Abstract

We experimentally ascertain the role of non locality in the spectral evolution of multifilament patterns generated by modulational instability in nematic liquid crystals.

© 2005 Optical Society of America

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References

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  1. J. J. Sakurai, �??Modern Quantum Mechanics�?? (Addison-Wesley, Reading, MA, 1994).
  2. R. A. Stern and J. F. Decker, �??Nonlocal Instability of Finite-Amplitude Ion Waves,�?? Phys. Rev. Lett. 27, 1266-1271 (1971)
    [CrossRef]
  3. B. Hessmo, P. Usachev, H. Heydari and G. Björk, "Experimental demonstration of single photon nonlocality," Phys. Rev. Lett. 92, 180401 (2004).
    [CrossRef] [PubMed]
  4. J. P. Gordon, R. C. Leite, R. S. Moore and J. R. Whinnery, �??Long-Transient Effects in Lasers with Inserted Liquid Samples,�?? J. Appl. Phys. 36, 3-8 (1965).
    [CrossRef]
  5. D. Suter and T. Blasberg, �??Stabilization of transverse solitary waves by a nonlocal response of nonlinear medium,�?? Phys. Rev. A 48, 4583-4587 (1993).
    [CrossRef] [PubMed]
  6. A. A. Zozulya and D. Z. Anderson, �??Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric-field,�?? Phys. Rev. A 51, 1520- 1531 (1995).
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  7. S. Gatz and J. Herrmann, �??Anisotropy, nonlocality and space-charge field displacement in (2+1)- dimensional self-trapping in biased photorefractive crystals,�?? Opt. Lett. 23, 1176-1178 (1998).
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  8. N. V. Tabiryan, A. V. Sukhov and B. Y Zel�??dovich, �??Orientational nonlinearity of liquid-crystals,�?? Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
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  9. I. C. Khoo, "Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena, "(Wiley, New York, 1995).
  10. A. W. Snyder and D. J. Mitchell, �??Accessible Solitons,�?? Science 276, 1538-1541 (1997).
    [CrossRef]
  11. W. Królikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen and D. Edmundson, �??Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,�?? J. Opt. B 6, S288-S294 (2004).
    [CrossRef]
  12. J. Wyller, W. Krolikowski, O. Bang and J. J. Rasmussen, �??Generic features of modulational instability in nonlocal Kerr media,�?? Phys. Rev. E 66, 066615 (2002).
    [CrossRef]
  13. M. Peccianti, C. Conti, G. Assanto, A. De Luca and C. Umeton, �??Routing of Highly Anisotropic Spatial Solitons and Modulational Instability in liquid crystals,�?? Nature 432, 733-737 (2004).
    [CrossRef] [PubMed]
  14. C. Conti, M. Peccianti and G. Assanto, �??Observation of optical solitons in a highly nonlocal medium,�?? Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  15. M. Peccianti and G. Assanto, �??Nematic liquid crystals: a suitable medium for self-confinement of coherent and incoherent light,�?? Phys. Rev. E 65, 035603 (2002).
    [CrossRef]
  16. M. Peccianti, C. Conti and G. Assanto, �??Interplay between nonlocality and nonlinearity in nematic liquid crystals,�?? Opt. Lett. 30, 415-417 (2005).
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  17. M. Peccianti, C. Conti, E. Alberici and G. Assanto, "Spatially incoherent modulational instability in a non local medium," Laser Phys. Lett. 2, 25-29 (2005).
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  18. M. Peccianti, C. Conti and G. Assanto, �??Optical modulational instability in a nonlocal medium,�?? Phys. Rev. E 68, 025602 (2003).
    [CrossRef]
  19. V. I. Bespalov and V. I. Talanov, �??Filamentary structure of light beams in nonlinear liquids,�?? JETP Lett. 3, 307-310 (1966).
  20. G. I. Stegeman, �??Spatial Beam Instabilities Due to Instantaneous Nonlinear Mechanisms,�?? Proc. NATO ASI/SUSSP56 on �??Ultrafast Photonics,�?? Ed. A. Miller (Inst. Physics Publishing, London, 2003).

J. Appl. Phys.

J. P. Gordon, R. C. Leite, R. S. Moore and J. R. Whinnery, �??Long-Transient Effects in Lasers with Inserted Liquid Samples,�?? J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

J. Opt. B

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

JETP Lett.

V. I. Bespalov and V. I. Talanov, �??Filamentary structure of light beams in nonlinear liquids,�?? JETP Lett. 3, 307-310 (1966).

