Abstract

We present a detailed bifurcation analysis of the nonlinear reorientation dynamics of a homeotropically aligned nematic liquid-crystal film excited by a circularly polarized beam at normal incidence with the light intensity as the control parameter. The secondary bifurcation above the optical Fréedericksz transition threshold is identified as a supercritical Hopf bifurcation leading to quasi-periodicity, and the subsequent discontinuous transition from quasi-periodicity to periodicity at higher intensity is identified as a homoclinic bifurcation. The bifurcation scenario is compared with the one obtained in the case of an ordinary light wave at small oblique incidence. Despite an analogous sequence of transitions, there are substantial differences.

© 2005 Optical Society of America

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  1. N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, "Orientational optical nonlinearity of liquid-crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
    [CrossRef]
  2. I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).
    [CrossRef]
  3. E. Santamato, "Giant optical nonlinearities in nematic liquid crystals," in Nonlinear Optical Material and Devices for Applications in Information Technology, A.Miller, K.R.Welford, and B.Daino, eds. (Kluwer Academic, 1995), pp. 103-139.
    [CrossRef]
  4. F. Simoni, Nonlinear Optical Properties of Liquid Crystals and Polymer Dispersed Liquid Crystals (World Scientific, 1997).
    [CrossRef]
  5. G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
    [CrossRef]
  6. G. Demeter and L. Kramer, "Transition to chaos via gluing bifurcations in optically excited nematic liquid crystals," Phys. Rev. Lett. 83, 4744-4747 (1999).
    [CrossRef]
  7. G. Demeter, "Complex nonlinear behavior in optically excited nematic liquid crystals," Phys. Rev. E 61, 6678-6688 (2000).
    [CrossRef]
  8. G. Demeter and L. Kramer, "Numerical investigation of optically induced director oscillations in nematic liquid crystals," Phys. Rev. E 64, 020701 (R) (2001).
    [CrossRef]
  9. E. Brasselet, "Comment on 'Numerical investigation of optically induced director oscillations in nematic liquid crystals/," Phys. Rev. E (to be published).
  10. B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, "Orbital and spin photon angular momentum transfer in liquid crystals," Phys. Rev. Lett. 86, 2285-2288 (2001).
    [CrossRef] [PubMed]
  11. A. Vella, A. Setaro, B. Piccirillo, and E. Santamato, "On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light," Phys. Rev. E 67, 051704 (2003).
    [CrossRef]
  12. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).
  13. A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].
  14. E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
    [CrossRef] [PubMed]
  15. A. S. Zolot'ko and A. P. Sukhorukov, "Fréedericksz transition induced in nematic liquid-crystal by circularly polarized-light wave," Pis/ma Zh. Eksp. Teor. Fiz. 52, 707-710 (1990) A. S. Zolot'ko and A. P. Sukhorukov, [JETP Lett. 52, 62-65 (1990)].
  16. L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
    [CrossRef]
  17. E. Brasselet and T. V. Galstian, "Optical control of molecular orientational dynamics in liquid crystals," Opt. Commun. 186, 291-302 (2000).
    [CrossRef]
  18. E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "New laser induced spatio-temporal transition in nematics," Phys. Lett. A 299, 212-216 (2002).
    [CrossRef]
  19. E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry," Phys. Rev. E 67, 031706 (2003).
    [CrossRef]
  20. E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: The role of finite beam size," Phys. Rev. E 69, 021701 (2004).
    [CrossRef]
  21. For a classification of the different types of bifurcation, the reader is invited to consult J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields (Springer-Verlag, 1983). See also Refs. and .
    [CrossRef]
  22. J. Hale and H. Koçak, Dynamics and Bifurcations (Springer-Verlag, 1991).
    [CrossRef]
  23. P. Glendinning, Stability, Instability and Chaos (Cambridge U. Press, 1996).
  24. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).
  25. B. Y. Zel'dovich and N. Tabiryan, "Theory of optically induced Fréedericksz transition," Zh. Eksp. Teor. Fiz. 82, 1126-1146 (1982) B. Y. Zel'dovich and N. Tabiryan, [Sov. Phys. JETP 55, 656-666 (1982)].
  26. From Merck datasheets. The refractive indices are measured at 20°C and lambda=589 nm.
  27. G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
    [CrossRef]
  28. E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
    [CrossRef] [PubMed]
  29. A. Vella, B. Piccirillo, and E. Santamato, "Coupled-mode approach to the nonlinear dynamics induced by an elliptically polarized laser field in liquid crystals at normal incidence," Phys. Rev. E 65, 031706 (2002).
    [CrossRef]
  30. D. O. Krimer, L. Kramer, E. Brasselet, T. V. Galstian, and L. J. Dubé, "Bifurcation analysis of optically induced dynamics in nematic liquid crystals: elliptical polarization at normal incidence," J. Opt. Soc. Am. B 22, 1681-1690 (2005).
    [CrossRef]
  31. S. D. Durbin, S. M. Arakelian, and Y. R. Shen, "Laser-induced diffraction rings from a nematic-liquid-crystal film," Opt. Lett. 6, 411-413 (1981).
    [PubMed]
  32. From the weakly nonlinear stability analysis, we find that the nature of the OFT is governed by the sign of the coefficient C=k1-(9/4)(epsilon_a/epsilon_||). C<0 corresponds to a subcritical OFT (i.e., first order), whereas C>0 corresponds to a supercritical OFT (i.e., second order). Incidentally, this criterion is identical to the one derived by Ong in the case of OFT under linearly polarized light.33 With the present parameters, C=0.154 and the OFT is actually supercritical. However, the solution branch turns over and becomes subcritical (and unstable) already at rho=1+deltarho where deltarho ~ or = 10-6. This explains why the OFT appears to be subcritical on the scale used in Fig. 2. In fact, although deltarho increases when the cell thickness is decreased, even at L=10 µm, the subcritical region is still too small (deltarho ~ or = 10-4) to be observed experimentally.
  33. H. L. Ong, "Optically induced Fréedericksz transition and bistability in a nematic liquid crystal," Phys. Rev. A 28, 2393-2407 (1983).
    [CrossRef]
  34. I. C. Khoo, T. H. Liu, and P. Y. Yan, "Nonlocal radial dependence of laser-induced molecular reorientation in a namatic liquid crystal: theory and experiment," J. Opt. Soc. Am. B 4, 115-120 (1987).
    [CrossRef]
  35. D. O. Krimer, G. Demeter, and L. Kramer, "Orientational dynamics induced by circularly polarized light in nematic liquid crystals," Mol. Cryst. Liq. Cryst. 421, 117-131 (2004).
    [CrossRef]
  36. V. Carbone, G. Cipparrone, and G. Russo, "Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films," Phys. Rev. E 63, 051701 (2001).
    [CrossRef]
  37. N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
    [CrossRef]
  38. For some recent research, see S. A. Jewell and J. R. Sambles, "Observation of backflow in the switch-on dynamics of hybrid aligned nematic," Appl. Phys. Lett. 84, 46-48 (2004).
    [CrossRef]
  39. D. O. Krimer, G. Demeter, and L. Kramer, "Influence of the backflow effect on the orientational dynamics induced by light in nematics," Phys. Rev. E 71, 051711 (2005).
    [CrossRef]
  40. D. O. Krimer, G. Demeter, and L. Kramer, "Pattern-forming instability induced by light in pure and dye-doped nematic liquid crystals," Phys. Rev. E 66, 031707 (2002).
    [CrossRef]
  41. I. Jánossy, A. D. Lloyd, and B. S. Wherrett, "Anomalous optical Fréedericksz transition in an absorbing liquid crystal," Mol. Cryst. Liq. Cryst. 179, 1-12 (1990).
  42. C. Brosseau, Fundamentals of Polarized Light: a Statistical Optics Approach (Wiley, 1998).

2005 (2)

2004 (3)

For some recent research, see S. A. Jewell and J. R. Sambles, "Observation of backflow in the switch-on dynamics of hybrid aligned nematic," Appl. Phys. Lett. 84, 46-48 (2004).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Orientational dynamics induced by circularly polarized light in nematic liquid crystals," Mol. Cryst. Liq. Cryst. 421, 117-131 (2004).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: The role of finite beam size," Phys. Rev. E 69, 021701 (2004).
[CrossRef]

2003 (2)

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry," Phys. Rev. E 67, 031706 (2003).
[CrossRef]

A. Vella, A. Setaro, B. Piccirillo, and E. Santamato, "On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light," Phys. Rev. E 67, 051704 (2003).
[CrossRef]

2002 (3)

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "New laser induced spatio-temporal transition in nematics," Phys. Lett. A 299, 212-216 (2002).
[CrossRef]

A. Vella, B. Piccirillo, and E. Santamato, "Coupled-mode approach to the nonlinear dynamics induced by an elliptically polarized laser field in liquid crystals at normal incidence," Phys. Rev. E 65, 031706 (2002).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Pattern-forming instability induced by light in pure and dye-doped nematic liquid crystals," Phys. Rev. E 66, 031707 (2002).
[CrossRef]

2001 (3)

V. Carbone, G. Cipparrone, and G. Russo, "Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films," Phys. Rev. E 63, 051701 (2001).
[CrossRef]

G. Demeter and L. Kramer, "Numerical investigation of optically induced director oscillations in nematic liquid crystals," Phys. Rev. E 64, 020701 (R) (2001).
[CrossRef]

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, "Orbital and spin photon angular momentum transfer in liquid crystals," Phys. Rev. Lett. 86, 2285-2288 (2001).
[CrossRef] [PubMed]

2000 (2)

G. Demeter, "Complex nonlinear behavior in optically excited nematic liquid crystals," Phys. Rev. E 61, 6678-6688 (2000).
[CrossRef]

E. Brasselet and T. V. Galstian, "Optical control of molecular orientational dynamics in liquid crystals," Opt. Commun. 186, 291-302 (2000).
[CrossRef]

1999 (1)

G. Demeter and L. Kramer, "Transition to chaos via gluing bifurcations in optically excited nematic liquid crystals," Phys. Rev. Lett. 83, 4744-4747 (1999).
[CrossRef]

1998 (1)

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

1995 (1)

G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
[CrossRef]

1993 (1)

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

1992 (1)

L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
[CrossRef]

1990 (3)

A. S. Zolot'ko and A. P. Sukhorukov, "Fréedericksz transition induced in nematic liquid-crystal by circularly polarized-light wave," Pis/ma Zh. Eksp. Teor. Fiz. 52, 707-710 (1990) A. S. Zolot'ko and A. P. Sukhorukov, [JETP Lett. 52, 62-65 (1990)].

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
[CrossRef] [PubMed]

I. Jánossy, A. D. Lloyd, and B. S. Wherrett, "Anomalous optical Fréedericksz transition in an absorbing liquid crystal," Mol. Cryst. Liq. Cryst. 179, 1-12 (1990).

1987 (1)

1986 (2)

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
[CrossRef] [PubMed]

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, "Orientational optical nonlinearity of liquid-crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

1983 (1)

H. L. Ong, "Optically induced Fréedericksz transition and bistability in a nematic liquid crystal," Phys. Rev. A 28, 2393-2407 (1983).
[CrossRef]

1982 (1)

B. Y. Zel'dovich and N. Tabiryan, "Theory of optically induced Fréedericksz transition," Zh. Eksp. Teor. Fiz. 82, 1126-1146 (1982) B. Y. Zel'dovich and N. Tabiryan, [Sov. Phys. JETP 55, 656-666 (1982)].

1981 (2)

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, "Laser-induced diffraction rings from a nematic-liquid-crystal film," Opt. Lett. 6, 411-413 (1981).
[PubMed]

Abbate, G.

L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
[CrossRef]

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
[CrossRef] [PubMed]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).

Arakelian, S. M.

Bartolino, R.

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

Brasselet, E.

D. O. Krimer, L. Kramer, E. Brasselet, T. V. Galstian, and L. J. Dubé, "Bifurcation analysis of optically induced dynamics in nematic liquid crystals: elliptical polarization at normal incidence," J. Opt. Soc. Am. B 22, 1681-1690 (2005).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: The role of finite beam size," Phys. Rev. E 69, 021701 (2004).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry," Phys. Rev. E 67, 031706 (2003).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "New laser induced spatio-temporal transition in nematics," Phys. Lett. A 299, 212-216 (2002).
[CrossRef]

E. Brasselet and T. V. Galstian, "Optical control of molecular orientational dynamics in liquid crystals," Opt. Commun. 186, 291-302 (2000).
[CrossRef]

E. Brasselet, "Comment on 'Numerical investigation of optically induced director oscillations in nematic liquid crystals/," Phys. Rev. E (to be published).

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: a Statistical Optics Approach (Wiley, 1998).

Carbone, V.

V. Carbone, G. Cipparrone, and G. Russo, "Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films," Phys. Rev. E 63, 051701 (2001).
[CrossRef]

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

Cipparrone, G.

V. Carbone, G. Cipparrone, and G. Russo, "Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films," Phys. Rev. E 63, 051701 (2001).
[CrossRef]

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
[CrossRef]

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

Csillag, L.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].

Daino, B.

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
[CrossRef] [PubMed]

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

Demeter, G.

D. O. Krimer, G. Demeter, and L. Kramer, "Influence of the backflow effect on the orientational dynamics induced by light in nematics," Phys. Rev. E 71, 051711 (2005).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Orientational dynamics induced by circularly polarized light in nematic liquid crystals," Mol. Cryst. Liq. Cryst. 421, 117-131 (2004).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Pattern-forming instability induced by light in pure and dye-doped nematic liquid crystals," Phys. Rev. E 66, 031707 (2002).
[CrossRef]

G. Demeter and L. Kramer, "Numerical investigation of optically induced director oscillations in nematic liquid crystals," Phys. Rev. E 64, 020701 (R) (2001).
[CrossRef]

G. Demeter, "Complex nonlinear behavior in optically excited nematic liquid crystals," Phys. Rev. E 61, 6678-6688 (2000).
[CrossRef]

G. Demeter and L. Kramer, "Transition to chaos via gluing bifurcations in optically excited nematic liquid crystals," Phys. Rev. Lett. 83, 4744-4747 (1999).
[CrossRef]

Doyon, B.

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: The role of finite beam size," Phys. Rev. E 69, 021701 (2004).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry," Phys. Rev. E 67, 031706 (2003).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "New laser induced spatio-temporal transition in nematics," Phys. Lett. A 299, 212-216 (2002).
[CrossRef]

Dubé, L. J.

D. O. Krimer, L. Kramer, E. Brasselet, T. V. Galstian, and L. J. Dubé, "Bifurcation analysis of optically induced dynamics in nematic liquid crystals: elliptical polarization at normal incidence," J. Opt. Soc. Am. B 22, 1681-1690 (2005).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: The role of finite beam size," Phys. Rev. E 69, 021701 (2004).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry," Phys. Rev. E 67, 031706 (2003).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "New laser induced spatio-temporal transition in nematics," Phys. Lett. A 299, 212-216 (2002).
[CrossRef]

Duca, D.

G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
[CrossRef]

Durbin, S. D.

Ferraiuolo, S.

L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
[CrossRef]

Galstian, T. V.

