OSA's Digital Library

Optics Letters

Optics Letters


  • Vol. 36, Iss. 15 — Aug. 1, 2011
  • pp: 2821–2823

Causality and the complete positivity of classical polarization maps

Omar Gamel and Daniel F. V. James  »View Author Affiliations

Optics Letters, Vol. 36, Issue 15, pp. 2821-2823 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (88 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Mueller and Jones matrices have been thoroughly studied as mathematical tools to describe the manipulation of the polarization state of classical light. In particular, the most general physical transformation on the polarization state has been represented as an ensemble of Jones matrices, as i V i Φ V i . But this has generally been directly assumed without proof by most authors. In this Letter, we derive this expression from simple physical principles and the matrix theory of positive maps.

© 2011 Optical Society of America

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(030.6600) Coherence and statistical optics : Statistical optics
(070.5040) Fourier optics and signal processing : Phase conjugation
(260.5430) Physical optics : Polarization

ToC Category:
Coherence and Statistical Optics

Original Manuscript: May 12, 2011
Revised Manuscript: June 10, 2011
Manuscript Accepted: June 20, 2011
Published: July 21, 2011

Omar Gamel and Daniel F. V. James, "Causality and the complete positivity of classical polarization maps," Opt. Lett. 36, 2821-2823 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).
  2. C. Brosseau, Fundamentals of Polarized light: a Statistical Optics Approach (Wiley-Interscience, 1998).
  3. N. Wiener, Acta Math. 55, 117 (1930). [CrossRef]
  4. E. Wolf, Nuovo Cimento 12, 884 (1954). [CrossRef]
  5. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge, 2007).
  6. H. Mueller, J. Opt. Soc. Am. A 38, 661 (A) (1948).
  7. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941). [CrossRef]
  8. K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433(1987). [CrossRef]
  9. R. Simon, Opt. Commun. 42, 293 (1982). [CrossRef]
  10. J. J. Gil, J. Opt. Soc. Am. A 17, 328 (2000). [CrossRef]
  11. B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010). [CrossRef] [PubMed]
  12. M. Choi, J. Oper. Theory 271 (1980).
  13. M. Choi, Linear Algebra Appl. 10, 285 (1975). [CrossRef]
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).
  15. M. Born and E. Wolf, Principles of Optics (Cambridge, 1959).
  16. R. Boyd, Nonlinear Optics (Academic, 2003).
  17. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited