Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films

V. Carbone; G. Cipparrone; G. Russo

doi:10.1103/PhysRevE.63.051701

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Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films

V. Carbone, G. Cipparrone, and G. Russo

Dipartimento di Fisica and Istituto di Fisica della Materia, Università della Calabria, 87036 Rende (CS), Italy

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Phys. Rev. E 63, 051701 – Published 13 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.051701

Abstract

An $s - p o l a r i z e d$ laser beam that impinges at small incidence angle on a homeotropically aligned nematic liquid crystal produces very interesting nonlinear phenomena. In this paper, we show that, due to the symmetry of the system, a cascade of successive homoclinic gluing bifurcations is responsible for the transition towards a stochastic regime in the experiment. We compare the experimental results with a model describing a sequence of gluing bifurcations.

References (15)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel’ovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986), and references therein; J. C. Koo, Prog. Opt. 26, 107 (1998), and references therein.
E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, Liq. Cryst. 25, 357 (1998), and references therein; ibid.A. S. Zolotko, V. F. Kitaeva, N. N. Sobolev, V. Y. Fedorovich, A. P. Sukhozukov, N. Kroo, and L. Csillag, 15, 787 (1993).
G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, Phys. Rev. E 47, 3741 (1993); ibid.V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, 54, 6948 (1996).
G. Russo, V. Carbone, and G. Cipparrone, Phys. Rev. E 62, 5036 (2000).
G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Carbone, Opt. Commun. 173, 1 (2000).
P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford University Press, Oxford, 1993).
G. Demeter and L. Kramer, Phys. Rev. Lett. 83, 4744 (1999).
A. Arneodo, P. Coullet, and C. Tresser, Phys. Lett. 81A, 197 (1981).
D. V. Lyubimov and M. A. Zaks, Physica D 9, 52 (1983).
J. Coste and N. Peyraud, Phys. Lett. 84A, 17 (1981); A. M. Rucklidge, Physica D 62, 323 (1993).
R. Herrero, J. Farjas, R. Pons, F. Pi, and G. Orriols, Phys. Rev. E 57, 5366 (1998).
E. Meron and I. Procaccia, Phys. Rev. A 35, 4008 (1987).
R. M. A. Azzam and N. M. Bashara, Elipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
J. N. Kaplan and J. A. Yorke, Commun. Math. Phys. 67, 93 (1979).

[c1] Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

[c2] N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel’ovich, Mol. Cryst. Liq. Cryst. 136, 1 (1986), and references therein; J. C. Koo, Prog. Opt. 26, 107 (1998), and references therein.

[c3] E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, Liq. Cryst. 25, 357 (1998), and references therein; ibid.A. S. Zolotko, V. F. Kitaeva, N. N. Sobolev, V. Y. Fedorovich, A. P. Sukhozukov, N. Kroo, and L. Csillag, 15, 787 (1993).

[c4] G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, Phys. Rev. E 47, 3741 (1993); ibid.V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, 54, 6948 (1996).

[c5] G. Russo, V. Carbone, and G. Cipparrone, Phys. Rev. E 62, 5036 (2000).

[c6] G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Carbone, Opt. Commun. 173, 1 (2000).

[c7] P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford University Press, Oxford, 1993).

[c8] G. Demeter and L. Kramer, Phys. Rev. Lett. 83, 4744 (1999).

[c9] A. Arneodo, P. Coullet, and C. Tresser, Phys. Lett. 81A, 197 (1981).

[c10] D. V. Lyubimov and M. A. Zaks, Physica D 9, 52 (1983).

[c11] J. Coste and N. Peyraud, Phys. Lett. 84A, 17 (1981); A. M. Rucklidge, Physica D 62, 323 (1993).

[c12] R. Herrero, J. Farjas, R. Pons, F. Pi, and G. Orriols, Phys. Rev. E 57, 5366 (1998).

[c13] E. Meron and I. Procaccia, Phys. Rev. A 35, 4008 (1987).

[c14] R. M. A. Azzam and N. M. Bashara, Elipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

[c15] J. N. Kaplan and J. A. Yorke, Commun. Math. Phys. 67, 93 (1979).

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Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films

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