Abstract

We present the experimental results of the all-optical control of instabilities generated by laser irradiation in a nematic liquid-crystal film. Because of interactions with an incident linearly polarized optical field at a small angle of incidence, the system undergoes a sequence of successive bifurcations toward a stochastic regime. Control of the dynamics is achieved through the addition of a counterpropagating laser beam that is orthogonally polarized with respect to the inducing beam. The control strategy starts with putting the system into a given dynamic state through the incident beam and then switching on the control beam. Below the first bifurcation a weak control beam is enough to drive the system toward a fixed point, thus stopping the nonlinear dynamics. Above the first bifurcation, the behavior of the system strongly depends on the value of the intensity of the control beam used, and different dynamic regimes can be observed and investigated.

© 2004 Optical Society of America

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  1. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196–1199 (1990).
    [CrossRef] [PubMed]
  2. K. Pyragas, “Control of chaos via extended delay feedback,” Phys. Lett. A 206, 323–330 (1995).
    [CrossRef]
  3. S. Boccaletti, C. Grebogi, Y. C. Lai, and D. Maza, “The control of chaos: Theory and applications,” Phys. Rep. 329, 103–197 (2000).
    [CrossRef]
  4. E. Ott, Chaos in Dynamical Systems (Cambridge U. Press, Cambridge, 1997).
  5. F. T. Arecchi, E. Allaria, A. Di Garbo, and L. S. Tsimring, “Delayed self-synchronization in homoclinic chaos,” Phys. Rev. E 65, 046237 (2002).
    [CrossRef]
  6. G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).
  7. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1995).
  8. N. V. Tabiryan, A. Sukhov, and B. Ya. Zel’dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1–131 (1986).
    [CrossRef]
  9. E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, “Experimental study of the molecular reorientation induced by the ordinary wave in nematic liquid crystal film,” Liq. Cryst. 25, 357–362 (1998).
    [CrossRef]
  10. V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
    [CrossRef]
  11. G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
    [CrossRef]
  12. 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]
  13. P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, New York, 1993), and references therein.
  14. 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]
  15. G. Demeter and L. Kramer, “Numerical investigation of optically induced director oscillations in nematic liquid crystals,” Phys. Rev. E 64, 020701 (2001).
    [CrossRef]
  16. A. Arneodo, P. Coullet, and C. Tresser, “A possible new mechanism for the onset of turbulence,” Phys. Lett. A 81, 197–201 (1981).
    [CrossRef]
  17. P. Holmes, J. L. Lumley, and G. Barkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge U. Press, Cambridge, 1996).
  18. G. Russo, G. Cipparrone, and V. Carbone, “Controlling the nonlinear dynamics during the light induced reorientation in nematic liquid crystal films,” Europhys. Lett. 63, 180–185 (2003).
    [CrossRef]

2003 (1)

G. Russo, G. Cipparrone, and V. Carbone, “Controlling the nonlinear dynamics during the light induced reorientation in nematic liquid crystal films,” Europhys. Lett. 63, 180–185 (2003).
[CrossRef]

2002 (1)

F. T. Arecchi, E. Allaria, A. Di Garbo, and L. S. Tsimring, “Delayed self-synchronization in homoclinic chaos,” Phys. Rev. E 65, 046237 (2002).
[CrossRef]

2001 (2)

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 (2001).
[CrossRef]

2000 (2)

S. Boccaletti, C. Grebogi, Y. C. Lai, and D. Maza, “The control of chaos: Theory and applications,” Phys. Rep. 329, 103–197 (2000).
[CrossRef]

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
[CrossRef]

1999 (2)

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

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)

E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, “Experimental study of the molecular reorientation induced by the ordinary wave in nematic liquid crystal film,” Liq. Cryst. 25, 357–362 (1998).
[CrossRef]

1996 (1)

V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
[CrossRef]

1995 (1)

K. Pyragas, “Control of chaos via extended delay feedback,” Phys. Lett. A 206, 323–330 (1995).
[CrossRef]

1990 (1)

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196–1199 (1990).
[CrossRef] [PubMed]

1986 (1)

N. V. Tabiryan, A. Sukhov, and B. Ya. Zel’dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1–131 (1986).
[CrossRef]

1981 (1)

A. Arneodo, P. Coullet, and C. Tresser, “A possible new mechanism for the onset of turbulence,” Phys. Lett. A 81, 197–201 (1981).
[CrossRef]

Allaria, E.

F. T. Arecchi, E. Allaria, A. Di Garbo, and L. S. Tsimring, “Delayed self-synchronization in homoclinic chaos,” Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, E. Allaria, A. Di Garbo, and L. S. Tsimring, “Delayed self-synchronization in homoclinic chaos,” Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Arneodo, A.