D. O. Krimer, L. Kramer, E. Brasselet, T. V. Galstian, and L. J. Dubé, "Bifurcation analysis of optically induced dynamics in nematic liquid crystals: elliptical polarization at normal incidence," J. Opt. Soc. Am. B 22, 1681-1690 (2005).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: The role of finite beam size," Phys. Rev. E 69, 021701 (2004).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry," Phys. Rev. E 67, 031706 (2003).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "New laser induced spatio-temporal transition in nematics," Phys. Lett. A 299, 212-216 (2002).
[CrossRef]

E. Brasselet and T. V. Galstian, "Optical control of molecular orientational dynamics in liquid crystals," Opt. Commun. 186, 291-302 (2000).
[CrossRef]

Glendinning, P.

P. Glendinning, Stability, Instability and Chaos (Cambridge U. Press, 1996).

Guckenheimer, J.

For a classification of the different types of bifurcation, the reader is invited to consult J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields (Springer-Verlag, 1983). See also Refs. and .
[CrossRef]

Hale, J.

J. Hale and H. Koçak, Dynamics and Bifurcations (Springer-Verlag, 1991).
[CrossRef]

Holmes, P.

For a classification of the different types of bifurcation, the reader is invited to consult J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields (Springer-Verlag, 1983). See also Refs. and .
[CrossRef]

Jánossy, I.

I. Jánossy, A. D. Lloyd, and B. S. Wherrett, "Anomalous optical Fréedericksz transition in an absorbing liquid crystal," Mol. Cryst. Liq. Cryst. 179, 1-12 (1990).

Jewell, S. A.

For some recent research, see S. A. Jewell and J. R. Sambles, "Observation of backflow in the switch-on dynamics of hybrid aligned nematic," Appl. Phys. Lett. 84, 46-48 (2004).
[CrossRef]

Khoo, I. C.

Kitaeva, V. F.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].

Koçak, H.

J. Hale and H. Koçak, Dynamics and Bifurcations (Springer-Verlag, 1991).
[CrossRef]

Kramer, L.

D. O. Krimer, G. Demeter, and L. Kramer, "Influence of the backflow effect on the orientational dynamics induced by light in nematics," Phys. Rev. E 71, 051711 (2005).
[CrossRef]

D. O. Krimer, L. Kramer, E. Brasselet, T. V. Galstian, and L. J. Dubé, "Bifurcation analysis of optically induced dynamics in nematic liquid crystals: elliptical polarization at normal incidence," J. Opt. Soc. Am. B 22, 1681-1690 (2005).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Orientational dynamics induced by circularly polarized light in nematic liquid crystals," Mol. Cryst. Liq. Cryst. 421, 117-131 (2004).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Pattern-forming instability induced by light in pure and dye-doped nematic liquid crystals," Phys. Rev. E 66, 031707 (2002).
[CrossRef]

G. Demeter and L. Kramer, "Numerical investigation of optically induced director oscillations in nematic liquid crystals," Phys. Rev. E 64, 020701 (R) (2001).
[CrossRef]

G. Demeter and L. Kramer, "Transition to chaos via gluing bifurcations in optically excited nematic liquid crystals," Phys. Rev. Lett. 83, 4744-4747 (1999).
[CrossRef]

Krimer, D. O.

D. O. Krimer, L. Kramer, E. Brasselet, T. V. Galstian, and L. J. Dubé, "Bifurcation analysis of optically induced dynamics in nematic liquid crystals: elliptical polarization at normal incidence," J. Opt. Soc. Am. B 22, 1681-1690 (2005).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Influence of the backflow effect on the orientational dynamics induced by light in nematics," Phys. Rev. E 71, 051711 (2005).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Orientational dynamics induced by circularly polarized light in nematic liquid crystals," Mol. Cryst. Liq. Cryst. 421, 117-131 (2004).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Pattern-forming instability induced by light in pure and dye-doped nematic liquid crystals," Phys. Rev. E 66, 031707 (2002).
[CrossRef]

Kroo, N.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].

Liu, T. H.

Lloyd, A. D.

I. Jánossy, A. D. Lloyd, and B. S. Wherrett, "Anomalous optical Fréedericksz transition in an absorbing liquid crystal," Mol. Cryst. Liq. Cryst. 179, 1-12 (1990).

Maddalena, P.

L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
[CrossRef]

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
[CrossRef] [PubMed]

Marrucci, L.

L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
[CrossRef]

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
[CrossRef] [PubMed]

Ong, H. L.

H. L. Ong, "Optically induced Fréedericksz transition and bistability in a nematic liquid crystal," Phys. Rev. A 28, 2393-2407 (1983).
[CrossRef]

Piccirillo, B.

A. Vella, A. Setaro, B. Piccirillo, and E. Santamato, "On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light," Phys. Rev. E 67, 051704 (2003).
[CrossRef]

A. Vella, B. Piccirillo, and E. Santamato, "Coupled-mode approach to the nonlinear dynamics induced by an elliptically polarized laser field in liquid crystals at normal incidence," Phys. Rev. E 65, 031706 (2002).
[CrossRef]

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, "Orbital and spin photon angular momentum transfer in liquid crystals," Phys. Rev. Lett. 86, 2285-2288 (2001).
[CrossRef] [PubMed]

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

Romagnoli, M.

