Abstract

We investigate numerically the propagation of self-trapped optical beams in nematic liquid crystals. Our analysis includes both spatial and temporal behavior. We display the formation of stable solitons in a narrow threshold region of beam intensities for fixed birefringence, and depict their spatiotemporal instabilities as the input intensity and the birefringence are increased. We demonstrate the breathing and filamentation of solitons above the threshold with increasing input intensity, and discover a convective instability with increasing birefringence. We consider the propagation of complex beam structures in nematic liquid crystals, such as dipoles, beam arrays, and vortices.

© 2005 Optical Society of America

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  1. E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, �??Filamentation and undulation of self-focused laser beams in liquid crystals,�?? Europhys. Lett. 23, 239 (1993).
  2. M. A. Karpierz, �??Solitary waves in liquid crystalline waveguides,�?? Phys. Rev. E 66, 036603 (2002).
    [CrossRef]
  3. M. Warenghem, J. F. Henninot, and G. Abbate, �??Non linearly induced self waveguiding structure in dye doped nematic liquid crystals confined in capillaries,�?? Opt. Express 2, 483 (1998).
  4. F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, "A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,�?? J. Opt. A: Pure Appl. Opt. 2, 332 (2000).
    [CrossRef]
  5. M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, �??Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,�?? Appl. Phys. Lett. 77, 7 (2000).
    [CrossRef]
  6. M. Peccianti and G. Assanto, �??Incoherent spatial solitary waves in nematic liquid crystals,�?? Opt. Lett. 26, 1791 (2001).
  7. M. Peccianti, C. Conti, G. Assanto, �??Nonlocal optical propagation in nonlinear nematic liquid crystals,�?? J. Nonlin. Opt. Phys. Mater. 12, 525-538 (2003).
    [CrossRef]
  8. G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, �??Nonlinear wave propagation and spatial solitons in nematic liquid crystals,�?? J. Nonlin. Opt. Phys. Mater. 12, 123-134 (2003).
    [CrossRef]
  9. G. Assanto, M. Peccianti, and C. Conti, �??Optical Spatial Solitons in Nematic Liquid Crystals,�?? Opt. Phot. News 14, No. 2, 45 (2003).
  10. Yuri S. Kivshar and Govind P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).
  11. P. G. De Gennes and G. Prost, The Physics of Liquid Crystals, 2nd edn (Oxford, Clarendon, 1993).
  12. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).
  13. G. D�??Alessandro and A. A. Wheeler, "Bistability of liquid crystal micro-cavities,�?? (December 2, 2002).
  14. M. R. Belic, J. Leonardy, D. Timotijevic, and F. Kaiser, �??Spatiotemporal effects in double phase conjugation, �?? J. Opt. Soc. Amer. B 12, 1602 (1995).
  15. D. Traeger, A. Strini�?, J. Schroeder, C. Denz, M. Beli�?, M. Petrovi�?, S. Matern, H.G. Purwins, �??Interactions in large arrays of solitons in photorefractive crystals,�?? J. Opt. A 5, S518-S523 (2003).
  16. W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, �??Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,�?? J. Opt. B 6, S288-S294 (2004).
  17. C. Conti, M. Peccianti, and G. Assanto, �??Route to Nonlocality and Observation of Accessible Solitons,�?? PRL 91, 073901 (2003).
    [CrossRef]
  18. M. Peccianti, C. Conti, and G. Assanto, �??Optical modulational instability in a nonlocal medium,�?? PRE 68, 025602(R) (2003).
  19. On transverse patterns, consult C. Denz, M. Schwab, and C. Weilnau, Transverse Pattern Formation in Photorefractive Optics (Springer, Berlin, 2003).
  20. A. W. Snyder and D. J. Mitchell, �??Accessible Solitons,�?? Science 276, 1538-1541 (1997).
    [CrossRef]
  21. D. Mitchell and A. Snyder, �??Soliton dynamics in a nonlocal medium,�?? JOSA B 16, 236-239 (1999).
  22. M. Petrovi�? , D. Traeger, A. Strini�?, M. Beli�?, J. Schroeder, C. Denz, �??Solitonic lattices in photorefractive crystals,�?? Phys. Rev. E 68, 055601(R) (2003).
    [CrossRef]
  23. Z. Chen and K. McCarthy, �??Spatial soliton pixels from partially incoherent light,�?? Opt. Lett. 27, 2019 (2002).

Appl. Phys. Lett. (1)

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, �??Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,�?? Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Europhys. Lett. (1)

E. Braun, L. Faucheux, A. Libchaber, D. McLaughlin, D. Muraki, and M. Shelley, �??Filamentation and undulation of self-focused laser beams in liquid crystals,�?? Europhys. Lett. 23, 239 (1993).

J. Nonlin. Opt. Phys. Mater. (2)

M. Peccianti, C. Conti, G. Assanto, �??Nonlocal optical propagation in nonlinear nematic liquid crystals,�?? J. Nonlin. Opt. Phys. Mater. 12, 525-538 (2003).
[CrossRef]

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, �??Nonlinear wave propagation and spatial solitons in nematic liquid crystals,�?? J. Nonlin. Opt. Phys. Mater. 12, 123-134 (2003).
[CrossRef]

J. Opt. A (1)

D. Traeger, A. Strini�?, J. Schroeder, C. Denz, M. Beli�?, M. Petrovi�?, S. Matern, H.G. Purwins, �??Interactions in large arrays of solitons in photorefractive crystals,�?? J. Opt. A 5, S518-S523 (2003).

J. Opt. A: Pure Appl. Opt. (1)

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, "A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,�?? J. Opt. A: Pure Appl. Opt. 2, 332 (2000).
[CrossRef]

J. Opt. B (1)

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, �??Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,�?? J. Opt. B 6, S288-S294 (2004).

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

M. R. Belic, J. Leonardy, D. Timotijevic, and F. Kaiser, �??Spatiotemporal effects in double phase conjugation, �?? J. Opt. Soc. Amer. B 12, 1602 (1995).

JOSA B (1)

D. Mitchell and A. Snyder, �??Soliton dynamics in a nonlocal medium,�?? JOSA B 16, 236-239 (1999).

Opt. Express (1)

Opt. Lett. (2)

Opt. Phot. News (1)

G. Assanto, M. Peccianti, and C. Conti, �??Optical Spatial Solitons in Nematic Liquid Crystals,�?? Opt. Phot. News 14, No. 2, 45 (2003).

Phys. Rev. E (2)

M. Petrovi�? , D. Traeger, A. Strini�?, M. Beli�?, J. Schroeder, C. Denz, �??Solitonic lattices in photorefractive crystals,�?? Phys. Rev. E 68, 055601(R) (2003).
[CrossRef]

M. A. Karpierz, �??Solitary waves in liquid crystalline waveguides,�?? Phys. Rev. E 66, 036603 (2002).
[CrossRef]

PRE (1)

M. Peccianti, C. Conti, and G. Assanto, �??Optical modulational instability in a nonlocal medium,�?? PRE 68, 025602(R) (2003).

PRL (1)

C. Conti, M. Peccianti, and G. Assanto, �??Route to Nonlocality and Observation of Accessible Solitons,�?? PRL 91, 073901 (2003).
[CrossRef]

Science (1)

A. W. Snyder and D. J. Mitchell, �??Accessible Solitons,�?? Science 276, 1538-1541 (1997).
[CrossRef]

Other (5)

On transverse patterns, consult C. Denz, M. Schwab, and C. Weilnau, Transverse Pattern Formation in Photorefractive Optics (Springer, Berlin, 2003).

Yuri S. Kivshar and Govind P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).

P. G. De Gennes and G. Prost, The Physics of Liquid Crystals, 2nd edn (Oxford, Clarendon, 1993).

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

G. D�??Alessandro and A. A. Wheeler, "Bistability of liquid crystal micro-cavities,�?? (December 2, 2002).

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