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Passage of Polarized Light Through Optical Elements

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Book cover Matrix Theory of Photoelasticity

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 11))

Abstract

In the previous chapter the modern methods of describing polarization form, based on the Poincaré sphere and the Stokes and Jones vectors, were described. All of these methods are characterized by extreme elegance and compactness; they provide, in a unified manner, for all forms of polarized light. Thus, any kind of polarization, regardless of whether elliptical or linear, can be represented by a point on the Poincaré sphere, which provides a clear and well-defined picture of all particular polarization forms. Similarly, by the Stokes vector, each kind of light, regardless of whether it is totally or partially polarized, can be characterized by a four-element vector. The elements of the vector completely define the degree and the state of polarization (azimuth, ellipticity, and handedness of the light ellipse) of each particular form of light. In the same way every form of elliptically polarized light can be completely described by the two-element complex Jones vector.

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References

  1. H. Poincaré: Théorie Mathématique de la Lumière, Vol. 2 (Gauthiers-Villars, Paris 1892) Chap. 12

    Google Scholar 

  2. J. Walker: Analytical Theory of Light (Cambridge, at the University Press 1904)

    Google Scholar 

  3. J. Becquerel: Communs. Phys. Lab. Univ. Leiden, No. 191C, 19 (1928)

    Google Scholar 

  4. J. Becquerel: Communs. Phys. Lab. Univ. Leiden, No. 211 A1 (1930)

    Google Scholar 

  5. C. A. Skinner: J. Opt. Soc. Am. 10, 491 (1925)

    ADS  Google Scholar 

  6. M. L. Chaumont: C.R. Acad. Sci. 150, 1604 (1913)

    Google Scholar 

  7. M. L. Chaumont: Ann. Phys. 4, 101 (1915)

    Google Scholar 

  8. G. Bruhat, P. Grivet: J. de Physique 6, 12 (1935)

    Google Scholar 

  9. Y. Björnstahl: Z. Phys. 40, 437 (1939)

    Google Scholar 

  10. Y. Björnstahl: Z. Instrumk. 59, 425 (1939)

    Google Scholar 

  11. O. Snellman, Y. Björnstahl: Kolloid Beih. 52, 403 (1941)

    Google Scholar 

  12. M. F. Bokstein: J. Techn. Phys. (USSR) 18, 673 (1948)

    Google Scholar 

  13. F. Pockels: Lehrbuch der Kristalloptik, Vol. 11–13 (Teubner, Leipzig 1906) pp. 267–283

    MATH  Google Scholar 

  14. H. G. Jerrard: J. Opt. Soc. Am. 44, 634 (1954)

    ADS  Google Scholar 

  15. C. J. Koester: J. Opt. Soc. Am. 49, 405 (1959)

    ADS  Google Scholar 

  16. N. H. Hartshorne, A. Stuart: Crystals and the Polarizing Microscope, 2nd ed. (Arnold Press, London 1950)

    Google Scholar 

  17. F. E. Wright: J. Opt. Soc. Am. 20, 529 (1930)

    ADS  Google Scholar 

  18. G. N. Ramachandran, S. Ramaseshan: “Crystal Optics”, in Crystal Optics, Diffraction, ed. by S. Flügge, Encyclopedia of Physics, Vol. 25/1 (Springer, Berlin, Göttingen, Heidelberg 1961) pp. 1–217

    Google Scholar 

  19. S. Pancharatnam: Proc. Indian Acad. Sci. A41, 130 (1955)

    Google Scholar 

  20. S. Pancharatnam: Proc. Indian Acad. Sci. A41, 137 (1955)

    Google Scholar 

  21. S. Pancharatnam: Proc. Indian Acad. Sci. A44, 247 (1956)

    MathSciNet  Google Scholar 

  22. S. Pancharatnam: Proc. Indian Acad. Sci. A44, 398 (1956)

    MathSciNet  Google Scholar 

  23. G. N. Ramachandran, S. Ramaseshan: J. Opt. Soc. Am. 42, 49 (1952)

    ADS  Google Scholar 

  24. G. N. Ramachandran, V. Chandrasekharan : Proc. Indian Acad. Sci. A33, 199 (1951)

    Google Scholar 

  25. S. Ramaseshan, V. Chandrasekharan: Current Sci. (India) 20, 150 (1951)

    Google Scholar 

  26. S. Ramaseshan: Proc. Indian Acad. Sci. A34, 32 (1951)

    Google Scholar 

  27. A. Robert: Int. J. Solids Struct. 6, 423 (1970)

    Google Scholar 

  28. A. J. Robert: Exp. Mech. 7, 224 (1967)

    Google Scholar 

  29. R. Mark: AIAA J. 2, 150 (1964)

    Google Scholar 

  30. J. D. Riera, R. Mark: Exp. Mech. 9, 9 (1969)

    Google Scholar 

  31. C. Whitney: J. Opt. Soc. Am. 61, 1207 (1971)

    ADS  Google Scholar 

  32. R. Plechata: Acta Techn. 2, 230 (1957)

    Google Scholar 

  33. H. J. Woods: J. Text. Inst. 55, 243 (1964)

    Google Scholar 

  34. H. Schwieger: Exp. Mech. 9, 67 (1969)

    Google Scholar 

  35. A. Robert: Polarimetrie et Photoélasticimétrie (Serv. Techn. Const. Armes Navales, Paris 1972)

    Google Scholar 

  36. W. A. Shurcliff, S. S. Ballard: Polarized Light (Van Nostrand, New Jersey 1964)

    Google Scholar 

  37. W. A. Shurcliff: Polarized Light. Production and Use (Harvard University Press, Cambridge, Mass. 1962)

    Google Scholar 

  38. J. W. Simmons, M. J. Gutmann: States, Waves and Photons: A Modern Introduction to Light (Addison-Wesley, Reading, Mass. 1970)

