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First-order Fréedericksz transition and front propagation in a liquid crystal light valve with feedback

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Abstract.

Fréedericksz transition can become subcritical in the presence of a feedback mechanism that leads to the dependence of the local electric field onto the liquid crystal re-orientation angle. We have characterized experimentally the first-order Fréedericksz transition in a Liquid Crystal Light Valve with optical feedback. The bistability region is determined, together with the Fréedericksz transition point and the Maxwell point. We show the propagation of fronts connecting the different metastable states and we estimate the front velocity. Theoretically, we derive an amplitude equation, valid close to the Fréedericksz transition point, which accounts for the subcritical character of the bifurcation.

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References

  1. See e.g. L. Kramer, W. Pesch, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer-Verlag, New York, 1996)

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

    Article  Google Scholar 

  3. Special issue Pattern Formation in Nonlinear Optical Systems, edited by R. Neubecker, T. Tschudi, Chaos, Solitons & Fractals 10 (4–5) (1999); F.T. Arecchi, S. Boccaletti, P.L. Ramazza, Phys. Rep. 318, 1 (1999)

    Article  Google Scholar 

  4. F.T. Arecchi, S. Boccaletti, S. Ducci, E. Pampaloni, P.L. Ramazza, S. Residori, J. Nonlin. Opt. Phys. Mat. 9, 183 (2000)

    Google Scholar 

  5. R. MacDonald, H.J. Eichler, Opt. Commun. 89, 289 (1992)

    Article  ADS  Google Scholar 

  6. E. Santamato, E. Ciaramella, M. Tamburrini, Mol. Cryst. Liq. Cryst. 251, 127 (1994)

    Article  Google Scholar 

  7. E. Louvergneaux, Phys. Rev. Lett. 87, 244501 (2001)

    Article  ADS  Google Scholar 

  8. V. Fréedericksz, V. Zolina, Trans. Faraday Soc. 29, 919 (1933)

    Article  Google Scholar 

  9. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd edn. (Oxford Science Publications, Clarendon Press, 1993)

  10. S. Chandrasekhar, Liquid Crystal (Cambridge, New York, 1992)

  11. M.O. Cáceres, F. Sagués, M. San Miguel, Phys. Rev. A 41, 6852 (1990)

    Article  ADS  Google Scholar 

  12. B.J. Frisken, P. Palffy-Muhoray, Phys. Rev. A 39, 1513 (1989); Phys. Rev. A 40, 6099 (1989)

    Article  ADS  Google Scholar 

  13. S. Garg, S. Saeed, U.D. Kini, Phys. Rev. E 51, 5846 (1995)

    Article  ADS  Google Scholar 

  14. S.D. Durbin, S.M. Arakelian, Y.R. Shen, Phys. Rev. Lett. 47, 1411 (1981); S.R. Nersisyan, N.V. Tabiryan, Mol. Cryst. Liq. Cryst. 116, 111 (1984); A.J. Karn, S.M. Arakelian, Y.R. Shen, H.L. Ong, Phys. Rev. Lett. 57, 448 (1986); E. Santamato, G. Abbate, R. Casaselice, P. Maddalena, A. Sasso, Phys. Rev. A 37, 1375 (1988)

    Article  ADS  Google Scholar 

  15. P.Y. Wang, H.J. Zhang, J.H. Dai, Opt. Lett. 12, 654 (1987)

    Article  ADS  Google Scholar 

  16. M.G. Clerc, S. Residori, C.S. Riera, Phys. Rev. E 63, 060701 (2001)

    Article  ADS  Google Scholar 

  17. R.A. Fisher, Ann. Eugenics 7, 335 (1937)

    Google Scholar 

  18. A.N. Kolmogorov, J. Petrovsky, N. Piskunov, Bull. Univ. Moskou Ser. Int. Se. 7(6), 1 (1937)

    Google Scholar 

  19. J.D. Murray, Mathematical Biology (Springer-Verlag, Berlin, 1993)

  20. P. Kife, Mathematical Aspects of Reacting and Diffusing System, edited by S. Levin, Lecture Notes in Biomathematics (Springer-Verlag, New-York, 1979), Vol. 28

  21. D. Walgraef, Spatio-temporal pattern formation (Springer-Verlag, New York, 1997)

  22. G. Dee, J.S. Langer, Phys. Rev. Lett. 50, 383 (1983)

    Article  ADS  Google Scholar 

  23. P. Manneville, Dissipative structures and weak turbulence (Academic Press, San Diego, 1990)

  24. M. Cross, P. Hohenberg, Rev. Mod. Phys. 65, 581 (1993)

    Article  Google Scholar 

  25. D.G. Aronson, H.F. Weinberger, Adv. Math. 30, 33 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  26. P. Collet, J.P. Eckmann, Instabilities and fronts in extended system (Princeton University Press, New Jersey, 1990)

  27. P.L. Ramazza, S. Ducci, F.T. Arecchi, Phys. Rev. Lett. 81, 4128 (1998); J. Bragard, P.L. Ramazza, F.T. Arecchi, S. Boccaletti, L. Kramer, Phys. Rev. E 61, R6045 (2000)

    Article  ADS  Google Scholar 

  28. E. Yao, F. Papoff, G.L. Oppo, Phys. Rev. E 59, 2918 (1999)

    Article  ADS  Google Scholar 

  29. L.D. Landau, E.M. Lifshitz, Statistical physics(Pergamon Press, New York, 1969)

  30. W.K. Burton, N. Cabrera, F.C. Frank, Phil. Trans. Roy. Soc. Lond. A 243, 299 (1951)

    Article  ADS  MATH  Google Scholar 

  31. Y. Pomeau, Physica D 23, 3 (1986)

    Article  ADS  Google Scholar 

  32. S.A. Akhmanov, M.A. Vorontsov, V.Yu. Ivanov, JETP Lett. 47, 707 (1988)

    ADS  Google Scholar 

  33. S. Residori, A. Petrossian, L. Gil, Phys. Rev. Lett. 88, 233901-1 (2002)

    Article  ADS  Google Scholar 

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Correspondence to S. Residori.

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Received: 21 October 2003, Published online: 6 January 2004

PACS:

05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 64.60.-i General studies of phase transitions

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Clerc, M.G., Nagaya, T., Petrossian, A. et al. First-order Fréedericksz transition and front propagation in a liquid crystal light valve with feedback. Eur. Phys. J. D 28, 435–445 (2004). https://doi.org/10.1140/epjd/e2003-00316-1

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