A. Arneodo, P. Coullet, and C. Tresser, “A possible new mechanism for the onset of turbulence,” Phys. Lett. A 81, 197–201 (1981).
[CrossRef]

Bartolino, R.

V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
[CrossRef]

Boccaletti, S.

S. Boccaletti, C. Grebogi, Y. C. Lai, and D. Maza, “The control of chaos: Theory and applications,” Phys. Rep. 329, 103–197 (2000).
[CrossRef]

Carbone, V.

G. Russo, G. Cipparrone, and V. Carbone, “Controlling the nonlinear dynamics during the light induced reorientation in nematic liquid crystal films,” Europhys. Lett. 63, 180–185 (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]

V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
[CrossRef]

Car-bone, V.

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
[CrossRef]

Cipparrone, G.

G. Russo, G. Cipparrone, and V. Carbone, “Controlling the nonlinear dynamics during the light induced reorientation in nematic liquid crystal films,” Europhys. Lett. 63, 180–185 (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]

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
[CrossRef]

V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
[CrossRef]

Coullet, P.

A. Arneodo, P. Coullet, and C. Tresser, “A possible new mechanism for the onset of turbulence,” Phys. Lett. A 81, 197–201 (1981).
[CrossRef]

Demeter, G.

G. Demeter and L. Kramer, “Numerical investigation of optically induced director oscillations in nematic liquid crystals,” Phys. Rev. E 64, 020701 (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]

Di Garbo, A.

F. T. Arecchi, E. Allaria, A. Di Garbo, and L. S. Tsimring, “Delayed self-synchronization in homoclinic chaos,” Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Firth, W. J.

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

Grebogi, C.

S. Boccaletti, C. Grebogi, Y. C. Lai, and D. Maza, “The control of chaos: Theory and applications,” Phys. Rep. 329, 103–197 (2000).
[CrossRef]

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196–1199 (1990).
[CrossRef] [PubMed]

Harkness, G. K.

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

Kramer, L.

G. Demeter and L. Kramer, “Numerical investigation of optically induced director oscillations in nematic liquid crystals,” Phys. Rev. E 64, 020701 (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]

Lai, Y. C.

S. Boccaletti, C. Grebogi, Y. C. Lai, and D. Maza, “The control of chaos: Theory and applications,” Phys. Rep. 329, 103–197 (2000).
[CrossRef]

Lord, A.

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

Maddalena, P.

E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, “Experimental study of the molecular reorientation induced by the ordinary wave in nematic liquid crystal film,” Liq. Cryst. 25, 357–362 (1998).
[CrossRef]

Marrucci, L.

E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, “Experimental study of the molecular reorientation induced by the ordinary wave in nematic liquid crystal film,” Liq. Cryst. 25, 357–362 (1998).
[CrossRef]

Martin, R.

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

Maza, D.

S. Boccaletti, C. Grebogi, Y. C. Lai, and D. Maza, “The control of chaos: Theory and applications,” Phys. Rep. 329, 103–197 (2000).
[CrossRef]

Oppo, G. L.

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

Ott, E.

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196–1199 (1990).
[CrossRef] [PubMed]

Piccirillo, B.

E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, “Experimental study of the molecular reorientation induced by the ordinary wave in nematic liquid crystal film,” Liq. Cryst. 25, 357–362 (1998).
[CrossRef]

Pyragas, K.

K. Pyragas, “Control of chaos via extended delay feedback,” Phys. Lett. A 206, 323–330 (1995).
[CrossRef]

Russo, G.

G. Russo, G. Cipparrone, and V. Carbone, “Controlling the nonlinear dynamics during the light induced reorientation in nematic liquid crystal films,” Europhys. Lett. 63, 180–185 (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]

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
[CrossRef]

Santamato, E.

E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, “Experimental study of the molecular reorientation induced by the ordinary wave in nematic liquid crystal film,” Liq. Cryst. 25, 357–362 (1998).
[CrossRef]

Scroggie, A. J.

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

Strangi, G.

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
[CrossRef]

Sukhov, A.

N. V. Tabiryan, A. Sukhov, and B. Ya. Zel’dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1–131 (1986).
[CrossRef]

Tabiryan, N. V.

N. V. Tabiryan, A. Sukhov, and B. Ya. Zel’dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1–131 (1986).
[CrossRef]

Tresser, C.

A. Arneodo, P. Coullet, and C. Tresser, “A possible new mechanism for the onset of turbulence,” Phys. Lett. A 81, 197–201 (1981).
[CrossRef]

Tsimring, L. S.