    Google Scholar 

  39. H. K. Aben: Integrated Photoelasticity (VALGUS, Tallin, USSR 1975)

    Google Scholar 

  40. A. Kuske: Exp. Mech. 6, 218 (1966)

    Google Scholar 

  41. A. Kuske: Int. Spannungsopt. Symp. Berlin, 11.–15.4.1961 (Akademie Verlag, Berlin 1962)

    Google Scholar 

  42. A. Kuske: Optik 19, 261 (1962)

    MathSciNet  Google Scholar 

  43. A. Kuske: Rev. Frans. de Méc. 9, 49 (1964)

    Google Scholar 

  44. H. Mueller: Rep. No 2 of the OSRD Project OEMsr-576, Nov. 15 (1943)

    Google Scholar 

  45. H. Mueller: J. Opt. Soc. Am. 38, 661 (1948)

    Google Scholar 

  46. P. Soleillet: Ann. Phys. 12, 23 (1929)

    MATH  Google Scholar 

  47. F. Perrin: J. Chem. Phys. 10, 415 (1942)

    ADS  Google Scholar 

  48. N. G. Parke: Ph. D. Thesis, Dept. of Physics, M.I.T., May 1 (1948)

    Google Scholar 

  49. N. G. Parke: Tech. Rep. No 70, Research Lab. of Electr., M.I.T., June 30 (1948)

    Google Scholar 

  50. N. G. Parke: Tech. Rep. No 95, Research Lab. of Electr., M.I.T., January 31 (1949)

    Google Scholar 

  51. N. G. Parke: Tech. Rep. No 119, Research Lab. of Electr., M.I.T., June 15 (1949)

    Google Scholar 

  52. M. J. Walker: Am. J. Phys. 22, 170 (1954)

    ADS  MATH  Google Scholar 

  53. U. Fano: J. Opt. Soc. Am. 39, 859 (1949)

    ADS  Google Scholar 

  54. U. Fano: Rev. Mod. Phys. 29, 74 (1957)

    MathSciNet  ADS  MATH  Google Scholar 

  55. W. H. McMaster: Am. J. Phys. 22, 351 (1954)

    ADS  MATH  Google Scholar 

  56. W. H. McMaster: Rev. Mod. Phys. 33, 8 (1961)

    MathSciNet  ADS  Google Scholar 

  57. B. H. Billings, E. H. Land: J. Opt. Soc. Am. 38, 819 (1948)

    ADS  Google Scholar 

  58. B. H. Billings: J. Opt. Soc. Am. 41, 966 (1951)

    ADS  Google Scholar 

  59. B. H. Billings: J. Opt. Soc. Am. 42, 12 (1952)

    ADS  Google Scholar 

  60. P. Roman: Nuovo Cimento 13, 974 (1959)

    MathSciNet  MATH  Google Scholar 

  61. R. W. Schmieder: J. Opt. Soc. Am. 59, 297 (1969)

    ADS  Google Scholar 

  62. D. W. Weeks: J. Math. Phys. 13, 380 (1957)

    Google Scholar 

  63. R. C. Jones: J. Opt. Soc. Am. 31, 488 (1941)

    ADS  Google Scholar 

  64. H. Hurwitz, R. C. Jones: J. Opt. Soc. Am. 31, 493 (1941)

    ADS  Google Scholar 

  65. R. C. Jones: J. Opt. Soc. Am. 31, 500 (1941)

    ADS  Google Scholar 

  66. R. C. Jones: J. Opt. Soc. Am. 32, 486 (1942)

    ADS  Google Scholar 

  67. R. C. Jones: J. Opt. Soc. Am. 37, 107 (1947)

    ADS  Google Scholar 

  68. R. C. Jones: J. Opt. Soc. Am. 37, 110 (1947)

    ADS  Google Scholar 

  69. R. C. Jones: J. Opt. Soc. Am. 38, 671 (1948)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  71. R. C. Jones: J. Opt. Soc. Am. 46, 528 (1956)

    ADS  Google Scholar 

  72. H. Y. Hsü, M. Richartz, Y. K. Liang: J. Opt. Soc. Am. 37, 99 (1947)

    ADS  Google Scholar 

  73. E. F. Dawson, N. O. Young: J. Opt. Soc. Am. 50, 170 (1960)

    ADS  Google Scholar 

  74. J. W. Evans: J. Opt. Soc. Am. 48, 142 (1958)

    ADS  Google Scholar 

  75. M. Richartz, H. Y. Hsü: J. Opt. Soc. Am. 39, 136 (1949)

    ADS  Google Scholar 

  76. J. Cernosek: J. Opt. Soc. Am. 61, 324 (1971)

    ADS  Google Scholar 

  77. G. B. Parrent, P. Roman: Nuovo Cimento 15, 370 (1960)

    MathSciNet  MATH  Google Scholar 

  78. H. K. Aben: Proc. Conf. on Exp. Methods of Investigating Stress and Strain in Structures, (Prague 1965), pp. 33–42

    Google Scholar 

  79. H. K. Aben: Exp. Mech. 10, 97 (1970)

    Google Scholar 

  80. H. K. Aben: Proc. 4th Int. Conf. Stress Anal. (Cambridge 1970), pp. 175–182

    Google Scholar 

  81. D. Clarke, J. F. Grainger: Polarized Light and Optical Measurement (Pergamon Press, Oxford 1971)

    Google Scholar 

Books

  • Aben, H.K.: Integrated Photoelasticity (Valgus Tallin, USSR 1975)

    Google Scholar 

  • Born, M., Wolf, E.: Principles of Optics, 5rd ed. (Pergamon Press, London 1975) Chap.10, pp.544–555

    Google Scholar 

  • Chandrasekhar, S.: Radiative Transfer (Oxford University Press, London 1950) pp.24–35

    MATH  Google Scholar 

  • Clarke, D., Grainger, J.F.: Polarized Light and Optical Measurement (Pergamon Press, Oxford 1971)

    Google Scholar 

  • Gerrard, A., Burch, Ü.M.: Introduction to Matrix Methods in Optics (Wiley and Sons, London 1975)

    Google Scholar 

  • Hartshorne, N.H., Stuart, A.: Crystals and the Polarizing Microscope, 2nd ed. (Arnold Press, London 1950)

    Google Scholar 

  • Pockels, F.: Lehrbuch der Kristalloptik, Vol. 11–13 (Teubner, Leipzig 1906) pp.267–283

    MATH  Google Scholar 

  • Poincaré, H.: Theorie Mathématique de la Lumière, Vol.2 (Gauthiers-Villars, Paris 1892) Chap.12

    Google Scholar 

  • Ramachandran, G.N., Ramaseshan, S.: “Crystal Optics”, in Crystal Optics Diffraction, ed. by S. Flügge, Encyclopedia of Physics, Vol.25/1 (Springer, Berlin, Göttingen, Heidelberg 1961) pp.1–217

    Google Scholar 

  • Shurcliff, W.A.: Polarized Light, Production and Use (Harvard University Press, Cambridge, Mass. 1962)

    Google Scholar 

  • Shurcliff, W.A., Ballard, S.S.: Polarized Light (Van Nostrand, Princeton, N.J. 1964)

    Google Scholar 

  • Simmons, J.W., Gutmann, M.J.: States, Waves and Photons: A Modern Introduction to Light (Addison-Wesley, Reading, Mass. 1970)

    Google Scholar 

  • Walker, J.: Analytical Theory of Light (Cambridge, at the University Press 1904)

    Google Scholar 

Papers

  • Aben, H.K.:“On the Matrix Representation of Optical Phenomena in Three-Dimensional Photoelasticity”, Proc. Conf. on Exp. Methods of Investigating Stress and Strain in Structures, Prague (Building Research Institute of the Technical University of Prague, Prague 1965) pp.33–42

    Google Scholar 

  • Aben, H.K.: Magnetophotoelasticity-photoelasticity in a magnetic field. Exp. Mech. 10, 97–105 (1970)

    Google Scholar 

  • Aben, H.K.: “Principles of Magnetophotoelasticity”, Proc. 4th Int. Conf. Exp. Stress Analysis, Cambridge, 1970, ed. by M.L. Meyer (The Institution of Mechanical Engineers, London 1971) pp.175–182

    Google Scholar 

  • Aben, H.K.: Discussion of “Towards the achromatic quarterwave plate”. Exp. Mech. 14, 249–250 (1974)

    Google Scholar 

  • Anile, A.M., Breuer, R.A.: Gravitational Stokes parameters. Astrophys. J. 189, 39–49 (1974)

    MathSciNet  ADS  Google Scholar 

  • Aspnes, D.E.: Measurement and correction of first-order errors in ellipsometry. J. Opt. Soc. Am. 61, 1077–1085 (1971)

    ADS  Google Scholar 

  • Azzam, R.M.A., Bashara, N.M.: Unified analysis of ellipsometry errors due to imperfect components, cell-window birefringence, and incorrect azimuth angles. J. Opt. Soc. Am. 61, 600–607 (1971)

    ADS  Google Scholar 

  • Azzam, R.M.A., Bashara, N.M.: General treatment of the effect of cell windows in ellipsometry. J. Opt. Soc. Am. 61, 773–776 (1971)

    ADS  Google Scholar 

  • Azzam, R.M.A., Bashara, N.M.: Ellipsometry with imperfect components including incoherent effects. J. Opt. Soc. Am. 61, 1380–1391 (1971)

    ADS  Google Scholar 

  • Azzam, R.M.A.: Polarization orthogonalization properties of optical systems. Appl. Phys. 13, 281–285 (1977)

    ADS  Google Scholar 

  • Beardsley, G.F.: Mueller scattering matrix of sea water. J. Opt. Soc. Am. 58, 52–57 (1968)

    ADS  Google Scholar 

  • Becquerel, J.: The existence in a mono-axial crystal of two different values for the magnetic rotation of polarisation in directions parallel with the axis and perpendicular to it. Commun. Phys. Lab. Univ. Leiden 191 C, 19–34 (1928)

    Google Scholar 

  • Becquerel, J.: Pouvoir rotatoire magnétique d’un cristal uniaxe suivant les directions obliques sur l’axe; détermination de la rotation de la tysonite suivant une direction voisine d’un axe binaire, à la température du nitrogéne liquide. Commun. Phys. Lab. Univ. Leiden 211 A, 1–18 (1930)

    Google Scholar 

  • Becquerel, J., De Haas, W.J.: Détermination du pouvoire rotatoire paramag-nétique d’un cristal de tysonite suivant une direction normale a l’axe optique, aux témpératures réalisables avec l’hydrogéne liquide. Commun. Phys. Lab. Univ. Leiden 211 A, 19–34 (1930)

    Google Scholar 

  • Becquerel, J., De Haas, W.J.: Anisotropic magnétooptique dans un plan normal a l’axe optique d’un cristal hexagonal. Pouvoirs rotatoires paramagnétiques dans les directions voisines des axes binaires, aux trés basses températures. Commun. Phys. Lab. Univ. Leiden 211 A, 35–51 (1930)

    Google Scholar 

  • Bigelow, J.E., Kashnow, R.A.: Poincaré sphere analysis of liquid crystal optics. Appl. Opt. 16, 2090–2096 (1977)

    ADS  Google Scholar 

  • Billings, B.H., Land, E.H.: A comparative survey of some possible systems of polarized headlights. J. Opt. Soc. Am. 38, 819–829 (1948)

    ADS  Google Scholar 

  • Billings, B.H.: A monochromatic depolarizer. J. Opt. Soc. Am. 41, 966–975 (1951)

    ADS  Google Scholar 

  • Billings, B.H.: The electro-optic effect in uniaxial crystals of the dihydrogen phosphate (XH2PO4) Type. IV. Angular field of the electro-optic shutter. J. Opt. Soc. Am. 42, 12–20 (1952)

    ADS  Google Scholar 

  • Björnstahl, Y.: Über die Bracesche Halbschattenmethode. Physik. Zeitschr. 40, 437–443 (1939)

    Google Scholar 

  • Björnstahl, Y.: Über die Methode von Brace mit variablem Halbschatten. Z. Instrumentenkd. 59, 425–430 (1939)

    Google Scholar 

  • Bolinder, E.F.: Geometric-analytic theory of noisy two-port networks. Proc. IRE 46, 1959–1960 (1958)

    Google Scholar 

  • Bolinder, E.F.: Theory of noisy two-port networks. J. Franklin Inst. 267, 1–23 (1959)

    Google Scholar 

  • Bolinder, E.F.: Geometric analysis of partially polarized electromagnetic waves. IEEE Trans. AP-15, 37–40 (1967)

    ADS  Google Scholar 

  • Bolinder, E.F.: Comments on “Poincaré sphere representation of partially polarized fields”. IEEE Trans. AP-23, 747–748 (1975)

    ADS  Google Scholar 

  • Bourret, R.: The depolarization of electromagnetic radiation in a random medium: Evolution of the Stokes parameters. Opt. Acta 21, 721–735 (1974)

    ADS  Google Scholar 

  • Bradshaw, J.A.: Discussion of “The Stokes parameters of a beam in a plasma”. Am. J. Phys. 37, 934–936 (1969)

    ADS  Google Scholar 

  • Bruhat, G., Grivet, P.: Le pouvoir rotatoire du quartz pour des rayons perpendiculaires à l’axe optique et sa dispersion dans l’ultra-violet. J. de Physique 6 (1), 12–26 (1935)

    Google Scholar 

  • Cernosek, J.: Simple geometrical method for analysis of elliptical polarization. J. Opt. Soc. Am. 61, 324–327 (1971)

    ADS  Google Scholar 

  • Cernosek, J.: Towards the achromatic quarterwave plate. Exp. Mech. 13, 83–85 (1973)

    Google Scholar 

  • Cernosek, J., Perla, M.: A new method of determining the isoclinic parameter. J. Strain. Anal. 5, 263–268 (1970)

    Google Scholar 

  • Chaumont, M.L.: Sur la théorie des appareils servant à l’étude de la lumière polarisée elliptiquement. C.R. Acad. Sci. 150, 1604–1606 (1913)

    Google Scholar 

  • Chaumont, M.L.: Recherches expérimentales sur le phénomène electro-optique de Kerr et sur les méthodes servant à l’étude de la lumière polarisée elliptiquement. Ann. Phys. (Leipzig) 4, 101–206 (1915)

    Google Scholar 

  • Cocke, W.J., Holm, D.A.: Lorentz transformation properties of the Stokes parameters. Nature (London) Phys. Sci. 240, 161–162 (1972)

    Google Scholar 

  • Collett, E.: The description of polarization in classical physics. Am. J. Phys. 36, 713–725 (1968)

    ADS  Google Scholar 

  • Collett, E.: Stokes parameters for quantum systems. Am. J. Phys. 38, 563–574 (1970)

    ADS  Google Scholar 

  • Collett, E.: Discussion of “Stokes matrices for light beams in a double rhomb”. Am. J. Phys. 39, 225–226 (1971)

    ADS  Google Scholar 

  • Collett, E.: Mueller-Stokes matrix formulation of Fresnel’s equations. Am. J. Phys. 39, 517–528 (1971)

    ADS  Google Scholar 

  • Collett, E.: Mathematical formulation of the Interference laws of Fresnel and Arago. Am. J. Phys. 39, 1483–1495 (1971)

    ADS  Google Scholar 

  • Dawson, E.F., Young, N.O.: Helical Kerr cell. J. Opt. Soc. Am. 50, 170–171 (1960)

    ADS  Google Scholar 

  • Degl’innocenti, E.L., Degl’innocenti, M.L.: A perturbative solution of the transfer equations for the Stokes parameters in a magnetic field. Solar Phys. 31, 299–305 (1973)

    Google Scholar 

  • Deschamps, G.A.: Geometrical representation of the polarization of a plane electromagnetic wave. Proc. Inst. Radio Eng. 39, 540–544 (1951)

    Google Scholar 

  • Deschamps, G.A.: New chart for the solution of transmission-line and polarization problems. Electrical Commun. 28, 247–254 (1953)

    Google Scholar 

  • Deschamps, G.A., Mast, P.E.: Poincaré sphere representation of partially polarized fields. IEEE Trans. AP-21, 474–478 (1973)

    ADS  Google Scholar 

  • Domanski, A.: The Mueller matrix formalism in diffraction phenomena. Opt. Commun. 14, 281–286 (1975)

    ADS  Google Scholar 

  • Evans, J.W.: Solc birefringent filter. J. Opt. Soc. Am. 48, 142–145 (1958)

    ADS  Google Scholar 

  • Falkoff, D.L., MacDonald, J.E.: On the Stokes parameters for polarized radiation. J. Opt. Soc. Am. 41, 861–862 (1951)

    ADS  Google Scholar 

  • Fano, U.: Remarks on the classical and quantum-mechanical treatment of partial polarization. J. Opt. Soc. Am. 39, 859–863 (1949)

    ADS  Google Scholar 

  • Fano, U.: A Stokes-parameter technique for the treatment of polarization in quantum mechanics. Phys. Rev. 93, 121–123 (1954)

    ADS  MATH  Google Scholar 

  • Fano, U.: Description of states in quantum mechanics by density matrix and operator techniques. Rev. Mod. Phys. 29, 74–93 (1957)

    MathSciNet  ADS  MATH  Google Scholar 

  • Grechushnikov, B.N., Konstantinova, A.F.: Müller matrices for optically active crystals. Sov. Phys.-Crystallogr. 16, 378–379 (1971)

    Google Scholar 

  • Hagyard, M.J.: Analytic solutions to the Unno transfer equations for the Stokes parameters in a Milne-Eddington atmosphere. Solar Phys. 16, 286–287 (1971)

    ADS  Google Scholar 

  • Hammerschlag, R.H.: Jones-Vektoren geschrieben in rechts- und linkszirkularen Komponenten. Optik 34, 595–597 (1972)

    ADS  Google Scholar 

  • Hecht, E.: Note on “An operational definition of the Stokes parameters”. Am. J. Phys. 38, 1156–1158 (1970)

    ADS  Google Scholar 

  • Hege, G., Leonhardt, K.: Polarisationseigenschaften von Tripelprismen-Angabe experimentell bestätigter Bauteilmatrizen. Optik 47, 167–184 (1977)

    Google Scholar 

  • Hewitt, M.H.: Polarization, cross section, and the Stokes parameters. Proc. IEEE 53, 1143–1144 (1965)

    Google Scholar 

  • Hillion, P.: Paramètres de Stokes et neutrino. Ann. Inst. Henri Poincaré, Sect. A 13, 253–261 (1970)

    Google Scholar 

  • Hodgdon, E.B.: Theory, design, and calibration of a uv spectrophotopolarimeter. Appl. Opt. 4, 1479–1483 (1965)

    ADS  Google Scholar 

  • Holoubek, J.: The use of Mueller matrices in the intensity methods of birefringence measurements. Czech. J. Phys. B 24, 1162–1167 (1974)

    ADS  Google Scholar 

  • Hsü, H.Y., Richartz, M., Liang, Y.K.: A generalized intensity formula for a system of retardation plates. J. Opt. Soc. Am. 37, 99–106 (1947)

    ADS  Google Scholar 

  • Hurwitz, H., Jones, R.C.: A new calculus for the treatment of optical systems. II. Proof of three general equivalence theorems. J. Opt. Soc. Am. 31, 493–499 (1941)

    ADS  Google Scholar 

  • Jerrard, H.G.: Transmission of light through birefringent and optically active media: The Poincaré sphere. J. Opt. Soc. Am. 44, 634–640 (1954)

    ADS  Google Scholar 

  • Jones, R.C.: A new calculus for the treatment of optical systems. I. Description and discussion of the calculus. J. Opt. Soc. Am. 31, 488–493 (1941)

