Abstract

The interaction between spatial optical solitons in undoped nematic liquid crystals is governed by reorientational nonlinearity with a significant nonlocality. We demonstrate several cases of interactions, including crossing, interlacing, and merging of spatial solitons in voltage-biased liquid-crystal cells. A scalar model accounts for the main features that were experimentally observed.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. I. Stegeman, D. N. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
    [CrossRef]
  2. S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, Berlin, 2001).
    [CrossRef]
  3. D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
    [CrossRef] [PubMed]
  4. A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
    [CrossRef]
  5. F. Reynaud and A. Barthelemy, Europhys. Lett. 12, 5 (1990).
    [CrossRef]
  6. M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
    [CrossRef]
  7. W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
    [CrossRef]
  8. E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
    [CrossRef]
  9. M. A. Karpierz, M. Sierakowski, M. Swillo, and T. Wolinski, Mol. Cryst. Liq. Cryst. 320, 157 (1998).
    [CrossRef]
  10. M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
    [CrossRef]
  11. J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).
  12. N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel’dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
    [CrossRef]
  13. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).
  14. M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
    [CrossRef]
  15. M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
    [CrossRef]
  16. D. Mitchell and A. Snyder, J. Opt. Soc. Am. B 16, 236 (1999).
    [CrossRef]
  17. W. Królikowski and S. Holmstrom, Opt. Lett. 22, 369 (1997).
    [CrossRef]

2001 (3)

M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
[CrossRef]

J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).

2000 (2)

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

G. I. Stegeman, D. N. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

1999 (1)

1998 (2)

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
[CrossRef]

M. A. Karpierz, M. Sierakowski, M. Swillo, and T. Wolinski, Mol. Cryst. Liq. Cryst. 320, 157 (1998).
[CrossRef]

1997 (3)

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

W. Królikowski and S. Holmstrom, Opt. Lett. 22, 369 (1997).
[CrossRef]

1996 (1)

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

1993 (1)

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

1990 (1)

F. Reynaud and A. Barthelemy, Europhys. Lett. 12, 5 (1990).
[CrossRef]

1986 (1)

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel’dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Abbate, G.

J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).

Assanto, G.

M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
[CrossRef]

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Barthelemy, A.

F. Reynaud and A. Barthelemy, Europhys. Lett. 12, 5 (1990).
[CrossRef]

Braun, E.

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

Christodoulides, D. N.

G. I. Stegeman, D. N. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

de Luca, A.

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Debailleul, M.

J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).

Denz, C.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
[CrossRef]

Derossi, A.

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Derrien, F.

J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).

Faucheux, L.

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

Henninot, J. F.

J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).

Holmstrom, S.

Karpierz, M. A.

M. A. Karpierz, M. Sierakowski, M. Swillo, and T. Wolinski, Mol. Cryst. Liq. Cryst. 320, 157 (1998).
[CrossRef]

Khoo, I. C.

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

Królikowski, W.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
[CrossRef]

W. Królikowski and S. Holmstrom, Opt. Lett. 22, 369 (1997).
[CrossRef]

Libchaber, A.

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

Luther-Davies, B.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
[CrossRef]

McLaughlin, D.

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

Mitchell, D.

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Muraki, D.

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

Peccianti, M.

M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
[CrossRef]

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Poladian, L.

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Reynaud, F.

F. Reynaud and A. Barthelemy, Europhys. Lett. 12, 5 (1990).
[CrossRef]

Saffman, M.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
[CrossRef]

Salamo, G.

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Segev, M.

G. I. Stegeman, D. N. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Shelley, M.

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

Shih, M.

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Sierakowski, M.

M. A. Karpierz, M. Sierakowski, M. Swillo, and T. Wolinski, Mol. Cryst. Liq. Cryst. 320, 157 (1998).
[CrossRef]

Snyder, A.

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Stegeman, G. I.

G. I. Stegeman, D. N. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

Stepken, A.

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
[CrossRef]

Sukhov, A. V.

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel’dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Swillo, M.

M. A. Karpierz, M. Sierakowski, M. Swillo, and T. Wolinski, Mol. Cryst. Liq. Cryst. 320, 157 (1998).
[CrossRef]

Tabiryan, N. V.

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel’dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Umeton, C.

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Warenghem, M.

J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).

Wolinski, T.

M. A. Karpierz, M. Sierakowski, M. Swillo, and T. Wolinski, Mol. Cryst. Liq. Cryst. 320, 157 (1998).
[CrossRef]

Zel’dovich, B. Ya.

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel’dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

M. Peccianti, A. Derossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Europhys. Lett. (2)

F. Reynaud and A. Barthelemy, Europhys. Lett. 12, 5 (1990).
[CrossRef]

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, Europhys. Lett. 23, 239 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

G. I. Stegeman, D. N. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

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

Mol. Cryst. Liq. Cryst. (2)

N. V. Tabiryan, A. V. Sukhov, and B. Ya. Zel’dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

M. A. Karpierz, M. Sierakowski, M. Swillo, and T. Wolinski, Mol. Cryst. Liq. Cryst. 320, 157 (1998).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (2)

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, Phys. Rev. Lett. 77, 271 (1996).
[CrossRef] [PubMed]

Quantum Semiclass. Opt. (1)

W. Królikowski, C. Denz, A. Stepken, M. Saffman, and B. Luther-Davies, Quantum Semiclass. Opt. 10, 823 (1998).
[CrossRef]

Science (1)

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

Synth. Met. (1)

J. F. Henninot, M. Debailleul, F. Derrien, G. Abbate, and M. Warenghem, Synth. Met. 1–5, 8915 (2001).

Other (2)

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

S. Trillo and W. E. Torruellas, eds., Spatial Solitons (Springer-Verlag, Berlin, 2001).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(a) Illustration of the reorientation of the NLC molecular director in the x,z plane as a result of the optical electric field. (b) Planar cell under planar NLC alignment and voltage-induced pretilt at π/4.

Fig. 2
Fig. 2

Simulated behavior of two three-dimensional spatial solitons launched by 10µm-waist beams of 0.1-mW power each, at a separation of 25 µm and a relative angle of 2° in the plane y,z, in two cases of reorientational nonlinearity: (a), (b) local Kerr-like with γ2×10-13 m2/V2 and (c), (d) nonlocal, with ne θ0=π/4=1.63909. Three-dimensional graphs (b) and (d) represent the induced index distribution at z=2zR in (a) and (c), respectively.

Fig. 3
Fig. 3

Interaction of two identical beams. The photos show light propagating in the plane y,z, after two beams (10µm waist) with a 28µm y separation and a 5° relative angle are launched: (a) linear behavior, (b) weak attraction between solitons of 2.8-mW power each, (c) stronger attraction at 3.6 mW, (d) crossing at powers of 4.5 mW.

Fig. 4
Fig. 4

Interlacing of 3-mW solitons launched parallel to one another at 11µm separation in z=0: multicrossing.

Fig. 5
Fig. 5

Interaction of two 3-mW spatial solitons launched in z=y=x=0 with a relative angle of 2.7° in the plane y,z: temporal sequence at (a) Δt=0s, (b) 1 s, and (c) 10 s after excitation. In (c) the solitons, already established in (b), collapse and merge for z>0.6 mm.

Equations (2)

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

2ikzA+2A+k02εa sinθ+θ0sinθ-θ0A=0,
K2θ-θ0+ε0εa sin2θA2/4=0,

Metrics