F. T. Arecchi, E. Allaria, A. Di Garbo, and L. S. Tsimring, “Delayed self-synchronization in homoclinic chaos,” Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Umeton, C.

V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
[CrossRef]

Versace, C.

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
[CrossRef]

V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
[CrossRef]

Yorke, J. A.

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196–1199 (1990).
[CrossRef] [PubMed]

Zel’dovich, B. Ya.

N. V. Tabiryan, A. Sukhov, and B. Ya. Zel’dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1–131 (1986).
[CrossRef]

Chaos Solitons Fractals (1)

G. L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, and W. J. Firth, “Control of spatio-temporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

Europhys. Lett. (1)

G. Russo, G. Cipparrone, and V. Carbone, “Controlling the nonlinear dynamics during the light induced reorientation in nematic liquid crystal films,” Europhys. Lett. 63, 180–185 (2003).
[CrossRef]

Liq. Cryst. (1)

E. Santamato, P. Maddalena, L. Marrucci, and B. Piccirillo, “Experimental study of the molecular reorientation induced by the ordinary wave in nematic liquid crystal film,” Liq. Cryst. 25, 357–362 (1998).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

N. V. Tabiryan, A. Sukhov, and B. Ya. Zel’dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1–131 (1986).
[CrossRef]

Opt. Commun. (1)

G. Cipparrone, G. Russo, C. Versace, G. Strangi, and V. Car-bone, “Polarimetric study of the optically induced dynamical behavior in nematic liquid crystal films,” Opt. Commun. 173, 1–10 (2000).
[CrossRef]

Phys. Lett. A (2)

A. Arneodo, P. Coullet, and C. Tresser, “A possible new mechanism for the onset of turbulence,” Phys. Lett. A 81, 197–201 (1981).
[CrossRef]

K. Pyragas, “Control of chaos via extended delay feedback,” Phys. Lett. A 206, 323–330 (1995).
[CrossRef]

Phys. Rep. (1)

S. Boccaletti, C. Grebogi, Y. C. Lai, and D. Maza, “The control of chaos: Theory and applications,” Phys. Rep. 329, 103–197 (2000).
[CrossRef]

Phys. Rev. E (4)

F. T. Arecchi, E. Allaria, A. Di Garbo, and L. S. Tsimring, “Delayed self-synchronization in homoclinic chaos,” Phys. Rev. E 65, 046237 (2002).
[CrossRef]

V. Carbone, G. Cipparrone, C. Versace, C. Umeton, and R. Bartolino, “Multifractal structure and intermittency of laser-generated turbulence in nematic liquid crystals,” Phys. Rev. E 54, 6948–6951 (1996).
[CrossRef]

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

Phys. Rev. Lett. (2)

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]

E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Phys. Rev. Lett. 64, 1196–1199 (1990).
[CrossRef] [PubMed]

Other (4)

E. Ott, Chaos in Dynamical Systems (Cambridge U. Press, Cambridge, 1997).

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1995).

P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, New York, 1993), and references therein.

P. Holmes, J. L. Lumley, and G. Barkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge U. Press, Cambridge, 1996).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup: M’s, mirrors; L1–L3, lenses; BS, beam splitter; P1–P3, polarizers; S, shutter; λ/2, half-wave plate; α, incidence angle. The NLC sample is also shown.

Fig. 2
Fig. 2

Time evolution of ellipticity e(t) for (a) Is=12,300 W/cm2 and R=0.01. The control is turned on at time t=2400 s after the start of the measurement.

Fig. 3
Fig. 3

Time evolution of ellipticity e(t) for (a) Is=13,700 W/cm2 and R=0.01. The control is turned on at time t=2400 s after the start of the measurement.

Fig. 4
Fig. 4

Time evolution of ellipticity e(t) for (a) Is=14,300 W/cm2 and R=0.01.

Fig. 5
Fig. 5

Time evolution of ellipticity e(t) for (a) Is=16,400 W/cm2 and (a) R=0.01, (b) R=0.10, (c) R=0.15, (d) R=0.20. The control is turned on at times (a) t=2400 s, (b) t=1710 s, (c) t=1680 s, (d) t=1200 s after the start of the measurement.

Fig. 6
Fig. 6

Time evolution of ellipticity e(t) for Is=19,900 W/cm2 and (a) R=0.01, (b) R=0.10, (c) R=0.15, (d) R=0.17. The control is turned on at times (a) t=2040 s, (b) t=2160 s, (c) t=1920 s, (d) t=1200 s after the start of the measurement. Insets, enlargement of the time series for (c) 2900 s<t<3000 s and (d) 1700 s<t<1800 s.

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