    ADS  Google Scholar 

  • Jones, R.C.: A new calculus for the treatment of optical systems. III. The Sohncke theory of optical activity. J. Opt. Soc. Am. 31, 500–503 (1941)

    ADS  Google Scholar 

  • Jones, R.C.: A new calculus for the treatment of optical systems. IV. J. Opt. Soc. Am. 32, 486–493 (1942)

    ADS  Google Scholar 

  • Jones, R.C.: A new calculus for the treatment of optical systems. V. A more general formulation, and description of another calculus. J. Opt. Soc. Am. 37, 107–110 (1947)

    ADS  Google Scholar 

  • Jones, R.C.: A new calculus for the treatment of optical systems. VI. Experimental determination of the matrix. J. Opt. Soc. Am. 37, 110–112 (1947)

    ADS  Google Scholar 

  • Jones, R.C.: A new calculus for the treatment of optical systems. VII. Properties of the N-matrices. J. Opt. Soc. Am. 38, 671–685 (1948)

    ADS  Google Scholar 

  • Jones, R.C.: New calculus for the treatment of optical systems. VIII. Electromagnetic theory. J. Opt. Soc. Am. 46, 126–131 (1956)

    ADS  Google Scholar 

  • Jones, R.C.: Transmittance of a train of three polarizers. J. Opt. Soc. Am. 46, 528–533 (1956)

    ADS  Google Scholar 

  • Kastner, S.O.: Polarization in multiple scattering using random Stokes vectors. J. Quant. Spectrosc. Radiat. Transfer. 6, 317–324 (1966)

    ADS  Google Scholar 

  • Ko, H.C.: The use of the statistical matrix and the Stokes vector in formulating the effective aperture of antennas. IRE Trans. AP-9, 581–582 (1961)

    Google Scholar 

  • Koester, C.J.: Achromatic combinations of half-wave plates. J. Opt. Soc. Am. 49, 405–409 (1959)

    ADS  Google Scholar 

  • Kuske, A.: “Beiträge zur spannungsoptischen Untersuchung von Flächentragwerken”. Int. Spannungsopt. Symp., Berlin, April 1961 (Akademie Verlag Berlin 1962) pp.115–126

    Google Scholar 

  • Kuske, A.: Die Gesetzmässigkeiten der Doppelbrechung. Optik 19, 261–272 (1962)

    MathSciNet  Google Scholar 

  • Kuske, A.: L’analyse des phénomènes optiques en photoélasticité à trois dimensions par la méthode du cercle de “J”. Rev. Fr. Méc. 9, 49–58 (1964)

    Google Scholar 

  • Kuske, A.: The J-circle method. Exp. Mech. 6, 218–224 (1966)

    Google Scholar 

  • De Lang, H.: Flow lines on the Poincaré sphere as an aid to the study of mode polarization in lasers. IEEE J. QE-7, 441–444 (1971)

    Google Scholar 

  • Lenhardt, K., Burckhardt, C.: Die Jonesmatrix eines Tripel Streifens. Optik 47, 215–222 (1977)

    Google Scholar 

  • Mark, R.: A simple geometric method for analyzing polarization states in photoelasticity. AIAA J. 2, 150–152 (1964)

    Google Scholar 

  • McDonough, R.: Comment on “Use of Mueller matrices for determination of the actual polarization of light”. J. Opt. Soc. Am. 59, 1004 (1969)

    Google Scholar 

  • McMaster, W.H.: Polarization and the Stokes parameters. Am. J. Phys. 22, 351–362 (1954)

    ADS  MATH  Google Scholar 

  • McMaster, W.H.: Matrix representation of polarization. Rev. Mod. Phys. 33, 8–28 (1961)

    MathSciNet  ADS  Google Scholar 

  • Meeks, M.L., Ball, J.A., Carter, J.C., Ingalls, R.P.: Stokes parameters for 1665-megacycles-per-second emission from OH near source W3. Science 153, 978–981 (1966)

    ADS  Google Scholar 

  • Mueller, H, H.: “Momorandum on the polarization optics of the photoelastic shutter”. Rpt. 2, OSRD Project OEMsr-576 (Nov. 1943)

    Google Scholar 

  • Mueller, H.: The foundation of optics. J. Opt. Soc. Am. 38, 661 (1948)

    Google Scholar 

  • O’Handley, R.C.: Modified Jones calculus for the analysis of errors in polarization-modulation ellipsometry. J, Opt. Soc. Am. 63, 523–528 (1973)

    ADS  Google Scholar 

  • Pancharatnam, S.: Achromatic combinations of birefringent plates. Pt. I. An achromatic circular polarizer. Proc. Indian Acad. Sci. A 41, 130–136 (1955)

    Google Scholar 

  • Pancharatnam, S.: Achromatic combinations of birefringent plates. Pt. II. An achromatic quarter-wave plate. Proc. Indian Acad. Sci. A 41, 137–144 (1955)

    Google Scholar 

  • Pancharatnam, S.: Generalized theory of interference, and its applications. Pt. I. Coherent pencils. Proc. Indian Acad. Sci. A 44, 247–262 (1956)

    MathSciNet  Google Scholar 

  • Pancharatnam, S.: Generalized theory of interference, and its applications. Pt. II. Partially coherent pencils. Proc. Indian Acad. Sci. A 44, 398–417 (1956)

