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
See e.g. L. Kramer, W. Pesch, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer-Verlag, New York, 1996)
N.V. Tabiryan, A.V. Sukhov, B.Ya. Zel’dovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986)
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)
F.T. Arecchi, S. Boccaletti, S. Ducci, E. Pampaloni, P.L. Ramazza, S. Residori, J. Nonlin. Opt. Phys. Mat. 9, 183 (2000)
R. MacDonald, H.J. Eichler, Opt. Commun. 89, 289 (1992)
E. Santamato, E. Ciaramella, M. Tamburrini, Mol. Cryst. Liq. Cryst. 251, 127 (1994)
E. Louvergneaux, Phys. Rev. Lett. 87, 244501 (2001)
V. Fréedericksz, V. Zolina, Trans. Faraday Soc. 29, 919 (1933)
P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd edn. (Oxford Science Publications, Clarendon Press, 1993)
S. Chandrasekhar, Liquid Crystal (Cambridge, New York, 1992)
M.O. Cáceres, F. Sagués, M. San Miguel, Phys. Rev. A 41, 6852 (1990)
B.J. Frisken, P. Palffy-Muhoray, Phys. Rev. A 39, 1513 (1989); Phys. Rev. A 40, 6099 (1989)
S. Garg, S. Saeed, U.D. Kini, Phys. Rev. E 51, 5846 (1995)
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)
P.Y. Wang, H.J. Zhang, J.H. Dai, Opt. Lett. 12, 654 (1987)
M.G. Clerc, S. Residori, C.S. Riera, Phys. Rev. E 63, 060701 (2001)
R.A. Fisher, Ann. Eugenics 7, 335 (1937)
A.N. Kolmogorov, J. Petrovsky, N. Piskunov, Bull. Univ. Moskou Ser. Int. Se. 7(6), 1 (1937)
J.D. Murray, Mathematical Biology (Springer-Verlag, Berlin, 1993)
P. Kife, Mathematical Aspects of Reacting and Diffusing System, edited by S. Levin, Lecture Notes in Biomathematics (Springer-Verlag, New-York, 1979), Vol. 28
D. Walgraef, Spatio-temporal pattern formation (Springer-Verlag, New York, 1997)
G. Dee, J.S. Langer, Phys. Rev. Lett. 50, 383 (1983)
P. Manneville, Dissipative structures and weak turbulence (Academic Press, San Diego, 1990)
M. Cross, P. Hohenberg, Rev. Mod. Phys. 65, 581 (1993)
D.G. Aronson, H.F. Weinberger, Adv. Math. 30, 33 (1978)
P. Collet, J.P. Eckmann, Instabilities and fronts in extended system (Princeton University Press, New Jersey, 1990)
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)
E. Yao, F. Papoff, G.L. Oppo, Phys. Rev. E 59, 2918 (1999)
L.D. Landau, E.M. Lifshitz, Statistical physics(Pergamon Press, New York, 1969)
W.K. Burton, N. Cabrera, F.C. Frank, Phil. Trans. Roy. Soc. Lond. A 243, 299 (1951)
Y. Pomeau, Physica D 23, 3 (1986)
S.A. Akhmanov, M.A. Vorontsov, V.Yu. Ivanov, JETP Lett. 47, 707 (1988)
S. Residori, A. Petrossian, L. Gil, Phys. Rev. Lett. 88, 233901-1 (2002)
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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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DOI: https://doi.org/10.1140/epjd/e2003-00316-1