Abstract

The propagation of polarized light within the cholesteric structure along its helical axis is conveniently expressed in terms of four 2-by-2 matrix operators. This description is useful in studying the change in the state of polarization of a beam propagating along the helical axis. The well-known properties of the liquid crystals come out as natural consequences of the properties of these operators. In particular, for a certain region of wavelengths as the beam propagates along the helical axis, a vector representing the state of polarization in Stokes space precesses about the <i>S</i><sub>3</sub> axis. The <i>S</i><sub>3</sub> axis stands for circular polarization. Furthermore, owing to the properties of the matrix operators, if the propagation of polarized light within the liquid crystal is described in diagonal form for propagation in one direction along the helical axis, then it cannot have a diagonal form for propagation in the opposite direction.

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References

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  1. C. W. Oseen, Trans. Faraday Soc. 29, 883 (1958).
  2. H. L. deVries, Acta Cryst. 4, 219 (1951).
  3. J. L. Fergason, in Liquid Crystals 2, edited by G. H. Brown (Gordon and Breach, New York, 1966), pp. 89–103; Electro-Technology 85, 41 (Jan. 1970).
  4. G. H. Conners, J. Opt. Soc. Am. 58, 875 (1968).
  5. J. W. Shelton and Y. R. Shen, private communication.
  6. D. W. Berreman and T. J. Scheffer, Mol. Cryst. Liq. Cryst. 11, 395 (1970).
  7. R. C. Jones, J. Opt. Soc. Am. 46, 126 (1956).
  8. W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, Mass., 1962).
  9. E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).
  10. I. S. Sokolnikoff and R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1958).
  11. A. S. Marathay, J. Opt. Soc. Am. 56, 619 (1966).
  12. A. S. Marathay, J. Opt. Soc. Am. 55, 969 (1965).
  13. See Ref. 12, Table II, p. 975.

Berreman, D. W.

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

Conners, G. H.

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

deVries, H. L.

H. L. deVries, Acta Cryst. 4, 219 (1951).

Fergason, J. L.

J. L. Fergason, in Liquid Crystals 2, edited by G. H. Brown (Gordon and Breach, New York, 1966), pp. 89–103; Electro-Technology 85, 41 (Jan. 1970).

Jones, R. C.

R. C. Jones, J. Opt. Soc. Am. 46, 126 (1956).

Marathay, A. S.

A. S. Marathay, J. Opt. Soc. Am. 56, 619 (1966).

A. S. Marathay, J. Opt. Soc. Am. 55, 969 (1965).

O’Neill, E. L.

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

Oseen, C. W.

C. W. Oseen, Trans. Faraday Soc. 29, 883 (1958).

Redheffer, R. M.

I. S. Sokolnikoff and R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1958).

Scheffer, T. J.

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

Shelton, J. W.

J. W. Shelton and Y. R. Shen, private communication.

Shen, Y. R.

J. W. Shelton and Y. R. Shen, private communication.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, Mass., 1962).

Sokolnikoff, I. S.

I. S. Sokolnikoff and R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1958).

Other

C. W. Oseen, Trans. Faraday Soc. 29, 883 (1958).

H. L. deVries, Acta Cryst. 4, 219 (1951).

J. L. Fergason, in Liquid Crystals 2, edited by G. H. Brown (Gordon and Breach, New York, 1966), pp. 89–103; Electro-Technology 85, 41 (Jan. 1970).

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

J. W. Shelton and Y. R. Shen, private communication.

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

R. C. Jones, J. Opt. Soc. Am. 46, 126 (1956).

W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, Mass., 1962).

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

I. S. Sokolnikoff and R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1958).

A. S. Marathay, J. Opt. Soc. Am. 56, 619 (1966).

A. S. Marathay, J. Opt. Soc. Am. 55, 969 (1965).

See Ref. 12, Table II, p. 975.

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