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
[CrossRef] [PubMed]

Russo, G.

V. Carbone, G. Cipparrone, and G. Russo, "Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films," Phys. Rev. E 63, 051701 (2001).
[CrossRef]

Sambles, J. R.

For some recent research, see S. A. Jewell and J. R. Sambles, "Observation of backflow in the switch-on dynamics of hybrid aligned nematic," Appl. Phys. Lett. 84, 46-48 (2004).
[CrossRef]

Santamato, E.

A. Vella, A. Setaro, B. Piccirillo, and E. Santamato, "On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light," Phys. Rev. E 67, 051704 (2003).
[CrossRef]

A. Vella, B. Piccirillo, and E. Santamato, "Coupled-mode approach to the nonlinear dynamics induced by an elliptically polarized laser field in liquid crystals at normal incidence," Phys. Rev. E 65, 031706 (2002).
[CrossRef]

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, "Orbital and spin photon angular momentum transfer in liquid crystals," Phys. Rev. Lett. 86, 2285-2288 (2001).
[CrossRef] [PubMed]

L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
[CrossRef]

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
[CrossRef] [PubMed]

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
[CrossRef] [PubMed]

E. Santamato, "Giant optical nonlinearities in nematic liquid crystals," in Nonlinear Optical Material and Devices for Applications in Information Technology, A.Miller, K.R.Welford, and B.Daino, eds. (Kluwer Academic, 1995), pp. 103-139.
[CrossRef]

Setaro, A.

A. Vella, A. Setaro, B. Piccirillo, and E. Santamato, "On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light," Phys. Rev. E 67, 051704 (2003).
[CrossRef]

Settembre, M.

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
[CrossRef] [PubMed]

Shen, Y. R.

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
[CrossRef] [PubMed]

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
[CrossRef] [PubMed]

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, "Laser-induced diffraction rings from a nematic-liquid-crystal film," Opt. Lett. 6, 411-413 (1981).
[PubMed]

Simoni, F.

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

F. Simoni, Nonlinear Optical Properties of Liquid Crystals and Polymer Dispersed Liquid Crystals (World Scientific, 1997).
[CrossRef]

Sobolev, N. N.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).

Sukhorukov, A. P.

A. S. Zolot'ko and A. P. Sukhorukov, "Fréedericksz transition induced in nematic liquid-crystal by circularly polarized-light wave," Pis/ma Zh. Eksp. Teor. Fiz. 52, 707-710 (1990) A. S. Zolot'ko and A. P. Sukhorukov, [JETP Lett. 52, 62-65 (1990)].

Sukhov, A. V.

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, "Orientational optical nonlinearity of liquid-crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Tabiryan, N.

B. Y. Zel'dovich and N. Tabiryan, "Theory of optically induced Fréedericksz transition," Zh. Eksp. Teor. Fiz. 82, 1126-1146 (1982) B. Y. Zel'dovich and N. Tabiryan, [Sov. Phys. JETP 55, 656-666 (1982)].

Tabiryan, N. V.

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
[CrossRef]

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, "Orientational optical nonlinearity of liquid-crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Tabiryan-Murazyan, A. L.

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

Toscano, C.

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, "Orbital and spin photon angular momentum transfer in liquid crystals," Phys. Rev. Lett. 86, 2285-2288 (2001).
[CrossRef] [PubMed]

Tschudi, T.

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

Umeton, C.

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
[CrossRef]

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

Vella, A.

A. Vella, A. Setaro, B. Piccirillo, and E. Santamato, "On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light," Phys. Rev. E 67, 051704 (2003).
[CrossRef]

A. Vella, B. Piccirillo, and E. Santamato, "Coupled-mode approach to the nonlinear dynamics induced by an elliptically polarized laser field in liquid crystals at normal incidence," Phys. Rev. E 65, 031706 (2002).
[CrossRef]

Versace, C.

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
[CrossRef]

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

Vetrano, F.

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, "Orbital and spin photon angular momentum transfer in liquid crystals," Phys. Rev. Lett. 86, 2285-2288 (2001).
[CrossRef] [PubMed]

Wherrett, B. S.

I. Jánossy, A. D. Lloyd, and B. S. Wherrett, "Anomalous optical Fréedericksz transition in an absorbing liquid crystal," Mol. Cryst. Liq. Cryst. 179, 1-12 (1990).

Wu, S. T.

I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).
[CrossRef]

Yan, P. Y.

Zel'dovich, B. Y.

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, "Orientational optical nonlinearity of liquid-crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

B. Y. Zel'dovich and N. Tabiryan, "Theory of optically induced Fréedericksz transition," Zh. Eksp. Teor. Fiz. 82, 1126-1146 (1982) B. Y. Zel'dovich and N. Tabiryan, [Sov. Phys. JETP 55, 656-666 (1982)].

Zolot'ko, A. S.

A. S. Zolot'ko and A. P. Sukhorukov, "Fréedericksz transition induced in nematic liquid-crystal by circularly polarized-light wave," Pis/ma Zh. Eksp. Teor. Fiz. 52, 707-710 (1990) A. S. Zolot'ko and A. P. Sukhorukov, [JETP Lett. 52, 62-65 (1990)].

