Abstract
Molecular reorientation processes induced in thin ferroelectric liquid crystal systems by strong alternating external electric fields are studied both by solving numerically the equation of reorientation motion of molecules and by measuring the electro-optic response of thin samples. It is shown that the occurrence of a wide band in nonlinear response spectra above the Goldstone-mode frequency is a consequence of complex partially uncorrelated molecular reorientations enforced within smectic layers by sufficiently high fields of high enough frequencies. Such nonlinear reorientational motions of molecules are argued to have a character of weakly chaotic long-lasting transients, related to almost periodic modulations of the amplitude of rotational oscillations performed by molecules with the field frequency. These modulations have been numerically proved to proceed with lower frequencies than the field frequency and with space-dependent depths of temporal changes. The occurrence of the modulations has experimentally been confirmed by registering distinct contributions to electro-optic response spectra at frequencies less than the running frequency of the applied electric field.
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References
J.R. Lalanne, J. Buchert, S. Kielich, in Modern Nonlinear Optics, Part 1, edited by M. Evans, S. Kielich (Wiley, New York, 1993).
M. Buscalia, T. Bellini, V. Degiorgio, F. Mantegazza, F. Simoni, Europhys. Lett. 48, 634 (1999).
G. Russo, V. Carbone, G. Cipparrone, Phys. Rev. E 62, 5036 (2000).
G. Cipparrone, G. Russo, C. Versace, G. Strangi, V. Carbone, Opt. Commun. 173, 1 (2000).
Y. Kimura, H. Isono, R. Hayakawa, Eur. Phys. J. E 9, 3 (2002).
S.M. Morris, A.D. Ford, M.N. Pivnenko, H.J. Coles, J. Opt. A 7, 215 (2005).
B. Piccirillo, A. Vella, A. Setaro, E. Santamato, Phys. Rev. E 73, 062701 (2006).
L. Lucchetti, M. Gentili, F. Simoni, S. Pavliuchenko, S. Subota, V. Reshetnyak, Phys. Rev. E 78, 061706 (2008).
S.T. Lagerwall, Ferroelectric and Antiferroelectric Liquid Crystals (Wiley-VCH, Weinheim, 1999). .
L. Lam, Z.C. Ou-Yang, M. Lax, Phys. Rev. A 37, 3469 (1988).
H. Orihara, A. Fukase, S. Izumi, Y. Ishibashi, Ferroelectrics 147, 411 (1993).
Y. Ishibashi, H. Orihara, Frerroelectrics 156, 185 (1994).
H. Orihara, Y. Isibashi, J. Phys. Soc. Jpn. 64, 3775 (1995).
Y. Ishibashi, H. Orihara, Physica B 219-220, 626 (1996).
G. Demeter, L. Kramer, Phys. Rev. Lett. 83, 4744 (1999).
Y. Kimura, S. Hara, R. Hayakawa, Ferroelectrics 245, 61 (2000).
Y. Kimura, S. Hara, R. Hayakawa, Phys. Rev. E 62, R5907 (2000).
T.D. Frank, Phys. Rev. E 72, 041703 (2005).
J.M. Leblond, R. Douali, C. Legrand, R. Dabrowski, Eur. Phys. J. Appl. Phys. 36, 157 (2006).
C. Thibierge, D. L’ote, F. Ladieu, R. Tourbot, Rev. Sci. Instrum. 79, 103905 (2008).
N.A. Clark, S.T. Lagerwall, in Ferroelectric Liquid Crystals, Principles, Properties and Applications, edited by J.W. Goodbye, R. Blinc, N.A. Clark, S.T. Lagerwall, M.A. Osipov, S.A. Pikin, T. Sakurai, K. Yoshino, B. Žekš (Gordon and Breach, Philadelphia, 1991).
W. Jezewski, W. Kuczyński, J. Hoffmann, Phys. Rev. E 83, 042701 (2011).
R.E. Amritkar, N. Gupte, Phys. Rev. A 44, R3403 (1991).
M.D. LaMar, G.D. Smith, Phys. Rev. E 2010 81, 046206 (2010).
W. Kuczyński, J. Hoffmann, J. Małecki, Ferroelectrics 150, 279 (1993).
W. Jezewski, W. Kuczyński, J. Hoffmann, Liq. Cryst. 34, 1299 (2007).
W. Jezewski, W. Kuczyński, J. Hoffmann, Phys. Rev. E 73, 061702 (2006).
W. Jezewski, W. Kuczyński, J. Hoffmann, Phys. Rev. B 77, 094101 (2008).
W. Jezewski, W. Kuczyński, Phys. Rev. B 79, 214206 (2009).
M.A. Handschy, N.A. Clark, S.T. Lagerwall, Phys. Rev. Lett. 51, 471 (1983).
J.E. Maclennan, M.A. Handschy, N.A. Clark, Liq. Cryst. 7, 787 (1990).
P.J. Davies, I. Polonsky, in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1972) p. 896.
E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993).
R.C.L. Wolf, J. R. Stat. Soc. B 54, 353 (1992).
F. Ali, M. Menzinger, Chaos 9, 348 (1999).
A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985).
G.M. Zaslavsky, R.Z. Sagdeev, D.A. Usikov, A.A. Chernikov, Weak Chaos and Quasi-Regular Patterns (Cambridge University Press, Cambridge, 1991).
R.C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, Oxford, 2000).
I.W. Stewart, T. Carlsson, F.M. Leslie, Ferroelectrics 148, 41 (1993).
H. Katz, P. Grassberger, Physica D 17, 75 (1985).
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Jeżewski, W., Śliwa, I. & Kuczyński, W. Strongly nonlinear dynamics of ferroelectric liquid crystals. Eur. Phys. J. E 36, 2 (2013). https://doi.org/10.1140/epje/i2013-13002-7
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DOI: https://doi.org/10.1140/epje/i2013-13002-7