    MathSciNet  Google Scholar 

  • Parke, N.G.: “Matrix Optics”; Ph. D. Thesis, Dept. of Physics (MIT, Cambridge, Mass. 1948) pp.181

    Google Scholar 

  • Parke, N.G.: “Matrix Algebra of Electromagnetic Waves”, Techn. Rpt. 70, Res. Lab. of Electr. (MIT, Cambridge, Mass. 1948) pp.28

    Google Scholar 

  • Parke, N.G.: “Statistical Optics: I. Radiation”, Techn. Rpt. No. 95, Res. Lab. of Electr. (MIT, Cambridge, Mass 1949) pp. 15

    Google Scholar 

  • Parke, N.G.: “Statistical Optics: II. Mueller phenomenological algebra”, Techn. Rpt. No. 119, Res. Lab. of Electr. (MIT, Cambridge, Mass. 1949) pp. 19

    Google Scholar 

  • Parrent, G.B., Roman, P.: On the matrix formulation of the theory of partial polarization in terms of observables. Nuovo Cimento 15, 370–388 (1960)

    MathSciNet  MATH  Google Scholar 

  • Pascu, M.L.: Semnificaţia şi ecuaţille de transformare ale parametrilor Stokes. Stud. Cercet! Fiz. 24, 253–264 (1972)

    Google Scholar 

  • Perrin, F.: Polarization of light scattered by isotropic opalescent media. J. Chem. Phys. 10, 415–427 (1942)

    ADS  Google Scholar 

  • Plechata, R.: A geometric interpretation of double refraction in photoelasticity. Acta Tech. Prague 2, 230–261 (1957).

    Google Scholar 

  • Pomraning, G.C.: The Stokes parameters for light arising from induced processes. Astrophys. J. 191, 183–189 (1974)

    ADS  Google Scholar 

  • Pospergelis, M.M.: Measurement and computation of the instrumental btokes vector. Sov. Astron.-AJ 12, 512–521 (1968)

    ADS  Google Scholar 

  • Priebe, J.R.: Operational form of the Mueller matrices. J. Opt. Soc. Am. 59, 176–180 (1969).

    ADS  Google Scholar 

  • Pritchard, B.S., Elliott, W.G.: Two instruments for atmospheric optics measurement. J. Opt. Soc. Am. 50, 191–202 (1960)

    ADS  Google Scholar 

  • Raimond, E., Eliasson, B.: Positions and Stokes parameters of seven OH-emission sources. Astrophys. J. 155, 817–830 (1969)

    ADS  Google Scholar 

  • Ramachandran, G.N., Chandrasekharan, V.: Photo-elastic constants of sodium chlorate. Proc. Indian Acad. Sci. A 33, 199–215 (1951).

    Google Scholar 

  • Ramachandran, G.N., Ramaseshan, S.: Magneto-optic rotation in birefringgentmedia-application of the Poincaré sphere. J. Opt. Soc. Am. 42, 49–5b (1952).

    ADS  Google Scholar 

  • Ramaseshan, S.: Faraday effect and birefringence-I. Proc. Indian Acad. Sci. A 34, 32–40 (1951)

    Google Scholar 

  • Ramaseshan, S., Chandrasekharan, V.: Faraday effect and birefringence. Curr. Sci. (India) 20, 150–151 (1951)

    Google Scholar 

  • Richartz, M., Hsü, H.Y.: Analysis of elliptical polarization. J. Opt. Soc. Am. 39, 136–157 (1949).

    Google Scholar 

  • Riera, J.D., Mark, R.: The optical-rotation effect in photoelastic shell analysis. Exp. Mech. 9, 9–16 (1969)

    Google Scholar 

  • Robert, A.J.: New methods in photoelasticity. Exp. Mech. 7, 224–232 (1967)

    Google Scholar 

  • Robert, A.: Application de la sphère de Poincaré à l’ellipsométrie de précision. Bull. Soc. Fr. Minéral. Cristallogr. 91, 415–421 (1968)

    Google Scholar 

  • Robert, A.: The application of Poincaré’s sphere to photoelasticity. Int. J. Solids Struct. 6, 423–432 (1970)

    Google Scholar 

  • Robert, A.: La sphère de Poincaré et ses applications á la mesureles formes de lumière et á la photoélasticimétrie classique. Sci. et techniques de l’Armement. 45, 309–379 (1971)

    Google Scholar 

  • Robert, A.: Polarimétrie et photoélasticimétrie. Serv. Techn. Const. Armes Navales, Paris, Chap. 7, 145–171 (1972)

    Google Scholar 

  • Rodimov, A.P., Potekhin, V.A.: Distribution of the probabilities of the position of the polarization point of a partially polarized wave on a Poincaré sphere. Radio Eng. 12, 2038–2039 (1967)

    Google Scholar 

  • Roman, P.: Generalized Stokes parameters for waves with arbitrary form. Nuovo Cimento 13, 974–982 (1959)

    MathSciNet  MATH  Google Scholar 

  • Schmieder, R.W.: Stokes-algebra formalism. J. Opt. Soc. Am. 59, 297–302 (1969).