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].

Appl. Phys. Lett. (1)

For some recent research, see S. A. Jewell and J. R. Sambles, "Observation of backflow in the switch-on dynamics of hybrid aligned nematic," Appl. Phys. Lett. 84, 46-48 (2004).
[CrossRef]

J. Opt. Soc. Am. B (2)

JETP Lett. (2)

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, "Light-induced Fréedericksz transition in an MBBA crystal," Pis/ma Zh. Eksp. Teor. Fiz. 34, 263-267 (1981) A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, and L. Csillag, [JETP Lett. 34, 250-254 (1981)].

A. S. Zolot'ko and A. P. Sukhorukov, "Fréedericksz transition induced in nematic liquid-crystal by circularly polarized-light wave," Pis/ma Zh. Eksp. Teor. Fiz. 52, 707-710 (1990) A. S. Zolot'ko and A. P. Sukhorukov, [JETP Lett. 52, 62-65 (1990)].

Mol. Cryst. Liq. Cryst. (3)

D. O. Krimer, G. Demeter, and L. Kramer, "Orientational dynamics induced by circularly polarized light in nematic liquid crystals," Mol. Cryst. Liq. Cryst. 421, 117-131 (2004).
[CrossRef]

N. V. Tabiryan, A. V. Sukhov, and B. Y. Zel'dovich, "Orientational optical nonlinearity of liquid-crystals," Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

I. Jánossy, A. D. Lloyd, and B. S. Wherrett, "Anomalous optical Fréedericksz transition in an absorbing liquid crystal," Mol. Cryst. Liq. Cryst. 179, 1-12 (1990).

Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A (1)

G. Cipparrone, D. Duca, C. Versace, C. Umeton, and N. V. Tabiryan, "Direct optical measurements of the ratio K3/gamma1 in nematic liquid crystals," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 266, 263-268 (1995).
[CrossRef]

Opt. Commun. (2)

E. Brasselet and T. V. Galstian, "Optical control of molecular orientational dynamics in liquid crystals," Opt. Commun. 186, 291-302 (2000).
[CrossRef]

N. V. Tabiryan, A. L. Tabiryan-Murazyan, V. Carbone, G. Cipparrone, C. Umeton, C. Versace, and T. Tschudi, "Temporal instability due to competing spatial patterns in liquid crystals in the light field," Opt. Commun. 154, 70-74 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "New laser induced spatio-temporal transition in nematics," Phys. Lett. A 299, 212-216 (2002).
[CrossRef]

Phys. Rev. A (2)

L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, "Self-stimulated light scattering in nematic liquid crystals: theory and experiment," Phys. Rev. A 46, 4859-4868 (1992).
[CrossRef]

H. L. Ong, "Optically induced Fréedericksz transition and bistability in a nematic liquid crystal," Phys. Rev. A 28, 2393-2407 (1983).
[CrossRef]

Phys. Rev. E (10)

D. O. Krimer, G. Demeter, and L. Kramer, "Influence of the backflow effect on the orientational dynamics induced by light in nematics," Phys. Rev. E 71, 051711 (2005).
[CrossRef]

D. O. Krimer, G. Demeter, and L. Kramer, "Pattern-forming instability induced by light in pure and dye-doped nematic liquid crystals," Phys. Rev. E 66, 031707 (2002).
[CrossRef]

A. Vella, A. Setaro, B. Piccirillo, and E. Santamato, "On-off intermittency in chaotic rotation induced in liquid crystals by competition between spin and orbital angular momentum of light," Phys. Rev. E 67, 051704 (2003).
[CrossRef]

V. Carbone, G. Cipparrone, and G. Russo, "Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films," Phys. Rev. E 63, 051701 (2001).
[CrossRef]

A. Vella, B. Piccirillo, and E. Santamato, "Coupled-mode approach to the nonlinear dynamics induced by an elliptically polarized laser field in liquid crystals at normal incidence," Phys. Rev. E 65, 031706 (2002).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry," Phys. Rev. E 67, 031706 (2003).
[CrossRef]

E. Brasselet, B. Doyon, T. V. Galstian, and L. J. Dubé, "Optically induced dynamics in nematic liquid crystals: The role of finite beam size," Phys. Rev. E 69, 021701 (2004).
[CrossRef]

G. Cipparrone, V. Carbone, C. Versace, C. Umeton, R. Bartolino, and F. Simoni, "Optically induced chaotic behavior in nematic liquid-crystal films," Phys. Rev. E 47, 3741-3744 (1993).
[CrossRef]

G. Demeter, "Complex nonlinear behavior in optically excited nematic liquid crystals," Phys. Rev. E 61, 6678-6688 (2000).
[CrossRef]

G. Demeter and L. Kramer, "Numerical investigation of optically induced director oscillations in nematic liquid crystals," Phys. Rev. E 64, 020701 (R) (2001).
[CrossRef]

Phys. Rev. Lett. (4)

G. Demeter and L. Kramer, "Transition to chaos via gluing bifurcations in optically excited nematic liquid crystals," Phys. Rev. Lett. 83, 4744-4747 (1999).
[CrossRef]

