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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 13435–13440
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Coherent backscattering and dynamical light localization in liquid crystals driven throughout chaotic regimes

Francesco Carbone, Antonio De Luca, Valentin Barna, Sameh Ferjani, Carlo Vena, Carlo Versace, and Giuseppe Strangi  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 13435-13440 (2009)
http://dx.doi.org/10.1364/OE.17.013435


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Abstract

An important effect of dynamical localization of light waves in liquid crystal electro-hydrodynamic instabilities is reported by investigating coherent backscattering effects. Recurrent multiple scattering in dynamic and chaotic complex fluids lead to a cone of enhanced backscattered light. The cone width and the related mean free path dependence on the dynamic scattering regimes emphasize the diverse light localization scales related to the internal structures present in the sample. The systems investigated up to now were mainly nano-powdered solutions or biological tissues, without any external control on the disorder. Here, an anisotropic complex fluid is “driven” throughout chaotic regimes by an external electric field, giving rise to dynamics that evolve through several spatio-temporal patterns.

© 2009 Optical Society of America

1. Introduction

Coherent backscattering (CBS), as precursor of the Anderson strong localization [1

1. P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109, 1492–1505 (1958). [CrossRef]

], has amplified the interest for photon weak localization phenomena in random media [2

2. F. C. Mackintosh and S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1998). [CrossRef]

]. CBS is a photon self-interference effect leading to an enhancement in the intensity cone profile, of width Δθ~λ/ (where is the scattering mean free path inside the medium and λ is the incident wavelenght) for the backscattering direction. The analysis of the CBS cone gives information on the properties of random media [3

3. D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental Evidence for Recurrent Multiple Scattering Events of Light in Disordered Media,” Phys. Rev. Lett. 74, 1739–1742 (1995). [CrossRef]

]. Among other materials, nematic liquid crystals (NLCs), with their anisotropic properties, represent an excellent candidate to investigate weak localization of light [4

4. H. K. M. Vithana, L. Asfaw, and D. L. Johnson, “Coherent backscattering of light in a nematic liquid crystal,” Phys. Rev. Lett. 23, 3561–3564 (1993). [CrossRef]

, 5

5. L. V. Kuzmin, V. P. Romanov, and L. A. Zubkov, “Coherent backscattering from anisotropic scatterers,” Phys. Rev. E 54, 6798–6801 (1996). [CrossRef]

]. NLCs are uniaxial fluids formed by rod-like molecules aligned on an average direction (described by a unit vector n(r) known as molecular director). Under the effect of a low frequency sinusoidal electric field, a planar aligned sample of NLC (with the director parallel to the glass substrates) having a negative dielectric anisotropy (Δε<0) can be driven through several regimes of increasing stochasticity by tuning the amplitude of the external field, and establishing a sequence of electro-hydrodynamic (EHD) instabilities. While increasing the electric field, the first encountered regime consists in a series of stationary convective rolls (Williams domains), whose periodicity is of the order of the sample thickness [6

6. N. Scaramuzza, C. Versace, and V. Carbone, “Alignment transition in a nematic liquid crystal due to field-induced breaking of anchoring,” Mol. Cryst. Liq. Cryst. 266, 85 (1995). [CrossRef]

]. This instability arises as result of two competing forces: a restoring dielectric torque owing to the negative dielectric anisotropy, and a force exerted on the bulk fluid due to the charge separation produced by the positive anisotropy of the conductivity (Δσ>0). These two forces lead to the formation of a recurrent pattern of convective roll structures, associated to the periodic distortion of the director field, n(r). When increasing the amplitude of the external field, bifurcations to more complicated spatio-temporal patterns are to be found (distortion of Williams domains and weak turbulence). At higher electric field a transient bimodality [7

7. S. Kai, M. Andoh, and S. Yamaguchi, “Transient bimodality in turbulence-1-turbulence-2 transition in electrohydrodynamic convection in nematic liquid crystals,” Phys. Rev. A 46, R7375–R7378 (1992). [CrossRef] [PubMed]

, 8

8. S. Nasuno, O. Sasaki, S. Kai, and W. Zimmermann, “Secondary instabilities in electroconvection in nematic liquid crystals,” Phys. Rev. A 46, 4954–4962 (1992). [CrossRef] [PubMed]

], from a first turbulent regime (called DSM1) to the fully developed turbulent regime (DSM2), is finally observed [9

9. V. Carbone, N. Scaramuzza, and C. Versace, “Multifractal structures in electro-convective turbulence,” Physica D 106, 314 (1997). [CrossRef]

, 10

10. G. Strangi, C. Versace, N. Scaramuzza, D. E. Lucchetta, V. Carbone, and R. Bartolino, “Photopolarimetric characterization of the transition between two turbulent states in a nematic liquid crystal film,” Phys. Rev. E 59, 5523–5527 (1999). [CrossRef]

].

In a NLC sample thermal fluctuations of the molecular director n(r)=n 0+δ n(r) leads to fluctuations of the dielectric tensor εαβ=ε δαβ+(ε -ε )nαnβ, this effect being the main responsible of the recurrent multiple scattering and the localization of light observed in such systems. In the case of thermal fluctuations [4

4. H. K. M. Vithana, L. Asfaw, and D. L. Johnson, “Coherent backscattering of light in a nematic liquid crystal,” Phys. Rev. Lett. 23, 3561–3564 (1993). [CrossRef]

] (and in absence of external stimuli), the ratio of the scattering cross–sections due to the variation of refraction index caused by thermal fluctuation in NLC sample SNLC, and that owing to arbitrary isotropic scatterers Siso is of the order of SNLC/Siso≃106 [12

12. P. G. De Gennes, The Physics of Liquid Crystals (Oxford Science Pub., 1993).

]. This indicates that, even in the absence of external stimuli, NLCs provide an important scattering environment, which already proved a striking optical feedback (localization) and is responsible for the random laser action observed in the case of several confinement geometries [13

13. G. Strangi, S. Ferjani, V. Barna, A. De Luca, C. Versace, N. Scaramuzza, and R. Bartolino, “Random lasing and weak localization of light in dye-doped nematic liquid crystals,” Opt. Express. 147737–7744 (2006). [CrossRef] [PubMed]

]. Thus, liquid crystalline materials, being interesting reconfigurable media able to reveal dynamical localization of light waves are used as model systems for investigating multiple scattering induced by chaotic dynamics.

2. Experiment

Fig. 1. Experimental Set-up. (a) Before rotation and (b) after the rotation of the frame and the sample S.
Fig. 2. Different electro-hydrodynamical regimes observed under an optical microscope as a function of the applied voltage.
Fig. 3. Backscattering cone for DSM2 regime at 70V and f=70 Hz.
Fig. 4. FWHM (circles) and scattering mean free path (squares) as a function of the applied voltage.

3. Conclusion

CBS experiments performed within this fully chaotic regime evidenced striking constructive interference of partial waves traversing momentum-reversed scattering paths in the backscattering direction, accompanied by an almost complete reduction in the amount of light transported throughout the turbulent media. The cone width enlargement during the transition DSM1-DSM2, for a fixed voltage above threshold, emphasizes that a dynamical critical behavior regulates the recurrent multiple scattering process inducing a decrement of the scattering mean free path (about 8µm). In fact, the DSMs bifurcation is regulated by a dramatic director field distortion, manifested as a very strong non-linear flow, since the stresses have surpassed the threshold value of the viscoelastic limit. In conclusion, a remarkable effect of light waves CBS in turbulent anisotropic complex fluids has been reported. The cascade of EHD instabilities in NLCs have been utilized as reconfigurable systems to investigate weak localization phenomena in dynamical regimes characterized by critical behavior. The net reduction of light transport in the forward direction and the robust interference phenomena that survive multiple scattering as evidenced by CBS measurements provide the signature of weak light waves localization effect. This interesting feature opens up fascinating horizons concerning the opportunity to study random laser action in chaotic systems in presence of high efficiency gain media.

References and links

1.

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109, 1492–1505 (1958). [CrossRef]

2.

F. C. Mackintosh and S. John, “Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media,” Phys. Rev. B 37, 1884–1897 (1998). [CrossRef]

3.

D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, “Experimental Evidence for Recurrent Multiple Scattering Events of Light in Disordered Media,” Phys. Rev. Lett. 74, 1739–1742 (1995). [CrossRef]

4.

H. K. M. Vithana, L. Asfaw, and D. L. Johnson, “Coherent backscattering of light in a nematic liquid crystal,” Phys. Rev. Lett. 23, 3561–3564 (1993). [CrossRef]

5.

L. V. Kuzmin, V. P. Romanov, and L. A. Zubkov, “Coherent backscattering from anisotropic scatterers,” Phys. Rev. E 54, 6798–6801 (1996). [CrossRef]

6.

N. Scaramuzza, C. Versace, and V. Carbone, “Alignment transition in a nematic liquid crystal due to field-induced breaking of anchoring,” Mol. Cryst. Liq. Cryst. 266, 85 (1995). [CrossRef]

7.

S. Kai, M. Andoh, and S. Yamaguchi, “Transient bimodality in turbulence-1-turbulence-2 transition in electrohydrodynamic convection in nematic liquid crystals,” Phys. Rev. A 46, R7375–R7378 (1992). [CrossRef] [PubMed]

8.

S. Nasuno, O. Sasaki, S. Kai, and W. Zimmermann, “Secondary instabilities in electroconvection in nematic liquid crystals,” Phys. Rev. A 46, 4954–4962 (1992). [CrossRef] [PubMed]

9.

V. Carbone, N. Scaramuzza, and C. Versace, “Multifractal structures in electro-convective turbulence,” Physica D 106, 314 (1997). [CrossRef]

10.

G. Strangi, C. Versace, N. Scaramuzza, D. E. Lucchetta, V. Carbone, and R. Bartolino, “Photopolarimetric characterization of the transition between two turbulent states in a nematic liquid crystal film,” Phys. Rev. E 59, 5523–5527 (1999). [CrossRef]

11.

P. E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55, 2696–2699 (1985). [CrossRef] [PubMed]

12.

P. G. De Gennes, The Physics of Liquid Crystals (Oxford Science Pub., 1993).

13.

G. Strangi, S. Ferjani, V. Barna, A. De Luca, C. Versace, N. Scaramuzza, and R. Bartolino, “Random lasing and weak localization of light in dye-doped nematic liquid crystals,” Opt. Express. 147737–7744 (2006). [CrossRef] [PubMed]

14.

C. Vena, C. Versace, G. Strangi, V. Bruno, N. Scaramuzza, and R. Bartolino, “Light Depolarization Effect by Electrohydrodynamic Turbulence in Nematic Liquid Crystals,” Mol. Cryst. Liq. Cryst. 4411 (2005). [CrossRef]

15.

C. Vena, C. Versace, G. Strangi, S. D’Elia, and R. Bartolino, “Light depolarization effects during the Fredericksz transition in nematic liquid crystals,” Opt. Express. 15 issue 2517063–17071 (2007). [CrossRef]

16.

D. S. Wiersma, Light in strongly scattering and amplifying random media (PhD thesis, 1995).

17.

A. Joets and R. Ribotta, “Caustics and symmetries in optical imaging. The example of convective flow visualization,” J. Phys. 4, 1013–1026 (1994).

