OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 10 — Apr. 1, 2012
  • pp: C184–C192

Vectorial pure operatorial Pauli algebraic approach in polarization optics: a theoretical survey and some applications

Tiberiu Tudor  »View Author Affiliations


Applied Optics, Vol. 51, Issue 10, pp. C184-C192 (2012)
http://dx.doi.org/10.1364/AO.51.00C184


View Full Text Article

Enhanced HTML    Acrobat PDF (317 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In the last decade we have elaborated a mathematical tool for the description of the interaction of polarized light with polarization devices, alternative to the standard matrix (Jones and Mueller) formalisms, namely a vectorial pure operatorial Pauli algebraic one. After a brief, coherent survey of this formalism, we present some applicative results obtained in this frame, referring to the gain and the modification of the state of polarization at the interaction of the polarized light with deterministic devices. Due to an adequate parameterization of the problem, specific to this method, symmetric expressions of the gain and of the generalized Malus’ law are obtained. On the other hand, the equation of the ellipsoid in which a Poincaré sphere of a given degree of polarization is mapped by such a device can be established.

© 2012 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization

History
Original Manuscript: November 28, 2011
Revised Manuscript: February 28, 2012
Manuscript Accepted: February 29, 2012
Published: March 30, 2012

Citation
Tiberiu Tudor, "Vectorial pure operatorial Pauli algebraic approach in polarization optics: a theoretical survey and some applications," Appl. Opt. 51, C184-C192 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-10-C184


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Lancaster and M. Tismenetsky, The Theory of Matrices with Applications (Academic, 1985).
  2. H. F. Jones, Groups, Representations and Physics (Taylor & Francis, 1998).
  3. T. Tudor, “Interaction of light with the polarization devices: a vectorial Pauli algebraic approach,” J. Phys. A 41, 4153031 (2008). [CrossRef]
  4. T. Tudor, “Pauli algebraic analysis of polarized light modulation,” Appl. Opt. 47, 2721–2728 (2008). [CrossRef]
  5. C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).
  6. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Deckker, 1993).
  7. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1996).
  8. J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. 40, 1–47 (2007). [CrossRef]
  9. W. A. Shurcliff, Polarized Light (Harvard University, 1962).
  10. U. Fano, “Remarks on the classical and quantum-mechanical treatment of partial polarization,” J. Opt. Soc. Am. 39, 859–863 (1949). [CrossRef]
  11. U. Fano, “Description of states in quantum mechanics by density matrix and operator techniques,” Rev. Mod. Phys. 29, 74–93 (1957). [CrossRef]
  12. R. W. Schmieder, “Stokes-algebra formalism,” J. Opt. Soc. Am. 59, 297–302 (1969). [CrossRef]
  13. A. S. Marathay, “Operator formalism in the theory of partial polarization,” J. Opt. Soc. Am. 55, 969–980 (1965). [CrossRef]
  14. C. Whitney, “Pauli-algebraic operators in polarization optics,” J. Opt. Soc. Am. 61, 1207–1213 (1971). [CrossRef]
  15. P. K. Aravind, “Simulating the Wigner angle with a parametric amplifier,” Phys. Rev. A 42, 4077–4084 (1990). [CrossRef]
  16. S. V. Savenkov, O. Sydoruk, and R. S. Muttiah, “Conditions for polarization elements to be dichroic and birefringent,” J. Opt. Soc. Am. A 22, 1447–1452 (2005). [CrossRef]
  17. L. C. Biedenharn, J. D. Louck, and P. A. Carruthers, Angular Momentum in Quantum Physics: Theory and Applications, Encyclopedia of Mathematics and Its Applications, G.-C. Rota, ed. (Addison-Wesley, 1981).
  18. B. DeBoo, J. Sasian, and R. Chipman, “Degree of polarization surfaces and maps for analysis of depolarization,” Opt. Express 12, 4941–4958 (2004). [CrossRef]
  19. S.-Y. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998). [CrossRef]
  20. J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of nondepolarizing optical systems from polar decomposition of its Mueller matrix,” Optik 76, 67–71 (1987).
  21. T. Tudor and V. Manea, “The ellipsoid of the polarization degree: a vectorial, pure operatorial Pauli algebraic approach,” J. Opt. Soc. Am. B 28, 596–601 (2011). [CrossRef]
  22. R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990). [CrossRef]
  23. G. N. Ramachandran and S. Ramaseshan, Crystal Optics, Handbuch der Physik XXV, S. Flügge, ed. (Springer Verlag, 1961).
  24. L. Dettwiller, “Interpretation and generalization of polarized light interferences by means of the Poincaré sphere,” Eur. J. Phys. 22, 575–586 (2001). [CrossRef]
  25. P. V. Polyanskii, “Complex degree of mutual polarization, generalized Malus law and optics of observable quantities,” Proc. SPIE 6254, 625405 (2006). [CrossRef]
  26. J. Lages, R. Giust, and J. M. Vigoureux, “Composition law for polarizers,” Phys. Rev. A 78, 033810 (2008). [CrossRef]
  27. T. Tudor and V. Manea, “Symmetry between partially polarised light and partial polarisers in the vectorial Pauli algebraic formalism,” J. Mod. Opt. 58, 845–852 (2011). [CrossRef]
  28. O. V. Angelsky, S. B. Yermolenko, C. Yu. Zenkova, and A. O. Angelskaya, “Polarization manifestations of correlation (intrinsic coherence) of optical fields,” Appl. Opt. 47, 5492–5499 (2008). [CrossRef]
  29. O. V. Angelsky, S. G. Hanson, C. Yu. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology (estimation) of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009). [CrossRef]
  30. S. E. Segre, “Evolution of the polarization state for radiation propagating in a nonuniform, birefringent, optically active, and dichroic medium: the case of a magnetized plasma,” J. Opt. Soc. Am. A 17, 95–100 (2000). [CrossRef]
  31. T. Tudor, “Vectorial pure operatorial Pauli algebraic approach in polarization optics: a theoretical survey and some applications,” Proc. SPIE 8338, 833804 (2011). [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.

Figures

Fig. 1. Fig. 2. Fig. 3.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited