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Journal Article

Polarimetric purity and the concept of degree of polarization


Norrman,  Andreas
Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Gil, J. J., Norrman, A., Friberg, A. T., & Setälä, T. (2018). Polarimetric purity and the concept of degree of polarization. Phys. Rev. A, 97, 023838. doi:10.1103/PhysRevA.97.023838.

Cite as: https://hdl.handle.net/21.11116/0000-0002-9863-3
The concept of degree of polarization for electromagnetic waves, in its general three-dimensional version, is revisited in the light of the implications of the recent findings on the structure of polarimetric purity and of the existence of nonregular states of polarization [J. J. Gil et al., Phys Rev. A 95, 053856 (2017)]. From the analysis of the characteristic decomposition of a polarization matrix R into an incoherent convex combination of (1) a pure state Rp, (2) a middle state Rm given by an equiprobable mixture of two eigenstates of R, and (3) a fully unpolarized state Ru−3D, it is found that, in general, Rm exhibits nonzero circular and linear degrees of polarization. Therefore, the degrees of linear and circular polarization of R cannot always be assigned to the single totally polarized component Rp. It is shown that the parameter P3D proposed formerly by Samson [J. C. Samson, Geophys. J. R. Astron. Soc. 34, 403 (1973)] takes into account, in a proper and objective form, all the contributions to polarimetric purity, namely, the contributions to the linear and circular degrees of polarization of R as well as to the stability of the plane containing its polarization ellipse. Consequently, P3D constitutes a natural representative of the degree of polarimetric purity. Some implications for the common convention for the concept of two-dimensional degree of polarization are also analyzed and discussed.