Abstract

We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.

© 2009 Optical Society of America

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  1. M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, Vol. 42, E.Wolf, ed. (North-Holland, 2001), p. 219.
    [CrossRef]
  2. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, North-Holland, 2005), p. 291.
    [CrossRef]
  3. A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
    [CrossRef]
  4. D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
    [CrossRef] [PubMed]
  5. A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, Phys. Rev. A 76, 063803 (2007).
    [CrossRef]
  6. Yu. S. Kivshar and G. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003), and references therein.
  7. Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601(R) (2006).
    [CrossRef]
  8. Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
    [CrossRef] [PubMed]
  9. A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
    [CrossRef] [PubMed]
  10. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacič, Phys. Rev. Lett. 84, 1164 (2000).
    [CrossRef] [PubMed]
  11. J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, Opt. Lett. 25, 643 (2000).
    [CrossRef]
  12. J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
    [CrossRef] [PubMed]
  13. Y. Lin and R.-K. Lee, Opt. Express 15, 8781 (2007).
    [CrossRef] [PubMed]
  14. C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
    [CrossRef] [PubMed]
  15. K. Motzek, Yu. S. Kivshar, M.-F. Shih, and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 22, 1437 (2005).
    [CrossRef]
  16. G. Assanto, N. F. Smyth, and A. L. Worthy, Phys. Rev. A 78, 013832 (2008).
    [CrossRef]
  17. A. A. Minzoni, N. F. Smyth, and A. L. Worthy, J. Opt. Soc. Am. B 24, 1549 (2007).
    [CrossRef]
  18. A. A. Minzoni, N. F. Smyth, Z. Xu, and Yu. S. Kivshar, submitted to Phys. Rev. A .

2008 (1)

G. Assanto, N. F. Smyth, and A. L. Worthy, Phys. Rev. A 78, 013832 (2008).
[CrossRef]

2007 (3)

2006 (3)

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601(R) (2006).
[CrossRef]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

2005 (3)

2000 (4)

J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, Opt. Lett. 25, 643 (2000).
[CrossRef]

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

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

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Agrawal, G.

Yu. S. Kivshar and G. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003), and references therein.

Alberucci, A.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Anastassiou, C.

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Anderson, D.

Assanto, G.

G. Assanto, N. F. Smyth, and A. L. Worthy, Phys. Rev. A 78, 013832 (2008).
[CrossRef]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Bang, O.

Briedis, D.

Carlsson, A. H.

Christodoulides, D. N.

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

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Desyatnikov, A. S.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, North-Holland, 2005), p. 291.
[CrossRef]

Dyadyusha, A.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Edmundson, D.

Eugenieva, E.

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

García-Ripoll, J. J.

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

Kaczmarek, M.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Kartashov, Y. V.

Kip, D.

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Kivshar, Yu. S.

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, Phys. Rev. A 76, 063803 (2007).
[CrossRef]

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

K. Motzek, Yu. S. Kivshar, M.-F. Shih, and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 22, 1437 (2005).
[CrossRef]

J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, Opt. Lett. 25, 643 (2000).
[CrossRef]

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

A. A. Minzoni, N. F. Smyth, Z. Xu, and Yu. S. Kivshar, submitted to Phys. Rev. A .

Yu. S. Kivshar and G. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003), and references therein.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, North-Holland, 2005), p. 291.
[CrossRef]

Krolikowski, W.

Lee, R.-K.

Lin, Y.

Lisak, M.

Malmberg, J. N.

Mihalache, D.

Minzoni, A. A.

A. A. Minzoni, N. F. Smyth, and A. L. Worthy, J. Opt. Soc. Am. B 24, 1549 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, Phys. Rev. A 76, 063803 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, Z. Xu, and Yu. S. Kivshar, submitted to Phys. Rev. A .

Motzek, K.

Musslimani, Z. H.

