Abstract

Light propagation along the helical axis of cholesteric liquid crystals, whose structure has been distorted by a magnetic or electric field perpendicular to the helix axis, is theoretically investigated. The solutions show several reflection bands whose centers are given by the Bragg condition <i>m</i> λ<sub><i>m</i></sub> = 2<i>S n</i> (<i>m</i> is an integer, <i>S</i> is the period of the distorted structure, and <i>n</i> is the average refractive index of the material). The bands with <i>m</i> ≥ 2 consist of three subbands, each characterized by the dependence of the reflection on the polarization of the incident beam. Thus, for example, an incident beam linearly polarized in the direction of the distorting field will be reflected at only two of these subbands. Except for very strong applied fields, the band <i>m</i> = 1 is composed of two subbands only. Outside the reflection bands, the modes of propagation are orthogonal linear polarizations.

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  1. C. W. Oseen, Trans. Faraday Soc. 29, 883 (1933).
  2. HI. de Vries, Acta Cryst. 4, 219 (1951).
  3. I. G. Chistyakov, Soviet Phys. Uspekhi 9, 551 (1967).
  4. G. H. Conners, J. Opt. Soc. Am. 58, 875 (1968).
  5. L. Melamed and D. Rubin, Appl. Opt. 10, 231 (1971).
  6. D. W. Berreman and T. J. Scheffer, Mol. Cryst. Liq. Cryst. 11, 395 (1970).
  7. R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).
  8. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 28.
  9. P. G. De Gennes, Solid State Commun. 6, 163 (1968).
  10. R. B. Meyer, Appl. Phys. Lett. 14, 208 (1969).
  11. G. Durand, L. Leger, F. Rondelez, and M. Veyssie, Phys. Rev. Lett. 22, 227 (1969).
  12. L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953), p. 139.
  13. IBM System 360, Scientific Subroutine Package, IBM Publication No. H20-0205-3 (1968), p. 275.
  14. F. J. Kahn, Appl. Phys. Lett. 18, 231 (1971).
  15. C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1967), Ch. 9.
  16. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  17. Reference 15, p. 255.
  18. Reference 15, p. 260.
  19. The matrix Al, Eq. (5), is used to compute the reflection coefficients from a finite slab whose thickness is lS (S is the period), by a method described in Ref. 8, p. 59.
  20. After completion of this work, we noticed that light transmission through a finite slab of distorted cholesteric liquid crystal was also calculated by S. C. Chou, L. Cheung, and R. B. Meyer, Solid State Commun. 11, 977 (1972).
  21. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1968), p. 269.
  22. C. Maugin, Bull. Soc. Franc. Miner. 34, 17 (1911).
  23. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1252 (1972).

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1252 (1972).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1252 (1972).

Berreman, D. W.

D. W. Berreman and T. J. Scheffer, Mol. Cryst. Liq. Cryst. 11, 395 (1970).

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 28.

Brillouin, L.

L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953), p. 139.

Cheung, L.

After completion of this work, we noticed that light transmission through a finite slab of distorted cholesteric liquid crystal was also calculated by S. C. Chou, L. Cheung, and R. B. Meyer, Solid State Commun. 11, 977 (1972).

Chistyakov, I. G.

I. G. Chistyakov, Soviet Phys. Uspekhi 9, 551 (1967).

Chou, S. C.

After completion of this work, we noticed that light transmission through a finite slab of distorted cholesteric liquid crystal was also calculated by S. C. Chou, L. Cheung, and R. B. Meyer, Solid State Commun. 11, 977 (1972).

Conners, G. H.

G. H. Conners, J. Opt. Soc. Am. 58, 875 (1968).

De Gennes, P. G.

P. G. De Gennes, Solid State Commun. 6, 163 (1968).

de Vries, HI.

HI. de Vries, Acta Cryst. 4, 219 (1951).

Dreher, R.

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).

Durand, G.

G. Durand, L. Leger, F. Rondelez, and M. Veyssie, Phys. Rev. Lett. 22, 227 (1969).

Kahn, F. J.

F. J. Kahn, Appl. Phys. Lett. 18, 231 (1971).

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1967), Ch. 9.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Leger, L.

G. Durand, L. Leger, F. Rondelez, and M. Veyssie, Phys. Rev. Lett. 22, 227 (1969).

Maugin, C.

C. Maugin, Bull. Soc. Franc. Miner. 34, 17 (1911).

Meier, G.

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).

Melamed, L.

L. Melamed and D. Rubin, Appl. Opt. 10, 231 (1971).

Meyer, R. B.

After completion of this work, we noticed that light transmission through a finite slab of distorted cholesteric liquid crystal was also calculated by S. C. Chou, L. Cheung, and R. B. Meyer, Solid State Commun. 11, 977 (1972).

R. B. Meyer, Appl. Phys. Lett. 14, 208 (1969).

Oseen, C. W.

C. W. Oseen, Trans. Faraday Soc. 29, 883 (1933).

Rondelez, F.

G. Durand, L. Leger, F. Rondelez, and M. Veyssie, Phys. Rev. Lett. 22, 227 (1969).

Rubin, D.

L. Melamed and D. Rubin, Appl. Opt. 10, 231 (1971).

Saupe, A.

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).

Scheffer, T. J.

D. W. Berreman and T. J. Scheffer, Mol. Cryst. Liq. Cryst. 11, 395 (1970).

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1968), p. 269.

Veyssie, M.

G. Durand, L. Leger, F. Rondelez, and M. Veyssie, Phys. Rev. Lett. 22, 227 (1969).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 28.

Other (23)

C. W. Oseen, Trans. Faraday Soc. 29, 883 (1933).

HI. de Vries, Acta Cryst. 4, 219 (1951).

I. G. Chistyakov, Soviet Phys. Uspekhi 9, 551 (1967).

G. H. Conners, J. Opt. Soc. Am. 58, 875 (1968).

L. Melamed and D. Rubin, Appl. Opt. 10, 231 (1971).

D. W. Berreman and T. J. Scheffer, Mol. Cryst. Liq. Cryst. 11, 395 (1970).

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 28.

P. G. De Gennes, Solid State Commun. 6, 163 (1968).

R. B. Meyer, Appl. Phys. Lett. 14, 208 (1969).

G. Durand, L. Leger, F. Rondelez, and M. Veyssie, Phys. Rev. Lett. 22, 227 (1969).

L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953), p. 139.

IBM System 360, Scientific Subroutine Package, IBM Publication No. H20-0205-3 (1968), p. 275.

F. J. Kahn, Appl. Phys. Lett. 18, 231 (1971).

C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1967), Ch. 9.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Reference 15, p. 255.

Reference 15, p. 260.

The matrix Al, Eq. (5), is used to compute the reflection coefficients from a finite slab whose thickness is lS (S is the period), by a method described in Ref. 8, p. 59.

After completion of this work, we noticed that light transmission through a finite slab of distorted cholesteric liquid crystal was also calculated by S. C. Chou, L. Cheung, and R. B. Meyer, Solid State Commun. 11, 977 (1972).

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1968), p. 269.

C. Maugin, Bull. Soc. Franc. Miner. 34, 17 (1911).

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1252 (1972).

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