Abstract

As in chiral nematic liquid crystals, one of the most striking optical properties of chiral smectic <i>C</i> liquid crystalline phases is the selective reflection of certain wavelengths of light. This Bragg-like scattering is a direct consequence of the periodic nature of the helical structure of these phases. In chiral nematics, the strong coupling of the light to the periodic structure leads to scattering in the dynamic (multiple-scattering) regime. In chiral smectic <i>C</i> phases, the strength of the coupling depends on the magnitude of the tilt angle between the long molecular axis and the layer normal. For small tilt angles, the kinematic (single-scattering) regime of light scattering occurs. Further, due to the nature of the modes of optical propagation in the chiral smectic <i>C</i> phase, some Bragg events occur as depolarized light scattering in the forward direction. A computer program has been written to calculate the light scattering from a chiral smectic <i>C</i> sample. The results of these calculations demonstrate the behavior of the light scattering in both the kinematic and dynamic regimes.

© 1978 Optical Society of America

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  1. H. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Cryst. 4, 219 (1951).
  2. J. L. Fergason, "Cholesteric structure. I. optical properties," Mol. Cryst. and Liq. Crystl. 1, 293 (1966).
  3. R. Nityananda, "On the theory of light propagation in cholesteric liquid crystals," Mol. Cyst. and Liq. Crystl. 21, 315 (1973).
  4. J. S. Prasad, "Circular dichroism in liquid crystals," J. de Phys. (Paris) 36-C1, 289 (1975).
  5. K. A. Suresh, "An experimental study of the anomalous transmission (Borrmann effect) in absorbing cholesteric liquid crystal," Mol. Cryst. and Liq. Crystl. 35, 267 (1976).
  6. D. W. Berreman, "Twisted smectic C phase: unique optical properties," Mol. Cryst. and Liq. Cryst. 22, 175 (1973).
  7. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970) pp. 665–686, 695–702.
  8. The coincidence of the axial and tilt planes is observed by the behavior of the conoscopic figure of an aligned chiral smectic C sample when an electric field is applied to the sample. For details see: S. Garoff, "Ferroelectric Liquid Crystals," Ph.D. Thesis, Harvard University, 1977, pp. 2.42–2.73 (unpublished).
  9. L. D. Landau and E. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass. 1966) p. 400.
  10. Conoscopic and refractometry investigations on a typical chiral smectic C phase indicate that this is a good approximation.
  11. C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1967), p. 57.
  12. B. W. Batterman and H. Cole, "Dynamical diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681 (1964).
  13. See Ref. 10, pp. 257–264.
  14. D. W. Berreman, "Optics in smoothly varying anisotropic planar structures: application to liquid crystal twist cells," J. Opt. Soc. Am. 63, 1374 (1973).
  15. R. Barakat and E. Baumann, "Mth power of an N × N matrix and its connection with the generalized Lucas polynomials," J. Math. Phys. 10, 1474 (1969).
  16. See Ref. 7, pp. 2.73–2.82 and Appendix II.
  17. In the conoscopic figure of a chiral smectic C sample, the center of the uniaxial cross is washed out by the structural, optical rotatory power of the material. However, for large angles of propagation, the uniaxial cross reappears. The reappearance of the uniaxial cross indicates nearly linearly polarized eigenmodes at these angles.

1976

K. A. Suresh, "An experimental study of the anomalous transmission (Borrmann effect) in absorbing cholesteric liquid crystal," Mol. Cryst. and Liq. Crystl. 35, 267 (1976).

1975

J. S. Prasad, "Circular dichroism in liquid crystals," J. de Phys. (Paris) 36-C1, 289 (1975).

1973

R. Nityananda, "On the theory of light propagation in cholesteric liquid crystals," Mol. Cyst. and Liq. Crystl. 21, 315 (1973).

D. W. Berreman, "Twisted smectic C phase: unique optical properties," Mol. Cryst. and Liq. Cryst. 22, 175 (1973).

D. W. Berreman, "Optics in smoothly varying anisotropic planar structures: application to liquid crystal twist cells," J. Opt. Soc. Am. 63, 1374 (1973).

1969

R. Barakat and E. Baumann, "Mth power of an N × N matrix and its connection with the generalized Lucas polynomials," J. Math. Phys. 10, 1474 (1969).

1966

J. L. Fergason, "Cholesteric structure. I. optical properties," Mol. Cryst. and Liq. Crystl. 1, 293 (1966).

1964

B. W. Batterman and H. Cole, "Dynamical diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681 (1964).

1951

H. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Cryst. 4, 219 (1951).

Barakat, R.