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

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, Opt. Lett. 25, 643 (2000).
[CrossRef]

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

Peccianti, M.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

Pérez-García, V. M.

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

Petersen, D. E.

Segev, M.

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

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Shih, M.-F.

Smyth, N. F.

G. Assanto, N. F. Smyth, and A. L. Worthy, Phys. Rev. A 78, 013832 (2008).
[CrossRef]

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, Phys. Rev. A 76, 063803 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, and A. L. Worthy, J. Opt. Soc. Am. B 24, 1549 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, Z. Xu, and Yu. S. Kivshar, submitted to Phys. Rev. A .

Soljacic, M.

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

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

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, Vol. 42, E.Wolf, ed. (North-Holland, 2001), p. 219.
[CrossRef]

Swartzlander, G. A.

Torner, L.

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601(R) (2006).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, North-Holland, 2005), p. 291.
[CrossRef]

Torres, J. P.

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, Vol. 42, E.Wolf, ed. (North-Holland, 2001), p. 219.
[CrossRef]

Vysloukh, V. A.

Worthy, A. L.

G. Assanto, N. F. Smyth, and A. L. Worthy, Phys. Rev. A 78, 013832 (2008).
[CrossRef]

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, Phys. Rev. A 76, 063803 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, and A. L. Worthy, J. Opt. Soc. Am. B 24, 1549 (2007).
[CrossRef]

Xu, Z.

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601(R) (2006).
[CrossRef]

A. A. Minzoni, N. F. Smyth, Z. Xu, and Yu. S. Kivshar, submitted to Phys. Rev. A .

Yakimenko, A. I.

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Zaliznyak, Yu. A.

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (3)

G. Assanto, N. F. Smyth, and A. L. Worthy, Phys. Rev. A 78, 013832 (2008).
[CrossRef]

A. A. Minzoni, N. F. Smyth, Z. Xu, and Yu. S. Kivshar, submitted to Phys. Rev. A .

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, Phys. Rev. A 76, 063803 (2007).
[CrossRef]

Phys. Rev. E (2)

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601(R) (2006).
[CrossRef]

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Phys. Rev. Lett. (4)

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Phys. Rev. Lett. 97, 153903 (2006).
[CrossRef] [PubMed]

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

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

C. Anastassiou, M. Soljačić, M. Segev, E. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Other (3)

Yu. S. Kivshar and G. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003), and references therein.

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, Vol. 42, E.Wolf, ed. (North-Holland, 2001), p. 219.
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, North-Holland, 2005), p. 291.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Field distribution for (a) a bright soliton and (b) a vortex beam. (c) Nonlinear correction to the refractive index. (d) Phase structure of the corresponding vortex beam shown in (b). Here ν = 1 , b 1 = 3 , and b 2 = 1.8 .

Fig. 2
Fig. 2

(a) Power of bright (dashed) and vortex (solid) beams for ν = 1 . (b) Existence domain (gray) of vector solitons as a function of ν (at b 1 = 3 ).

Fig. 3
Fig. 3

Dependence of the critical value of the amplitude for a bright soliton on the nonlocality degree ν.

Fig. 4
Fig. 4

(a), (b) Input and output of the intensity for an unstable vortex beam propagating alone in the medium. (c), (d) Stable propagation of the vortex beam coupled to the bright component. Here ν = 4 and a u T = 0.9 .

Equations (6)

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

i u z + 1 2 ( 2 u x 2 + 2 u y 2 ) + 2 u θ = 0 ,
i v z + 1 2 ( 2 v x 2 + 2 v y 2 ) + 2 v θ = 0 ,
ν ( 2 θ x 2 + 2 θ y 2 ) 2 θ = 2 ( u 2 + v 2 ) ,
u = a u sech ( r w u ) e i σ u z ,
v = a v r e r w v e i ϕ + i σ v z + i g e i ϕ + i σ v z ,
θ = α u sech 2 ( r β u ) .

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