Journal of the European Optical Society - Rapid publications, Vol 3 (2008)

Degree of polarization and quantum-mechanical purity

H. Moya-Cessa, J. R. Moya-Cessa, J.E.A. Landgrave, G. Martinez-Niconoff, A. Perez-Leija, A. T. Friberg


The purity parameter is used in quantum mechanics to discriminate
pure states from mixed states. We employ this concept to define a
degree of polarization for general, three-dimensional, classical
random electric fields. Our approach leads to a result that is
identical with a recent definition obtained by a decomposition of
the polarization matrix in terms of the Gell-Mann matrices. We
also give an expression for this degree of polarization based on
the constituent two-dimensional subsystems.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2008.08014]

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O. Crasser, H. Mack, and W.P. Schleich, "Could Fresnel optics be quantum mechanics in phase space?" Fluct. Noise Lett. 4, L43-L51 (2004).

M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, "Quantum computation by quantumlike systems" Phys. Lett. A 288, 132-138 (2001).

S. Chvez-Cerda, J.R. Moya-Cessa, and H. Moya-Cessa, "Quantumlike systems in classical optics: applications of quantum optical methods" J. Opt. Soc. Am. B 24, 404-407 (2007).

C. Brosseau, Fundamentals of polarized light: A statistical optics approach (Wiley, New York, 1998).

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, Cambridge, UK, 1995).

M. Born and E. Wolf, Principles of optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

M. Gell-Mann and Y. Ne'eman, The eightfold way (Benjamin, New York, 1964).

T. Setl, A. Shevchenko, M. Kaivola, and A.T. Friberg, "Degree of polarization for optical near fields" Phys. Rev. E 66, 016615 (2002).

R. Barakat, "Degree of polarization and the principal idempotents of the coherency matrix" Opt. Commun. 23, 147-150 (1977).

J. C. Samson and J. V. Olson, "Some comments on the descriptions of the polarization states of waves" Geophys. J. Roy. Astr. S. 61, 115_U129 (1980).

C. Brosseau and A. Dogariu, "Symmetry properties and polarization descriptors for an arbitrary electromagnetic wavefield" in Progress in Optics, E. Wolf, ed., Vol. 49, p. 315 (Elsevier, Amsterdam, 2006).

J.J. Gil, "Polarimetric characterization of light and media - Physical quantities involved in polarimetric phenomena" Eur. Phys. J. - Appl. Phys. 40, 1-47 (2007).

A. Luis, "Degree of polarization for three-dimensional fields as a distance between correlation matrices" Opt. Commun. 253, 10-14 (2005).

U. Leonhardt, Measuring the quantum state of light (Cambridge University Press, Cambridge, UK, 1997).

H. Moya-Cessa, "Decoherence in atom-field interactions: A treatment using superoperator techniques" Phys. Rep. 432, 1-41 (2006).

R. Barakat, "n-fold polarization measures and associated thermodynamic entropy of N partially coherent pencils of radiation" Opt. Acta 30, 1171-1182 (1983).

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

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field" Opt. Lett. 29, 1536-1538 (2004).

R. B. J. T. Allenby, Linear algebra, in Modular Mathematics (Butterworth-Heinemann, Oxford, UK, 1995).