Abstract

The effect of a plate of anisotropic material, such as a crystal, on a collimated beam of polarized light may always be represented mathematically as a linear transformation of the components of the electric vector of the light. The effect of a retardation plate, of an anisotropic absorber (plate of tourmaline; Polaroid sheeting), or of a crystal or solution possessing optical activity, may therefore be represented as a matrix which operates on the electric vector of the incident light. Since a plane wave of light is characterized by the phases and amplitudes of the two transverse components of the electric vector, the matrices involved are two-by-two matrices, with matrix elements which are in general complex. A general theory of optical systems containing plates of the type mentioned is developed from this point of view.

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  1. Registered trade-mark of the Polaroid Corporation. For a description of Polaroid sheeting, see Martin Grabau, J. Opt. Soc. Am. 27, 420 (1937).
  2. In Parts I and II we shall need only the algebraic properties of matrices, as they are presented on pp. 348–352 of E. C. Kemble, Fundamental Principles of Quantum Mechanics (McGraw-Hill Book Company, Inc., New York, 1937). In Part III, we shall find it necessary to use also the transformation properties of matrices; see the reference just given, or V. Rojansky, Introductory Quantum Mechanics (Prentice-Hall, New York, 1938), pp. 285–340.
  3. Max Born, Optik (Springer, Berlin, 1933), p. 23.

Born, Max

Max Born, Optik (Springer, Berlin, 1933), p. 23.

Grabau, Martin

Registered trade-mark of the Polaroid Corporation. For a description of Polaroid sheeting, see Martin Grabau, J. Opt. Soc. Am. 27, 420 (1937).

Kemble, E. C.

In Parts I and II we shall need only the algebraic properties of matrices, as they are presented on pp. 348–352 of E. C. Kemble, Fundamental Principles of Quantum Mechanics (McGraw-Hill Book Company, Inc., New York, 1937). In Part III, we shall find it necessary to use also the transformation properties of matrices; see the reference just given, or V. Rojansky, Introductory Quantum Mechanics (Prentice-Hall, New York, 1938), pp. 285–340.

Other

Registered trade-mark of the Polaroid Corporation. For a description of Polaroid sheeting, see Martin Grabau, J. Opt. Soc. Am. 27, 420 (1937).

In Parts I and II we shall need only the algebraic properties of matrices, as they are presented on pp. 348–352 of E. C. Kemble, Fundamental Principles of Quantum Mechanics (McGraw-Hill Book Company, Inc., New York, 1937). In Part III, we shall find it necessary to use also the transformation properties of matrices; see the reference just given, or V. Rojansky, Introductory Quantum Mechanics (Prentice-Hall, New York, 1938), pp. 285–340.

Max Born, Optik (Springer, Berlin, 1933), p. 23.

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