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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 5 — May. 1, 2000
  • pp: 920–926

Jones-matrix analysis with Pauli matrices: application to ellipsometry

ShiFang Li  »View Author Affiliations

JOSA A, Vol. 17, Issue 5, pp. 920-926 (2000)

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The coherency matrix formalism based on Pauli matrices is applied to analyze a general ellipsometer that is described by Jones matrices. Here the Jones matrices are represented as sums of appropriate coefficients times the Pauli matrices and the identity matrix, and intensities are represented as traces of coherency matrices. This approach allows us not only to treat partial polarizations explicitly but also to take advantage of various identities to reduce to algebra the operations necessary for system analysis. A general expression is obtained for the intensity transmitted through a polarizer–sample–compensator–analyzer (PSCA) ellipsometer. This general expression is applied to an ideal PSCA ellipsometer, and then the results are reduced to describe several simpler but commonly used configurations. The results provide insight regarding general capabilities and limitations and allow us to compare different ellipsometer systems directly. Finally, this expression is extended to include artifacts, the explicit representation of which allows a complete determination of their defects.

© 2000 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(260.2110) Physical optics : Electromagnetic optics
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization

Original Manuscript: July 12, 1999
Revised Manuscript: November 15, 1999
Manuscript Accepted: January 13, 2000
Published: May 1, 2000

ShiFang Li, "Jones-matrix analysis with Pauli matrices: application to ellipsometry," J. Opt. Soc. Am. A 17, 920-926 (2000)

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  1. H. G. Tompkins, W. A. McGahan, Spectroscopic Ellipsometry and Reflectrometry: A User’s Guide (Wiley, New York, 1999).
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  3. U. Fano, “A Stokes-parameter technique for the treatment of polarization in quantum mechanics,” Phys. Rev. 93, 121–123 (1954). [CrossRef]
  4. G. B. Parrent, P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento (Ser. 10) 15, 370–388 (1960). [CrossRef]
  5. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).
  6. See, for example, D. Bohm, Quantum Theory (Prentice-Hall, New York, 1954).
  7. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, UK, 1975).
  8. W. Swindell, ed., Polarized Light (Dowden Hutchinson & Ross, Stroudsburg, Pa., 1975).
  9. E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento (Ser. 10) 13, 1165–1181 (1959). [CrossRef]
  10. D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975). [CrossRef] [PubMed]
  11. C. V. Kent, J. Lawson, “A photometric method for the determination of the parameters of elliptically polarized light,” J. Opt. Soc. Am. 27, 117–119 (1937). [CrossRef]
  12. D. E. Aspnes, “Optimizing precision of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 639–646 (1974). [CrossRef]

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