R. Barakat and E. Baumann, "Mth power of an N × N matrix and its connection with the generalized Lucas polynomials," J. Math. Phys. 10, 1474 (1969).

Batterman, B. W.

B. W. Batterman and H. Cole, "Dynamical diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681 (1964).

Baumann, E.

R. Barakat and E. Baumann, "Mth power of an N × N matrix and its connection with the generalized Lucas polynomials," J. Math. Phys. 10, 1474 (1969).

Berreman, D. W.

D. W. Berreman, "Optics in smoothly varying anisotropic planar structures: application to liquid crystal twist cells," J. Opt. Soc. Am. 63, 1374 (1973).

D. W. Berreman, "Twisted smectic C phase: unique optical properties," Mol. Cryst. and Liq. Cryst. 22, 175 (1973).

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970) pp. 665–686, 695–702.

Cole, H.

B. W. Batterman and H. Cole, "Dynamical diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681 (1964).

de Vries, H.

H. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Cryst. 4, 219 (1951).

Fergason, J. L.

J. L. Fergason, "Cholesteric structure. I. optical properties," Mol. Cryst. and Liq. Crystl. 1, 293 (1966).

Garoff, S.

The coincidence of the axial and tilt planes is observed by the behavior of the conoscopic figure of an aligned chiral smectic C sample when an electric field is applied to the sample. For details see: S. Garoff, "Ferroelectric Liquid Crystals," Ph.D. Thesis, Harvard University, 1977, pp. 2.42–2.73 (unpublished).

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1967), p. 57.

Landau, L. D.

L. D. Landau and E. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass. 1966) p. 400.

Lifshitz, E.

L. D. Landau and E. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass. 1966) p. 400.

Nityananda, R.

R. Nityananda, "On the theory of light propagation in cholesteric liquid crystals," Mol. Cyst. and Liq. Crystl. 21, 315 (1973).

Prasad, J. S.

J. S. Prasad, "Circular dichroism in liquid crystals," J. de Phys. (Paris) 36-C1, 289 (1975).

Suresh, K. A.

K. A. Suresh, "An experimental study of the anomalous transmission (Borrmann effect) in absorbing cholesteric liquid crystal," Mol. Cryst. and Liq. Crystl. 35, 267 (1976).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970) pp. 665–686, 695–702.

Acta Cryst.

H. de Vries, "Rotatory power and other optical properties of certain liquid crystals," Acta Cryst. 4, 219 (1951).

J. de Phys.

J. S. Prasad, "Circular dichroism in liquid crystals," J. de Phys. (Paris) 36-C1, 289 (1975).

J. Math. Phys.

R. Barakat and E. Baumann, "Mth power of an N × N matrix and its connection with the generalized Lucas polynomials," J. Math. Phys. 10, 1474 (1969).

J. Opt. Soc. Am.

Mol. Cryst. and Liq. Cryst.

D. W. Berreman, "Twisted smectic C phase: unique optical properties," Mol. Cryst. and Liq. Cryst. 22, 175 (1973).

Mol. Cryst. and Liq. Crystl.

K. A. Suresh, "An experimental study of the anomalous transmission (Borrmann effect) in absorbing cholesteric liquid crystal," Mol. Cryst. and Liq. Crystl. 35, 267 (1976).

J. L. Fergason, "Cholesteric structure. I. optical properties," Mol. Cryst. and Liq. Crystl. 1, 293 (1966).

Mol. Cyst. and Liq. Crystl.

R. Nityananda, "On the theory of light propagation in cholesteric liquid crystals," Mol. Cyst. and Liq. Crystl. 21, 315 (1973).

Rev. Mod. Phys.

B. W. Batterman and H. Cole, "Dynamical diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681 (1964).

Other

See Ref. 10, pp. 257–264.

See Ref. 7, pp. 2.73–2.82 and Appendix II.

In the conoscopic figure of a chiral smectic C sample, the center of the uniaxial cross is washed out by the structural, optical rotatory power of the material. However, for large angles of propagation, the uniaxial cross reappears. The reappearance of the uniaxial cross indicates nearly linearly polarized eigenmodes at these angles.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970) pp. 665–686, 695–702.

The coincidence of the axial and tilt planes is observed by the behavior of the conoscopic figure of an aligned chiral smectic C sample when an electric field is applied to the sample. For details see: S. Garoff, "Ferroelectric Liquid Crystals," Ph.D. Thesis, Harvard University, 1977, pp. 2.42–2.73 (unpublished).

L. D. Landau and E. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass. 1966) p. 400.

Conoscopic and refractometry investigations on a typical chiral smectic C phase indicate that this is a good approximation.

C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1967), p. 57.

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