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(160.3710) Materials : Liquid crystals
(280.7060) Remote sensing and sensors : Turbulence
(280.1350) Remote sensing and sensors : Backscattering

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: April 20, 2009
Revised Manuscript: June 13, 2009
Manuscript Accepted: June 15, 2009
Published: July 21, 2009

Citation
Francesco Carbone, Antonio De Luca, Valentin Barna, Sameh Ferjani, Carlo Vena, Carlo Versace, and Giuseppe Strangi, "Coherent backscattering and dynamical light localization in liquid crystals driven throughout chaotic regimes," Opt. Express 17, 13435-13440 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13435


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References

  1. P. W. Anderson, "Absence of Diffusion in Certain Random Lattices," Phys. Rev. 109, 1492 - 1505 (1958). [CrossRef]
  2. F. C. Mackintosh and S. John, "Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media," Phys. Rev. B 37, 1884 - 1897 (1998). [CrossRef]
  3. D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, and A. Lagendijk, "Experimental Evidence for Recurrent Multiple Scattering Events of Light in Disordered Media," Phys. Rev. Lett. 74, 1739 - 1742 (1995). [CrossRef]
  4. H. K. M. Vithana, L. Asfaw, and D. L. Johnson, "Coherent backscattering of light in a nematic liquid crystal," Phys. Rev. Lett. 23, 3561 - 3564 (1993). [CrossRef]
  5. L. V. Kuzmin, V. P. Romanov, and L. A. Zubkov, "Coherent backscattering from anisotropic scatterers," Phys. Rev. E 54, 6798 - 6801 (1996). [CrossRef]
  6. N. Scaramuzza, C. Versace, V. Carbone, "Alignment transition in a nematic liquid crystal due to field-induced breaking of anchoring," Mol. Cryst. Liq. Cryst. 266, 85 (1995). [CrossRef]
  7. S. Kai, M. Andoh, and S. Yamaguchi, "Transient bimodality in turbulence-1-turbulence-2 transition in electrohydrodynamic convection in nematic liquid crystals," Phys. Rev. A 46, R7375 - R7378 (1992). [CrossRef] [PubMed]
  8. S. Nasuno, O. Sasaki, S. Kai, and W. Zimmermann, "Secondary instabilities in electroconvection in nematic liquid crystals," Phys. Rev. A 46, 4954 - 4962 (1992). [CrossRef] [PubMed]
  9. V. Carbone, N. Scaramuzza, C. Versace, "Multifractal structures in electro-convective turbulence," Physica D 106, 314 (1997). [CrossRef]
  10. G. Strangi, C. Versace, N. Scaramuzza, D. E. Lucchetta, V. Carbone, and R. Bartolino, "Photopolarimetric characterization of the transition between two turbulent states in a nematic liquid crystal film," Phys. Rev. E 59, 5523- 5527 (1999). [CrossRef]
  11. P. E. Wolf, and G. Maret, "Weak Localization and Coherent Backscattering of Photons in Disordered Media," Phys. Rev. Lett. 55, 2696 - 2699 (1985). [CrossRef] [PubMed]
  12. P. G. De Gennes, The Physics of Liquid Crystals (Oxford Science Pub., 1993).
  13. G. Strangi, S. Ferjani, V. Barna, A. De Luca, C. Versace, N. Scaramuzza and R. Bartolino, "Random lasing and weak localization of light in dye-doped nematic liquid crystals," Opt. Express. 147737-7744 (2006). [CrossRef] [PubMed]
  14. C. Vena, C. Versace, G. Strangi, V. Bruno, N. Scaramuzza, R. Bartolino, "Light Depolarization Effect by Electrohydrodynamic Turbulence in Nematic Liquid Crystals," Mol. Cryst. Liq. Cryst. 4411 (2005). [CrossRef]
  15. C. Vena, C. Versace, G. Strangi, S. D’Elia, R. Bartolino, "Light depolarization effects during the Fredericksz transition in nematic liquid crystals," Opt. Express.  1517063-17071 (2007). [CrossRef]
  16. D. S. Wiersma, Light in strongly scattering and amplifying random media (PhD thesis, 1995).
  17. A. Joets and R. Ribotta, "Caustics and symmetries in optical imaging. The example of convective flow visualization," J. Phys. 4, 1013 - 1026 (1994).

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