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, "Orbital and spin photon angular momentum transfer in liquid crystals," Phys. Rev. Lett. 86, 2285-2288 (2001).
[CrossRef] [PubMed]

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, "Laser-induced nonlinear dynamics in a nematic liquid-crystal film," Phys. Rev. Lett. 64, 1377-1380 (1990).
[CrossRef] [PubMed]

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, "Collective rotation of molecules driven by the angular momentum of light in a nematic film," Phys. Rev. Lett. 57, 2423-2426 (1986).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

B. Y. Zel'dovich and N. Tabiryan, "Theory of optically induced Fréedericksz transition," Zh. Eksp. Teor. Fiz. 82, 1126-1146 (1982) B. Y. Zel'dovich and N. Tabiryan, [Sov. Phys. JETP 55, 656-666 (1982)].

Other (12)

From Merck datasheets. The refractive indices are measured at 20°C and lambda=589 nm.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, 1993).

From the weakly nonlinear stability analysis, we find that the nature of the OFT is governed by the sign of the coefficient C=k1-(9/4)(epsilon_a/epsilon_||). C<0 corresponds to a subcritical OFT (i.e., first order), whereas C>0 corresponds to a supercritical OFT (i.e., second order). Incidentally, this criterion is identical to the one derived by Ong in the case of OFT under linearly polarized light.33 With the present parameters, C=0.154 and the OFT is actually supercritical. However, the solution branch turns over and becomes subcritical (and unstable) already at rho=1+deltarho where deltarho ~ or = 10-6. This explains why the OFT appears to be subcritical on the scale used in Fig. 2. In fact, although deltarho increases when the cell thickness is decreased, even at L=10 µm, the subcritical region is still too small (deltarho ~ or = 10-4) to be observed experimentally.

E. Brasselet, "Comment on 'Numerical investigation of optically induced director oscillations in nematic liquid crystals/," Phys. Rev. E (to be published).

I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).
[CrossRef]

E. Santamato, "Giant optical nonlinearities in nematic liquid crystals," in Nonlinear Optical Material and Devices for Applications in Information Technology, A.Miller, K.R.Welford, and B.Daino, eds. (Kluwer Academic, 1995), pp. 103-139.
[CrossRef]

F. Simoni, Nonlinear Optical Properties of Liquid Crystals and Polymer Dispersed Liquid Crystals (World Scientific, 1997).
[CrossRef]

For a classification of the different types of bifurcation, the reader is invited to consult J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields (Springer-Verlag, 1983). See also Refs. and .
[CrossRef]

J. Hale and H. Koçak, Dynamics and Bifurcations (Springer-Verlag, 1991).
[CrossRef]

P. Glendinning, Stability, Instability and Chaos (Cambridge U. Press, 1996).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).

C. Brosseau, Fundamentals of Polarized Light: a Statistical Optics Approach (Wiley, 1998).

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Figures (12)

Fig. 1
Fig. 1

(a) Interaction geometry in the Cartesian coordinate system ( x , y , z ) , where k is the wave vector of the circularly polarized excitation light, NLC is the nematic liquid-crystal film, and L is the cell thickness. (b) Representation of the director n = ( sin ϴ cos Φ , sin ϴ sin Φ , cos ϴ ) in terms of the standard spherical angles ϴ and Φ.

Fig. 2
Fig. 2

(a) Δ 2 π on a log scale versus ρ for ρ < 2 and Δ < 50 π . (b) Δ 2 π on a linear scale versus ρ for ρ < 4 and Δ < 3 π . Solid (dashed) curves correspond to stable (unstable) solutions.

Fig. 3
Fig. 3

Experimental setup. Laser: Verdi laser (from Coherent) operating at 532 nm; BS, beam splitter; λ 4 , quarter-wave plate; L, lens; d, diaphragm; PBS, polarizing beam splitter; D i , photodetectors.

Fig. 4
Fig. 4

(a) Experimental I center ( ρ ) t (filled circles). The vertical bars are the standard deviation of I center ( t ) for the corresponding value of ρ, and the solid curve is to guide the eye of the extrema of I center ( t ) . (b) Calculated Δ ( ρ ) ( Δ < 3 π ) .

Fig. 5
Fig. 5

Precession frequency f 0 ( ρ ) . (a) Experiment (filled circles). The solid curve is to guide the eye. (b) Theory.

Fig. 6
Fig. 6

Director trajectory at ρ = 1.55 . (a) Quasi-periodic behavior in the laboratory frame ( n x , n y ) . (b) Periodic limit cycle in the f 0 -rotating frame ( n x rot , n y rot ) .

Fig. 7
Fig. 7

Scaling law for the amplitude A of the limit cycle born at the transition UP 1 NUP . Experimental data (filled circles) fitted by ( ρ ρ 2 ) γ near ρ 2 , whose best fit gives γ = 0.46 ± 0.08 . Inset: theory (solid curve) by which the best fit (dashed curve) near ρ 2 gives γ = 1 2 .

Fig. 8
Fig. 8

Scaling law for the frequency of the limit cycle born through the transition UP 1 NUP . Experiment (filled circles) with linear fit near the bifurcation threshold (dashed line). Inset: theory (solid curve) with linear fit near ρ 2 (dashed line).

