[CrossRef]

1996 (1)

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

1993 (1)

B. Crosignani and P. Di Porto, Opt. Lett. 18, 1394 (1993); A. W. Snyder and D. J. Mitchell, Opt. Lett. 22, 16 (1997); V. Tichonenko, Opt. Lett. 23, 594 (1998).
[CrossRef] [PubMed]

1975 (1)

A. Hasegawa, Phys. Fluids 18, 77 (1975).
[CrossRef]

1974 (1)

G. A. Pasmanik, Sov. Phys. JETP 39, 234 (1974); V. A. Aleshkevich, S. S. Lebedev, and A. N. Matveev, Sov. J. Quantum Electron. 11, 647 (1981).
[CrossRef]

Akhmediev, N.

N. Akhmediev, W. Krolikowski, and A. W. Snyder, Phys. Rev. Lett. 81, 4632 (1998); W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Phys. Rev. E 59, 4654 (1999).
[CrossRef]

Anderson, D. Z.

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

Bang, O.

W. Krolikowski, D. Edmundson, and O. Bang, Phys. Rev. E 61, 3122 (2000).
[CrossRef]

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

Chen, Z.

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
[CrossRef]

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

Christodoulides, D. N.

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 80, 2310 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
[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]

Coskun, T. H.

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 80, 2310 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
[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.

B. Crosignani and P. Di Porto, Opt. Lett. 18, 1394 (1993); A. W. Snyder and D. J. Mitchell, Opt. Lett. 22, 16 (1997); V. Tichonenko, Opt. Lett. 23, 594 (1998).
[CrossRef] [PubMed]

Di Porto, P.

B. Crosignani and P. Di Porto, Opt. Lett. 18, 1394 (1993); A. W. Snyder and D. J. Mitchell, Opt. Lett. 22, 16 (1997); V. Tichonenko, Opt. Lett. 23, 594 (1998).
[CrossRef] [PubMed]

Edmundson, D.

W. Krolikowski, D. Edmundson, and O. Bang, Phys. Rev. E 61, 3122 (2000).
[CrossRef]

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

Ettenberg, M.

H. Kressel, M. Ettenberg, J. P. Wittke, and I. Ladany, in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 2.

Hasegawa, A.

A. Hasegawa, Phys. Fluids 18, 77 (1975).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1998).
[CrossRef]

Kressel, H.

H. Kressel, M. Ettenberg, J. P. Wittke, and I. Ladany, in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 2.

Krolikowski, W.

W. Krolikowski, D. Edmundson, and O. Bang, Phys. Rev. E 61, 3122 (2000).
[CrossRef]

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

N. Akhmediev, W. Krolikowski, and A. W. Snyder, Phys. Rev. Lett. 81, 4632 (1998); W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Phys. Rev. E 59, 4654 (1999).
[CrossRef]

Ladany, I.

H. Kressel, M. Ettenberg, J. P. Wittke, and I. Ladany, in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 2.

Mitchell, D. J.

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

Mitchell, M.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 80, 2310 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
[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]

Pasmanik, G. A.

G. A. Pasmanik, Sov. Phys. JETP 39, 234 (1974); V. A. Aleshkevich, S. S. Lebedev, and A. N. Matveev, Sov. J. Quantum Electron. 11, 647 (1981).
[CrossRef]

Salamo, G.

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999); A. Stepken, M. R. Belic, F. Keiser, W. Krolikowski, and B. Luther-Davies, Phys. Rev. Lett. 82, 540 (1999).
[CrossRef]

Segev, M.

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 80, 2310 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
[CrossRef]

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

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999); A. Stepken, M. R. Belic, F. Keiser, W. Krolikowski, and B. Luther-Davies, Phys. Rev. Lett. 82, 540 (1999).
[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]

Shih, M.

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999); A. Stepken, M. R. Belic, F. Keiser, W. Krolikowski, and B. Luther-Davies, Phys. Rev. Lett. 82, 540 (1999).
[CrossRef]

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. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

Snyder, A. W.

N. Akhmediev, W. Krolikowski, and A. W. Snyder, Phys. Rev. Lett. 81, 4632 (1998); W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Phys. Rev. E 59, 4654 (1999).
[CrossRef]

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

Soljacic, M.

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Vishwanath, A.

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Wittke, J. P.

H. Kressel, M. Ettenberg, J. P. Wittke, and I. Ladany, in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 2.

Opt. Lett. (3)

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, M. Mitchell, Z. Chen, and M. Segev, Opt. Lett. 23, 418 (1998).
[CrossRef]

B. Crosignani and P. Di Porto, Opt. Lett. 18, 1394 (1993); A. W. Snyder and D. J. Mitchell, Opt. Lett. 22, 16 (1997); V. Tichonenko, Opt. Lett. 23, 594 (1998).
[CrossRef] [PubMed]

Phys. Fluids (1)

A. Hasegawa, Phys. Fluids 18, 77 (1975).
[CrossRef]

Phys. Rev. E (1)

W. Krolikowski, D. Edmundson, and O. Bang, Phys. Rev. E 61, 3122 (2000).
[CrossRef]

Phys. Rev. Lett. (10)

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999); A. Stepken, M. R. Belic, F. Keiser, W. Krolikowski, and B. Luther-Davies, Phys. Rev. Lett. 82, 540 (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]

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

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

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

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

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

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 80, 2310 (1998).
[CrossRef]

N. Akhmediev, W. Krolikowski, and A. W. Snyder, Phys. Rev. Lett. 81, 4632 (1998); W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Phys. Rev. E 59, 4654 (1999).
[CrossRef]

Sov. Phys. JETP (1)

G. A. Pasmanik, Sov. Phys. JETP 39, 234 (1974); V. A. Aleshkevich, S. S. Lebedev, and A. N. Matveev, Sov. J. Quantum Electron. 11, 647 (1981).
[CrossRef]

Other (1)

H. Kressel, M. Ettenberg, J. P. Wittke, and I. Ladany, in Semiconductor Devices for Optical Communication, H. Kressel, ed. (Springer-Verlag, New York, 1980), Chap. 2.

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Figures (3)

Fig. 1
Fig. 1

Intensity evolution of an elliptic Gaussian soliton beam when r=3, θ0x=0.283°, θ0y=0.2°, and Δn=1.42×10-4: a, along the x axis; b, along the y axis. Gray-scale images: c, input and d, output elliptic soliton and e, its diffraction after 2 cm.

Fig. 2
Fig. 2

Gray-scale images of (a–d) the total intensity distribution and (e–h) the intensity distribution of a single elliptic soliton beam at (a, e) z=0 cm, (b, f) z=1.6 cm, (c, g) z=2.12 cm, and (d, h) z=4.7 cm.

Fig. 3
Fig. 3

Trajectories of the centers of gravity in the transverse plane of two elliptic soliton beams initially centered on the y axis and tilted at 45° with respect to x axis. Points A, B, C, and D occur at z values of 0, 1.6, 2.12, and 4.7 cm, respectively.

Equations (4)

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

ifz+θxfx+θyfy+12k2f-kΔnn01+INf=0,
IN=--fx,y,z,θx,θy2dθxdθy,
fx,y,0,θx,θy=r1/2GN1/2θx,θyΦ0x,y.
GNθx,θy=πθ0xθ0y-1 exp-θx2θ0x2-θy2θ0y2,

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