Abstract

The half-leaky guided-mode (HLGM) technique has been used to explore a hybrid-aligned nematic (HAN) liquid-crystal cell. With a suitably oriented cell the optical response of the system, as a function of incident angle, has some unusual features. It is found that beyond a particular angle of incidence, with light incident from the homeotropically aligned side, the apparent mode spacing increases with increasing angle, which is entirely opposite to that found for an isotropic slab of material. This clearly indicates that the effective cell thickness varies with incident angles, an effect caused by the director profile within the cell, leading to bent trajectories for the beams propagating inside the cell. For this situation the depths of the reflectivity minima associated with excitation of the waveguide modes are particularly sensitive to the imaginary parts of the permittivities of the liquid crystal. This has enabled the two imaginary parts of the parallel and perpendicular permittivities of the liquid crystals to be determined separately. The technique is a very useful and accurate method for determining the whole optical tensor of the liquid crystal.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. A. Jewell and J. R. Sambles, "Fully-leaky guided mode measurement of surface polarization in a HAN liquid crystal cell," J. Appl. Phys. 92, 19-24 (2002).
    [CrossRef]
  2. S. A. Jewell and J. R. Sambles, "Backflow in the relaxation of a hybrid aligned nematic cell," Appl. Phys. Lett. 82, 3156-3158 (2003).
    [CrossRef]
  3. S. A. Jewell and J. R. Sambles, "Optical characterization of a dual-frequency hybrid aligned nematic liquid crystal cell," Opt. Express 13, 2627-2633 (2005).
    [CrossRef] [PubMed]
  4. J. A. Olivares, R. F. Rodriguez, and J. A. Reyes, "Ray tracing and reflectivity measurements in nematic hybrid cells," Opt. Commun. 221, 223-239 (2003).
    [CrossRef]
  5. C. I. Mendoza, J. A. Olivares, and J. A. Reyes, "Electrically controlled total internal reflection in nematic hybrid cells," Phys. Rev. E 70, 062701 (2004).
    [CrossRef]
  6. F. Yang and J. R. Sambles, "The optical tensor configuration in a surface stabilized ferroelectric liquid crystal determined by using half leaky guided modes," Liq. Cryst. 13, 1-13 (1993).
    [CrossRef]
  7. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic, 1983).
  8. D. Y. K. Ko and J. R. Sambles, "Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals," J. Opt. Soc. Am. A 5, 1863-1866 (1988).
    [CrossRef]

2005

2004

C. I. Mendoza, J. A. Olivares, and J. A. Reyes, "Electrically controlled total internal reflection in nematic hybrid cells," Phys. Rev. E 70, 062701 (2004).
[CrossRef]

2003

J. A. Olivares, R. F. Rodriguez, and J. A. Reyes, "Ray tracing and reflectivity measurements in nematic hybrid cells," Opt. Commun. 221, 223-239 (2003).
[CrossRef]

S. A. Jewell and J. R. Sambles, "Backflow in the relaxation of a hybrid aligned nematic cell," Appl. Phys. Lett. 82, 3156-3158 (2003).
[CrossRef]

2002

S. A. Jewell and J. R. Sambles, "Fully-leaky guided mode measurement of surface polarization in a HAN liquid crystal cell," J. Appl. Phys. 92, 19-24 (2002).
[CrossRef]

1993

F. Yang and J. R. Sambles, "The optical tensor configuration in a surface stabilized ferroelectric liquid crystal determined by using half leaky guided modes," Liq. Cryst. 13, 1-13 (1993).
[CrossRef]

1988

Jewell, S. A.

S. A. Jewell and J. R. Sambles, "Optical characterization of a dual-frequency hybrid aligned nematic liquid crystal cell," Opt. Express 13, 2627-2633 (2005).
[CrossRef] [PubMed]

S. A. Jewell and J. R. Sambles, "Backflow in the relaxation of a hybrid aligned nematic cell," Appl. Phys. Lett. 82, 3156-3158 (2003).
[CrossRef]

S. A. Jewell and J. R. Sambles, "Fully-leaky guided mode measurement of surface polarization in a HAN liquid crystal cell," J. Appl. Phys. 92, 19-24 (2002).
[CrossRef]

Ko, D. Y. K.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic, 1983).

Mendoza, C. I.

C. I. Mendoza, J. A. Olivares, and J. A. Reyes, "Electrically controlled total internal reflection in nematic hybrid cells," Phys. Rev. E 70, 062701 (2004).
[CrossRef]

Olivares, J. A.

C. I. Mendoza, J. A. Olivares, and J. A. Reyes, "Electrically controlled total internal reflection in nematic hybrid cells," Phys. Rev. E 70, 062701 (2004).
[CrossRef]

J. A. Olivares, R. F. Rodriguez, and J. A. Reyes, "Ray tracing and reflectivity measurements in nematic hybrid cells," Opt. Commun. 221, 223-239 (2003).
[CrossRef]

Reyes, J. A.

C. I. Mendoza, J. A. Olivares, and J. A. Reyes, "Electrically controlled total internal reflection in nematic hybrid cells," Phys. Rev. E 70, 062701 (2004).
[CrossRef]

J. A. Olivares, R. F. Rodriguez, and J. A. Reyes, "Ray tracing and reflectivity measurements in nematic hybrid cells," Opt. Commun. 221, 223-239 (2003).
[CrossRef]

Rodriguez, R. F.

J. A. Olivares, R. F. Rodriguez, and J. A. Reyes, "Ray tracing and reflectivity measurements in nematic hybrid cells," Opt. Commun. 221, 223-239 (2003).
[CrossRef]

Sambles, J. R.

S. A. Jewell and J. R. Sambles, "Optical characterization of a dual-frequency hybrid aligned nematic liquid crystal cell," Opt. Express 13, 2627-2633 (2005).
[CrossRef] [PubMed]

S. A. Jewell and J. R. Sambles, "Backflow in the relaxation of a hybrid aligned nematic cell," Appl. Phys. Lett. 82, 3156-3158 (2003).
[CrossRef]

S. A. Jewell and J. R. Sambles, "Fully-leaky guided mode measurement of surface polarization in a HAN liquid crystal cell," J. Appl. Phys. 92, 19-24 (2002).
[CrossRef]

F. Yang and J. R. Sambles, "The optical tensor configuration in a surface stabilized ferroelectric liquid crystal determined by using half leaky guided modes," Liq. Cryst. 13, 1-13 (1993).
[CrossRef]

D. Y. K. Ko and J. R. Sambles, "Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals," J. Opt. Soc. Am. A 5, 1863-1866 (1988).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic, 1983).

Yang, F.

F. Yang and J. R. Sambles, "The optical tensor configuration in a surface stabilized ferroelectric liquid crystal determined by using half leaky guided modes," Liq. Cryst. 13, 1-13 (1993).
[CrossRef]

Appl. Phys. Lett.

S. A. Jewell and J. R. Sambles, "Backflow in the relaxation of a hybrid aligned nematic cell," Appl. Phys. Lett. 82, 3156-3158 (2003).
[CrossRef]

J. Appl. Phys.

S. A. Jewell and J. R. Sambles, "Fully-leaky guided mode measurement of surface polarization in a HAN liquid crystal cell," J. Appl. Phys. 92, 19-24 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Liq. Cryst.

F. Yang and J. R. Sambles, "The optical tensor configuration in a surface stabilized ferroelectric liquid crystal determined by using half leaky guided modes," Liq. Cryst. 13, 1-13 (1993).
[CrossRef]

Opt. Commun.

J. A. Olivares, R. F. Rodriguez, and J. A. Reyes, "Ray tracing and reflectivity measurements in nematic hybrid cells," Opt. Commun. 221, 223-239 (2003).
[CrossRef]

Opt. Express

Phys. Rev. E

C. I. Mendoza, J. A. Olivares, and J. A. Reyes, "Electrically controlled total internal reflection in nematic hybrid cells," Phys. Rev. E 70, 062701 (2004).
[CrossRef]

Other

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic, 1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) HAN cell geometry; (b) HLGM experimental arrangement.

Fig. 2
Fig. 2

Experimentally recorded in-plane reflectivity data, R p p (x’s) and theoretical fit (solid curve) for a HAN cell.

Fig. 3
Fig. 3

Experimentally recorded in-plane and out-of-plane reflectivity data for a HAN cell for higher angles of incidence. (Inset, mode spacing against mode position for both in-plane and out-of-plane cases for a HAN cell over the higher incident angles.)

Fig. 4
Fig. 4

(a). Modulus of the optical E Z -field distribution through the HAN cell for two different incident angles for the in-plane case. (b) Modulus of the optical E Z -field distribution through the HAN cell for two different incident angles for the out-of-plane case. Arb., arbitrary units.

Fig. 5
Fig. 5

Plot of sin 2 ( π D e 2 D ) against sin 2 β of a HAN cell for the in-plane situation. (Inset, effective thickness of a HAN cell waveguide against the angular mode position for the in-plane situation.)

Fig. 6
Fig. 6

(a) Influence of three different imaginary parts of the perpendicular permittivity of the liquid crystal for the in-plane case: (1) ϵ i = 0.0001 , (2) ϵ i = 0.0002 , (3) ϵ i = 0.0003 . (b) Effects of the three different imaginary parts of the parallel permittivity of the liquid crystal for the in-plane case: (1) ϵ i = 0.0001 , (2) ϵ i = 0.0002 , (3) ϵ i = 0.0003 .

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

n 1 sin β e = n e ,
n e = n o n e n e 2 sin 2 θ ( D e ) + n o 2 cos 2 θ ( D e ) ,
n 1 2 sin 2 β e = n e 2 1 + [ ( n e 2 n o 2 ) n o 2 ] sin 2 ( π D e 2 D ) ,
1 sin 2 β e = n 1 2 n e 2 + ( n 1 2 n o 2 n 1 2 n e 2 ) sin 2 ( π D e 2 D ) .

Metrics