Fig. 9
Fig. 9

Reconstructed experimental nutation phase space X ( t + τ d ) versus X ( t ) , where X = I center ρ and τ d is a time delay. Light gray dots, the UP1 state between the OFT and the secondary Hopf instability [ ρ ( 1 + ρ 2 ) 2 ] ; black dots, the NUP state between the Hopf and the homoclinic bifurcation [ ρ ( ρ 2 + ρ 3 ) 2 ] ; and dark gray dots, the UP2 state just above the homoclinic bifurcation at ρ = ρ 3 . The time delay is τ d = 6 s .

Fig. 10
Fig. 10

Characterization of the homoclinic bifurcation f 1 1 ( ρ ) = O [ ln ( ρ 3 ρ ) ] near ρ 3 . The solid curve is the best fit to the theoretically calculated values (filled circles).

Fig. 11
Fig. 11

Homoclinic trajectory in (a) the laboratory frame ( n x , n y ) and (b) the f 0 -rotating frame ( n x rot , n y rot ) just below ρ = ρ 3 ( ρ = 1.748542389055 ) .

Fig. 12
Fig. 12

Calculated dynamics just below ρ = ρ 3    ( ρ = 1.748542389055 ) . (a) Phase shift Δ ( t ) . (b) Instantaneous angular velocity Ω ( t ) = d Φ 0 d t .

Tables (1)

Tables Icon

Table 1 Calculated Values of the Thresholds ρ 2 and ρ 3 versus the Number of Modes N and M Retained in the Modal Expansion Defined in the Text

Equations (27)

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ϴ ( z , t ) = n = 1 ϴ n ( t ) sin ( n π z L ) ,
Φ ( z , t ) = Φ 0 ( t ) + n = 1 Φ n ( t ) sin [ ( n + 1 ) π z L ] sin ( π z L ) .
f 0 = 1 2 π ( d Φ 0 d t ) UP .
Δ ( t ) = 2 π λ 0 L [ n e ( z , t ) n o ] d z .
n x rot = n y sin ( 2 π f 0 t ) + n x cos ( 2 π f 0 t ) ,
n y rot = n y cos ( 2 π f 0 t ) n x sin ( 2 π f 0 t ) .
S ( Δ ) = { m f 1 } ,
S ( n x , y ) = { f 0 , m f 1 ± f 0 } ,
S ( I x , y ) = { 2 f 0 , m f 1 ± 2 f 0 } .
ϴ τ = [ 1 ( 1 k 1 ) sin 2 ϴ ] 1 π 2 2 ϴ ξ 2 sin 2 ϴ 2 { ( 1 k 1 ) ( 1 π ϴ ξ ) 2 + [ 1 2 ( 1 k 2 ) sin 2 ϴ ] ( 1 π Φ ξ ) 2 2 ρ n e 4 n o 4 A e 2 } ,
Φ τ = 1 π 2 sin 2 ϴ ξ { [ 1 ( 1 k 2 ) sin 2 ϴ ] sin 2 ϴ Φ ξ } + ρ n e 2 n o 2 [ A e A o * exp [ i ψ ( ξ , τ ) ] + c . c . ] .
E o ( ξ , τ ) = A o ( ξ , τ ) exp ( i κ 0 n o ξ ) ,
E e ( ξ , τ ) = A e ( ξ , τ ) exp [ i κ 0 0 ξ n e ( ξ , τ ) d ξ ] ,
n e ( ξ , τ ) = n o n E ( n E 2 cos 2 ϴ + n o 2 sin 2 ϴ ) 1 2 ,
A o ξ = Φ ξ n c n o exp [ i ψ ( ξ , τ ) ] A e ,
A e ξ = 1 2 n e n e ξ A e + Φ ξ n o n e exp [ i ψ ( ξ , τ ) ] A o ,
ψ ( ξ , τ ) = κ 0 0 ξ [ n e ( ξ , τ ) n o ] d ξ .
Δ ( τ ) = ψ ( 1 , τ ) .
d ϴ n d τ = 2 0 1 ϴ τ sin ( n π ξ ) d ξ ,
d Φ n d τ = 2 0 1 Φ τ sin [ ( n + 1 ) π ξ ] sin ( π ξ ) d ξ .
ϴ ( 0 , τ ) = ϴ ( 1 , τ ) = 0 ,
Φ ξ ( 0 , τ ) = Φ ξ ( 1 , τ ) = 0
A o ( 0 , τ ) 2 = 1 2 { 1 cos [ 2 Φ ( 0 , τ ) ] cos 2 χ } ,
A e ( 0 , τ ) 2 = 1 2 { 1 + cos [ 2 Φ ( 0 , τ ) ] cos 2 χ } ,
A e ( 0 , τ ) A o ( 0 , τ ) * = 1 2 { sin [ 2 Φ ( 0 , τ ) ] cos 2 χ + i sin 2 χ } ,
A e ( 0 , τ ) 2 = A o ( 0 , τ ) 2 = 1 2 ,
A e ( 0 , τ ) A o ( 0 , τ ) * = i 2 .

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