    ADS  Google Scholar 

  • Schwieger, H.: Graphical methods for determining the resulting photoelastic effect of compound states of stress. Exp. Mech. 9, 67–74 (1969)

    Google Scholar 

  • Skinner, C.A.: A universal Polarimeter. J. Opt. Soc. Am. 10, 491–520 (1925)

    ADS  Google Scholar 

  • Smirnov, V.S.: Relativistic transformation of the Stokes parameters and the coherency matrix. Opt. Spectrosc. USSR 28, 557–558 (1970)

    Google Scholar 

  • Snellman, O., Björnstahl, Y.: Einige Untersuchungen über Strömungsdoppel — brechung. Kolloid Beih. 52, 403–466 (1941)

    Google Scholar 

  • Soleillet, P.: Sur les paramètres charactérisant la polarisation partielle de la lumière dans les phénomènes de fluorescence. Ann. Phys. (Paris) 12, 23–97 (1929)

    MATH  Google Scholar 

  • Stokes, G.G.: On the composition and resolution of streams of polarized light from different sources. Trans. Cambridge Philos. Soc. 9, 399–416 (1852)

    ADS  Google Scholar 

  • Tewarson, S.P.: Reciprocity equations for isotropic opalescent scattering media. Indian J. Phys. 40, 281–293 (1966)

    Google Scholar 

  • Tewarson, S.P.: Orientation effect on the reciprocity relation for Stokes vectors of scattered light. Kolloid z. u. Z. Polymere 225, 52–54 (1968)

    Google Scholar 

  • Tewarson, S.P.: Matrix Optics in dipolar scattering. Kolloid Z. u. Z. Polymere 225, 69–71 (1968)

    Google Scholar 

  • Tewarson, S.P., Vachaspati: Reciprocity relation for Stokes vectors of scattered light. Kolloid Z. u. Z. Polymere 213, 131–134 (1966)

    Google Scholar 

  • Tronko, V.D., Golovach, G.P.: Jones and Mueller matrices of a phase-shifting slab with a rotating axis of the highest velocity. Sov. Phys.-Crystallogr. 18, 291–294 (1973)

    Google Scholar 

  • Troshin, B.I., Bagaev, S.N.: Use of the Poincaré sphere method for the analysis of the polarization characteristics of a laser with an anisotropic element. Opt. Spectrosc. USSR 23, 424–425 (1967)

    ADS  Google Scholar 

  • Uri, J.B.: Polarization and interference in optics, Pt. I: The transfer function-OTF. Optik 47, 337–350 (1977)

    ADS  Google Scholar 

  • Uri, J.B.: Polarization and interference in optics, Pt. II: Interference, coherency matrix and degree of polarization. Optik 47, 405–420 (1977)

    Google Scholar 

  • Uri, J.B.: Polarization and interference in optics, Pt. III: Reflection, refraction, and diffraction. Optik 48, 1–22 (1977)

    Google Scholar 

  • Vasil’yev, B.I.: Use of Mueller matrices for determination of the actual polarization of light. Sov. J. Opt. Techno;. 35, 87–89 (1968)

    Google Scholar 

  • Walker, M.J.: Matrix calculus and the Stokes parameters of polarized radiation. Am. J. Phys. 22, 170–174 (1954)

    ADS  MATH  Google Scholar 

  • Weeks, D.W.: A study of sixteen coherency matrices. J. Math. Phys. (N.Y.) 13, 380–386 (1957)

    Google Scholar 

  • Whitney, C.: Pauli-algebraic operators in polarization optics. J. Opt. Soc. Am. 61, 1207–1213 (1971)

    ADS  Google Scholar 

  • Wittmann, A.: Computation and observation of Zeeman multiplet polarization in Fraunhofer lines, Pt. I: Photographic measurement of Stokes parameters. Sol. Phys. 33, 107–118 (1973)

    ADS  Google Scholar 

  • Wittmann, A.: Computation and observation of Zeeman multiplet polarization in Fraunhofer lines, Pt. II: Computation of Stokes parameter profiles. Sol. Phys. 35, 11–29 (1974)

    ADS  Google Scholar 

  • Wolf, E.: Optics in terms of observable quantities. Nuovo Cimento 12, 884–888 (1954)

    MATH  Google Scholar 

  • Woods, H.J.: The optical properties of twisted fibres. J. Text. Inst. 55, 243–250 (1964)

    Google Scholar 

  • Wright, F.E.: A spherical projection chart for use in the study of elliptically polarized light. J. Opt. Soc. Am. 20, 529–564 (1930)

    ADS  Google Scholar 

  • De Young, D.S.: Relativistic spinor formulation of Stokes parameters with application to the inverse compton effect. J. Math. Phys. 7, 1916–1923 (1966)

    ADS  Google Scholar 

  • Zamkov, V.A., Kondratyev, A.S., Kuchma, A.Y.: Jones and Mueller matrices for a uniaxial Plane-parallel plate. Opt. Spectrosc. USSR 38, 592–593 (1975)

    ADS  Google Scholar 

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Theocaris, P.S., Gdoutos, E.E. (1979). Passage of Polarized Light Through Optical Elements. In: Matrix Theory of Photoelasticity. Springer Series in Optical Sciences, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-35789-6_4

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