OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 27 — Sep. 20, 2007
  • pp: 6700–6709

Eigenanalysis of dichroic, birefringent, and degenerate polarization elements: a Jones-calculus study

Sergey N. Savenkov, Oleksiy I. Sydoruk, and Ranjan S. Muttiah  »View Author Affiliations

Applied Optics, Vol. 46, Issue 27, pp. 6700-6709 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (546 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A theoretical analysis of eigenpolarizations and eigenvalues pertaining to the Jones matrices of dichroic, birefringent, and degenerate polarization elements is presented. The analysis is carried out employing a general model of a polarization element. Expressions for the corresponding polarization elements are derived and analyzed. It is shown that, despite the presence of birefringence, a polarization element can, in a general case, demonstrate a totally dichroic behavior. Moreover, it is proved that birefringence necessarily accompanies dichroic elements with orthogonal eigenpolarizations. A transition between degenerate, dichroic, and birefringent eigenvalues is studied, and examples of synthesis of polarization elements are given.

© 2007 Optical Society of America

OCIS Codes
(260.0260) Physical optics : Physical optics
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

Original Manuscript: March 8, 2007
Revised Manuscript: April 26, 2007
Manuscript Accepted: June 6, 2007
Published: September 11, 2007

Sergey N. Savenkov, Oleksiy I. Sydoruk, and Ranjan S. Muttiah, "Eigenanalysis of dichroic, birefringent, and degenerate polarization elements: a Jones-calculus study," Appl. Opt. 46, 6700-6709 (2007)

Sort:  Year  |  Journal  |  Reset  


  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).
  2. R. A. Chipman, "Polarimetry," in Handbook of Optics, M.Bass, ed. (McGraw-Hill, 1995), Vol. II, Chap. 22.
  3. P. Huard, Polarization of Light (Wiley, 1997).
  4. C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).
  5. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge U. Press, 1999). [PubMed]
  6. S.-Y. Lu and R. A. Chipman, "Homogeneous and inhomogeneous Jones matrices," J. Opt. Soc. Am. A 11, 766-773 (1994). [CrossRef]
  7. S. N. Savenkov, O. I. Sydoruk, and R. S. Muttiah, "Conditions for polarization elements to be dichroic and birefringent," J. Opt. Soc. Am. A 22, 1447-1452 (2005). [CrossRef]
  8. H. de Lang, "Polarization properties of optical resonators passive and active," Ph.D. dissertation (University of Utrecht, 1966).
  9. H. Hurwitz and R. C. Jones, "A new calculus for the treatment of optical systems. 2. Proof of three general equivalence theorems," J. Opt. Soc. Am. 31, 493-499 (1941).
  10. C. Whitney, "Pauli-algebraic operators in polarization optics," J. Opt. Soc. Am. 61, 1207-1213 (1971). [CrossRef]
  11. J. J. Gil and E. Bernabeu, "Obtainment of the polarizing and retardation parameters of nondepolarizing optical system from polar decomposition of its Mueller matrix," Optik (Stuttgart) 76, 67-71 (1987).
  12. S.-Y. Lu and R. Chipman, "Interpretation of the Mueller matrices based on polar decomposition," J. Opt. Soc. Am. A 13, 1106-1113 (1996). [CrossRef]
  13. H. Hammer, "Characteristic parameters in integrated photoelasticity: an application of Poincare's equivalence theorem," J. Mod. Opt. 51, 597-618 (2004).
  14. Sudha and A. V. Gopala Rao, "Polarization elements: a group-theoretical study," J. Opt. Soc. Am. A 18, 3130-3134 (2001). [CrossRef]
  15. T. Tudor, "Generalized observables in polarization optics," J. Phys. A 36, 9577-9590 (2003). [CrossRef]
  16. M. V. Berry and M. R. Dennis, "Black polarization sandwiches are square roots of zero," J. Opt. A 6,S24-S25 (2004).
  17. T. Tudor, "Non-Hermitian polarizers: a biorthogonal analysis," J. Opt. Soc. Am. A 23, 1513-1522 (2006). [CrossRef]
  18. J. R. L. Moxon and A. R. Renshow, "The simultaneous measurement of optical activity and circular dichroism in birefringent linearly dichroic crystal section: 1. Introduction and description of the method," J. Phys. Condens. Matter 2, 6807-6836 (1990). [CrossRef]
  19. S. N. Savenkov, V. V. Marienko, E. A. Oberemok, and O. Sydoruk, "Generalized matrix equivalence theorem for polarization theory," Phys. Rev. E 74, 056607 (2006). [CrossRef]
  20. T. Tudor and A. Gheondea, "Pauli algebraic forms of normal and nonnormal operators," J. Opt. Soc. Am. A 24, 204-210 (2007). [CrossRef]
  21. P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985).
  22. R. Barakat, "Jones matrix equivalence theorems for polarization theory," Eur. J. Phys. 19, 209-216 (1998). [CrossRef]
  23. K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990). [CrossRef]
  24. J. A. Davis, I. Moreno, and P. Tsai, "Polarization eigenstates for twisted-nematic liquid-crystal displays," Appl. Opt. 37, 937-945 (1998). [CrossRef]
  25. X. Zhu, Q. Hong, Y. Huang, and S.-T. Wu, "Eigenmodes of a reflective twisted-nematic liquid-crystal cell," J. Appl. Phys. 94, 2868-2873 (2003). [CrossRef]
  26. M. Yamauchi, "Jones-matrix models for twisted-nematic liquid-crystal devices," Appl. Opt. 44, 4484-4493 (2005). [CrossRef] [PubMed]
  27. D. Tentori, C. Ayala-Díaz, F. Treveñino-Martínez, F. J. Mendieta-Jiménez, and H. Soto-Ortriz, "Birefringence evaluation of helically wound optical fibers," J. Mod. Opt. 48, 1767-1780 (2001).
  28. H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, "Jones matrix for second-order polarization mode dispersion," Opt. Lett. 25, 19-21 (2000). [CrossRef]
  29. F. Heismann, "Extended Jones matrix for first-order polarization mode dispersion," Opt. Lett. 30, 1111-1113 (2005). [CrossRef] [PubMed]
  30. D. J. Donohue, B. J. Stoyanov, R. L. McCally, and R. A. Farrell, "Numerical modeling of the cornea's lamellar structure and birefringence properties," J. Opt. Soc. Am. A 12, 1425-1438 (1995). [CrossRef]
  31. V. F. Izotova, I. L. Maksimova, I. S. Nefedov, and S. V. Romanov, "Investigation of Mueller matrices of anisotropic nonhomogeneous layers in application to an optical model of the cornea," Appl. Opt. 36, 164-169 (1997). [CrossRef] [PubMed]
  32. R. A. Farrell, D. Rouseff, and R. L. McCally, "Propagation of polarized light through two- and three-layer anisotropic stacks," J. Opt. Soc. Am. A 22, 1981-1992 (2005). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited