Abstract

<p>The preceding papers of this series have examined the properties of an optical calculus which represented each of the separate elements of an optical system by means of a single matrix <b>M.</b> This paper is concerned with the properties of matrices, denoted by <b>N</b>, which refer not to the complete element, but only to a given infinitesimal path length within the element.</p><p>If <b>M</b> is the matrix of the optical element up to the point z, where z is measured along the light path, then the <b>N</b>matrix at the point z is defined by <b>N</b> ≡ (<i>d</i><b>M</b>/<i>d</i>z)<b>M</b><sup>-1</sup>. (A) Thus one may write symbolically, <b>N</b>=<i>d</i>log<b>M</b>/<i>d</i>z (B) and <b>M</b> = <b>M</b><sub>0</sub>exp(∫N<i>d</i>z). (C)</p><p>A general introduction is contained in Part I. The definition and general properties of the <b>N</b>-matrices are treated in Part II. Part III contains a detailed discussion of the important special case in which the optical medium is homogeneous, so that <b>N</b> is independent of z; Part III contains in Eq. (3.26) the explicit relation which corresponds to the symbolic relation (C). Part IV describes a systematic method, based on the <b>N</b>-matrices, by which the optical properties of the system at each point may be described uniquely and quantitatively as a combination of a certain amount of linear birefringence, a certain amount of circular dichroism, etc.; the method of resolution is indicated in Table I. Part V treats the properties of the inhomogeneous crystal which is obtained by twisting a homogeneous crystal about an axis parallel to the light path.</p>

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References

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  1. I.—J. Opt. Soc. Am. 31, 488–493 (1941); II.—ibid., 31, 493–499 (1941); III.—ibid., 31, 500–503 (1941); IV.—ibid., 32, 486–493 (1942); V.—ibid., 37, 107–110 (1947); VI.—ibid., 37, 110–112 (1947).
  2. H. Poincaré, Thbérie Mathématique de la Lumière (Gauthier-Villars et Fils, Paris, 1892).

Poincaré, H.

H. Poincaré, Thbérie Mathématique de la Lumière (Gauthier-Villars et Fils, Paris, 1892).

Other

I.—J. Opt. Soc. Am. 31, 488–493 (1941); II.—ibid., 31, 493–499 (1941); III.—ibid., 31, 500–503 (1941); IV.—ibid., 32, 486–493 (1942); V.—ibid., 37, 107–110 (1947); VI.—ibid., 37, 110–112 (1947).

H. Poincaré, Thbérie Mathématique de la Lumière (Gauthier-Villars et Fils, Paris, 1892).

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