Abstract

We study theoretically the collisions between 2+1D rotating-dipole-type bimodal solitons and find that such interactions exhibit many interesting exchanges of angular momentum.

© 2001 Optical Society of America

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  1. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  2. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [CrossRef] [PubMed]
  3. M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
    [CrossRef] [PubMed]
  4. M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Lett. 18, 1406 (1993).
    [CrossRef] [PubMed]
  5. A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
    [CrossRef] [PubMed]
  6. M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
    [CrossRef]
  7. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
    [CrossRef] [PubMed]
  8. Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 86, 799 (2001).
    [CrossRef] [PubMed]
  9. Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 61 (2000).
    [CrossRef]
  10. Z. H. Musslimani, M. Soljačić, M. Segev, and D. N. Christodoulides, Phys. Rev. E 63, 66608 (2001).
    [CrossRef]
  11. 2+1D multimode dark solitons were suggested by A. P. Sheppard and M. Haelterman, Opt. Lett. 19, 859 (1994).
    [CrossRef] [PubMed]
  12. J. J. Garcia-Ripoll, V. M. Perez-Garcia, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
    [CrossRef] [PubMed]
  13. T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 1113 (2000).
    [CrossRef]
  14. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
    [CrossRef] [PubMed]
  15. A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. Garcia-Ripoll, and V. M. Perez-Garcia, Opt. Lett. 26, 435 (2001).
    [CrossRef]
  16. A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” submitted to Phys. Rev. Lett.
  17. T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
    [CrossRef]
  18. The transformation to physical units for x,y means dividing by 2π/λ2Δn0/n01/2 and for z by 2π/λΔn0/n0. One diffraction length for the propeller is ≈1.2 z (normalized).
  19. A. W. Snyder, D. J. Mitchell, L. Polodian, and F. Ladouceur, Opt. Lett. 16, 21 (1991).
    [CrossRef] [PubMed]

2001

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 86, 799 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljačić, M. Segev, and D. N. Christodoulides, Phys. Rev. E 63, 66608 (2001).
[CrossRef]

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. Garcia-Ripoll, and V. M. Perez-Garcia, Opt. Lett. 26, 435 (2001).
[CrossRef]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

2000

J. J. Garcia-Ripoll, V. M. Perez-Garcia, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 1113 (2000).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 61 (2000).
[CrossRef]

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

1999

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

1998

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

1994

1993

1991

1988

Anastassiou, C.

Carmon, T.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 1113 (2000).
[CrossRef]

Christodoulides, D. N.

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 86, 799 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljačić, M. Segev, and D. N. Christodoulides, Phys. Rev. E 63, 66608 (2001).
[CrossRef]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 61 (2000).
[CrossRef]

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

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 1113 (2000).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
[CrossRef] [PubMed]

Denz, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Desyatnikov, A. S.

Garcia-Ripoll, J. J.

Geisser, M.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Haelterman, M.

Hewlett, S. J.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Joseph, R. I.

Kip, D.

Kivshar, Y. S.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. Garcia-Ripoll, and V. M. Perez-Garcia, Opt. Lett. 26, 435 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

J. J. Garcia-Ripoll, V. M. Perez-Garcia, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” submitted to Phys. Rev. Lett.

Krolikowski, W.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. Garcia-Ripoll, and V. M. Perez-Garcia, Opt. Lett. 26, 435 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Ladouceur, F.

Lan, S.

Luther-Davies, B.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. Garcia-Ripoll, and V. M. Perez-Garcia, Opt. Lett. 26, 435 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

McCarthy, G.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Mitchell, D. J.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

A. W. Snyder, D. J. Mitchell, L. Polodian, and F. Ladouceur, Opt. Lett. 16, 21 (1991).
[CrossRef] [PubMed]

Mitchell, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Musslimani, Z. H.

Z. H. Musslimani, M. Soljačić, M. Segev, and D. N. Christodoulides, Phys. Rev. E 63, 66608 (2001).
[CrossRef]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 86, 799 (2001).
[CrossRef] [PubMed]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 1113 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 61 (2000).
[CrossRef]

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

Nepomnyashchy, A.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

Neshev, D.

Ostrovskaya, E. A.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. Garcia-Ripoll, and V. M. Perez-Garcia, Opt. Lett. 26, 435 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

J. J. Garcia-Ripoll, V. M. Perez-Garcia, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

Perez-Garcia, V. M.

Pigier, C.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

Polodian, L.

Segev, M.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

Z. H. Musslimani, M. Soljačić, M. Segev, and D. N. Christodoulides, Phys. Rev. E 63, 66608 (2001).
[CrossRef]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 86, 799 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 61 (2000).
[CrossRef]

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

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Opt. Lett. 25, 1113 (2000).
[CrossRef]

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

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Sheppard, A. P.

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

Snyder, A. W.

Soljacic, M.

Z. H. Musslimani, M. Soljačić, M. Segev, and D. N. Christodoulides, Phys. Rev. E 63, 66608 (2001).
[CrossRef]

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]

Tratnik, M. V.

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

Uzdin, R.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

Weilnau, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

Phys. Rev. E

Z. H. Musslimani, M. Soljačić, M. Segev, and D. N. Christodoulides, Phys. Rev. E 63, 66608 (2001).
[CrossRef]

Phys. Rev. Lett.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

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

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 86, 799 (2001).
[CrossRef] [PubMed]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

J. J. Garcia-Ripoll, V. M. Perez-Garcia, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

Science

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

Other

The transformation to physical units for x,y means dividing by 2π/λ2Δn0/n01/2 and for z by 2π/λΔn0/n0. One diffraction length for the propeller is ≈1.2 z (normalized).

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” submitted to Phys. Rev. Lett.

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Figures (2)

Fig. 1
Fig. 1

(a) Collision of two corotating, symmetrically arranged propeller solitons at θ=0. The propagation length of 100 z units is 120 diffraction lengths. (b) Evolution of the angular momentum of ψ1 (solid curve), of ψ2 (dotted curve), and total Lz (dashed curve) in the rightmost outgoing beam. Each component has oscillating angular momentum, but their sum is constant. The leftmost outgoing beam has identical behavior. (c) Input–output configurations of the dipole mode. The initial conditions (in normalized units) are as follows: For ψ1, FWHM, 2.9; peak intensity, 4. For ψ2 peak-to-peak separation, 3.6; peak intensity, 0.49; distance between the input propellers, 8. The rotation rate of the envelope is 9°/z. For λ=0.488 μm and Δn0/n0=10-4, the FWHM of ψ1 is 9.7 μm, the peak-to-peak separation of ψ2 is 11.7 μm, and the distance between the input propellers is 26.2 μm.

Fig. 2
Fig. 2

(a) Collision of two counterrotating, symmetrically arranged propeller solitons at θ<θc. The collision angle in dimensional units is θ×2Δn0/n01/2; e.g., for Δn0/n0=10-4 the collision angle is 0.57°. (b) Illustration of the input–output configurations of the dipole mode. The negative poles collide, and each breaks into two nonequal portions. The central parts fuse and together form a nonrotating - pole. The outer parts are captured by the original positive poles, and each forms a nonsymmetric rotating dipole. (c) Collision of two corotating, antisymmetrically arranged propeller solitons for the same θ as in (a). The distance between the input propellers is 20 [normalized units] =65.5 μm (for the parameters of Fig.  1) in both cases. Other initial conditions are as in Fig.  1.

Equations (1)

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iψjz+122ψj-ψj1+I=0,

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