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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 11 — Nov. 1, 1980
  • pp: 1364–1370

Extension of the Jones matrix formalism to reflection problems and magnetic materials

R.J. Vernon and B. D. Huggins  »View Author Affiliations


JOSA, Vol. 70, Issue 11, pp. 1364-1370 (1980)
http://dx.doi.org/10.1364/JOSA.70.001364


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Abstract

A simple relation is developed between the Jones propagation matrix in anisotropic materials and the reflection and interface transmission matrices for normal incidence upon a plane interface between isotropic and anisotropic materials. The case of anisotropic permittivity and/or conductivity and the case of anisotropic permeability are both considered. It is shown that, for small anisotropies, the reflection and interface transmission matrices can be decomposed into matrices representing the effects of linear and circular birefringence and dichroism. The case of multiple reflections in a planar slab is also treated.

© 1980 Optical Society of America

Citation
R.J. Vernon and B. D. Huggins, "Extension of the Jones matrix formalism to reflection problems and magnetic materials," J. Opt. Soc. Am. 70, 1364-1370 (1980)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-70-11-1364


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References

  1. (a) R. C. Jones, "New calculus for the treatment of optical systems. I. Description and discussion of the calculus," J. Opt. Soc. Am. 31, 488–493 (1941); (b) H. Hurwitz, Jr. and R. C. Jones," New calculus for the treatment of optical systems. II. Proof of three general equivalence theorems," ibid. 31, 493–500 (19410); (c) R. C. Jones, New calculus for the treatment of optical systems. III. The Sohncke theory of optical activity," ibid. 31, 500–503 (1941); (d) "New calculus for the treatment of optical systems. IV." ibid. 32, 486–493 (1942); (e) "A new calculus for the treatment of optical systems. V. More general formulation and description of another calculus," ibid. 37, 107–110 (1947); (f) "New calculus for the treatment of optical systems. VI. Experimental determination of the matrix," ibid. 37, 110–112 (1947); (g) "New calculus for the treatment of optical systems. VII. Properties of the N matrices," ibid. 38, 671–685 (1948); (h) "New calculus for the treatment of optical systems. VIII. Properties of the N matrices," ibid. 46, 126–131 (1956). These eight papers appear together in Polarized Light, Benchmark Papers in Optics, Vol. 1 edited by William Swindell (Dowden, Hutchinson, and Ross, New York, 1975).
  2. S. Teitler and B. W. Henvis, "Refraction in stratified, anisotropic media," J. Opt. Soc. Am. 60, 830–834 (1970).
  3. D. W. Berreman, "Optics in stratified and anisotropic media: 4 × 4 matrix formulation," J. Opt. Soc. Am. 62, 502–510 (1972).
  4. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).
  5. Since Jones considers propagation in only one direction, this double sign does not appear in Ref. 1(g). Also our sign convention is somewhat different than that used by Jones.
  6. Note that gl1, and gl2 characterize birefringence whereas gc characterizes dichroism; pl1 and Pl2 characterize dichroism whereas Pc characterizes birefringence.
  7. V. M.Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitions (Interscience, New York, 1966).

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