Laser Phys. Lett.

M. Peccianti, C. Conti, E. Alberici and G. Assanto, "Spatially incoherent modulational instability in a non local medium," Laser Phys. Lett. 2, 25-29 (2005).
[CrossRef]

Mol. Cryst. Liq. Cryst.

N. V. Tabiryan, A. V. Sukhov and B. Y Zel�??dovich, �??Orientational nonlinearity of liquid-crystals,�?? Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Nature

M. Peccianti, C. Conti, G. Assanto, A. De Luca and C. Umeton, �??Routing of Highly Anisotropic Spatial Solitons and Modulational Instability in liquid crystals,�?? Nature 432, 733-737 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

D. Suter and T. Blasberg, �??Stabilization of transverse solitary waves by a nonlocal response of nonlinear medium,�?? Phys. Rev. A 48, 4583-4587 (1993).
[CrossRef] [PubMed]

A. A. Zozulya and D. Z. Anderson, �??Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric-field,�?? Phys. Rev. A 51, 1520- 1531 (1995).
[CrossRef] [PubMed]

Phys. Rev. E

J. Wyller, W. Krolikowski, O. Bang and J. J. Rasmussen, �??Generic features of modulational instability in nonlocal Kerr media,�?? Phys. Rev. E 66, 066615 (2002).
[CrossRef]

M. Peccianti, C. Conti and G. Assanto, �??Optical modulational instability in a nonlocal medium,�?? Phys. Rev. E 68, 025602 (2003).
[CrossRef]

M. Peccianti and G. Assanto, �??Nematic liquid crystals: a suitable medium for self-confinement of coherent and incoherent light,�?? Phys. Rev. E 65, 035603 (2002).
[CrossRef]

Phys. Rev. Lett.

C. Conti, M. Peccianti and G. Assanto, �??Observation of optical solitons in a highly nonlocal medium,�?? Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

R. A. Stern and J. F. Decker, �??Nonlocal Instability of Finite-Amplitude Ion Waves,�?? Phys. Rev. Lett. 27, 1266-1271 (1971)
[CrossRef]

B. Hessmo, P. Usachev, H. Heydari and G. Björk, "Experimental demonstration of single photon nonlocality," Phys. Rev. Lett. 92, 180401 (2004).
[CrossRef] [PubMed]

Proc. NATO ASI/SUSSP56

G. I. Stegeman, �??Spatial Beam Instabilities Due to Instantaneous Nonlinear Mechanisms,�?? Proc. NATO ASI/SUSSP56 on �??Ultrafast Photonics,�?? Ed. A. Miller (Inst. Physics Publishing, London, 2003).

Science

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

Other

J. J. Sakurai, �??Modern Quantum Mechanics�?? (Addison-Wesley, Reading, MA, 1994).

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

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Figures (5)

Fig. 1.
Fig. 1.

Experimental geometry: a highly elliptical Gaussian beam (U>>V) is injected into a planar nematic liquid crystal cell with wavevector k normal to the input interface.

Fig. 2.
Fig. 2.

Transverse cutoff wavenumber versus angle θ0 between director n̂ and wavevector k̂.

Fig. 3.
Fig. 3.

Beam propagation in NLC at (a) 30, (b) 60 and (c) 90mW input powers, respectively. The pattern produced via modulational instability (a) eventually results into several solitons as the power increases (b). At higher excitations, adjacent solitons group owing to non locality and “global” self-focusing (c). In the photographs, birefringent walk-off is artificially compensated by rotating the camera axis by about 7°.

Fig. 4.
Fig. 4.

Transverse spectral gain, i. e. the transverse intensity spectrum versus z normalized to the input spectrum in z=0, for three different excitations: (a) P=30, (b) 60 and (c) 90mW, respectively.

Fig. 5.
Fig. 5.

Transverse intensity spectra in z=3.5mm for three input powers as in Fig. 4.

Equations (3)

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K 2 Ψ A ( θ 0 ) Ψ + ε 0 Δ ε 4 sin [ 2 ( θ 0 δ ) ] E e 2 = 0
A ( θ 0 ) = K π 2 L 2 cos ( θ 0 ) ( sin ( 2 θ 0 ) 2 θ 0 cos ( 2 θ 0 ) )
Ψ ˜ = ε 0 Δ ε 4 sin [ 2 ( θ 0 δ ) ] K k y 2 + A ( θ 0 ) { E e 2 }

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