Abstract

We experimentally observed a counterpropagating dipole-mode vector soliton in a photorefractive SBN:60Ce crystal. We investigated the transient formation dynamics and show that the formation process differs significantly from the copropagating geometry. The experimental results are compared with fully anisotropic numerical simulations and show good qualitative agreement.

© 2005 Optical Society of America

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References

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  1. M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
    [Crossref]
  2. O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
    [Crossref]
  3. O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
    [Crossref]
  4. C. Rotschild, O. Cohen, O. Manela, T. Carmon, and M. Segev, J. Opt. Soc. Am. B 21, 1354 (2004).
    [Crossref]
  5. M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
    [Crossref]
  6. K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
    [Crossref]
  7. W. Królikowski, 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]
  8. T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, and M. Segev, Opt. Lett. 25, 1113 (2000).
    [Crossref]
  9. J. J. Garcia-Ripoll, V. M. Perez-Garcia, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
    [Crossref] [PubMed]
  10. C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
    [Crossref]
  11. W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
    [Crossref]
  12. A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
    [Crossref] [PubMed]

2004 (1)

2003 (2)

M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
[Crossref]

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

2002 (2)

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[Crossref]

O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
[Crossref]

2000 (3)

W. Królikowski, 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]

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

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

1999 (2)

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

1995 (1)

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

1993 (1)

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[Crossref]

Anastassiou, C.

Anderson, D. Z.

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Belic, M.

M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
[Crossref]

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

Belic, M. R.

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

Carmon, T.

Cohen, O.

Denz, C.

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
[Crossref]

W. Królikowski, 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]

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

Desyatnikov, A.

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
[Crossref]

Fleischer, J. W.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[Crossref]

Garcia-Ripoll, J. J.

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

Geisser, M.

W. Królikowski, 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]

Giordmaine, J. A.

Haelterman, M.

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[Crossref]

Jander, P.

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
[Crossref]

Kaiser, F.

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

Kip, D.

Kivshar, Y. S.

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

W. Królikowski, 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]

Królikowski, W.

W. Królikowski, 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]

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

Lan, S.

Luther-Davies, B.

W. Królikowski, 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]

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

Manela, O.

McCarthy, G.

W. Królikowski, 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]

Motzek, K.

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

Musslimani, Z. H.

Odoulov, S.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[Crossref]

Ostrovskaya, E. A.

W. Królikowski, 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]

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.

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

Petter, J.

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

Rotschild, C.

Segev, M.

Sheppard, A. P.

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[Crossref]

Snyder, A. W.

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[Crossref]

Stepken, A.

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

Strinic, A.

M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
[Crossref]

Tschudi, T.

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[Crossref]

Weilnau, C.

W. Królikowski, 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]

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

Zozulya, A. A.

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Appl. Phys. B (1)

W. Królikowski, B. Luther-Davies, C. Denz, J. Petter, C. Weilnau, A. Stepken, and M. R. Beli?, Appl. Phys. B 68, 975 (1999).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

A. A. Zozulya and D. Z. Anderson, Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Phys. Rev. E (3)

C. Denz, W. Królikowski, J. Petter, C. Weilnau, T. Tschudi, M. R. Beli?, F. Kaiser, and A. Stepken, Phys. Rev. E 60, 6222 (1999).
[Crossref]

M. Beli?, P. Jander, A. Strini?, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601(R) (2003).
[Crossref]

K. Motzek, P. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[Crossref]

Phys. Rev. Lett. (3)

W. Królikowski, 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]

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

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for a CP dipole-mode vector soliton: PH, pinhole; F’s, lenses; λ 2 , half-wave plate; PBS; polarizing beam splitter; BSs, beam splitters; GP, glass plate; M’s, mirrors; PM, piezo-driven mirror.

Fig. 2
Fig. 2

Images of the dipole exit face of the crystal (the beam from the FM input face to the camera is blocked). In each figure the spot in the middle is the reflection of the FM input, serving as a reference. (a) Linear propagation. Soliton formation at times (b) t = 25 s (c) t = 128 s , and (d) t = 500 s after the nonlinearity has been turned on. (e) Stable state after t 35 min . (f) Individually propagating dipole approximately t = 5 min after the FM beam was blocked.

Fig. 3
Fig. 3

Images of the dipole input face at steady state 35 min after the nonlinearity has been turned on. (a) The output of the FM beam is displaced to the left of the dipole input. (b) Output of the FM when the dipole is immediately blocked; a small fraction of the FM beam has coupled into the dipole waveguide.

Fig. 4
Fig. 4

Numerical simulations of the dipole-mode vector soliton. The images show the exit face of the dipole at (a) t = 100 τ and (b) t = 280 τ after the start of the simulation. The locations of the input beams are indicated by the dashed ellipses.

Equations (3)

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τ 1 + I t Δ ϕ + Δ ϕ + ln ( 1 + I ) ϕ = E ext x ln ( 1 + I ) + κ { Δ ln ( 1 + I ) + [ ln ( 1 + I ) ] 2 }
z F i 2 2 F + i 2 γ ( E ext F x ϕ F ) = 0 ,
z B i 2 2 B + i 2 γ ( E ext B x ϕ B ) = 0 ,

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