Resumen: 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 R-p, (2) a middle state R-m given by an equiprobable mixture of two eigenstates of R, and (3) a fully unpolarized state Ru-3D, it is found that, in general, R-m 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 R-p. It is shown that the parameter P-3D 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, P-3D 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. Idioma: Inglés DOI: 10.1103/PhysRevA.97.023838 Año: 2018 Publicado en: Physical Review A 97, 2 (2018), 023838 [4 pp] ISSN: 2469-9926 Factor impacto JCR: 2.907 (2018) Categ. JCR: PHYSICS, ATOMIC, MOLECULAR & CHEMICAL rank: 13 / 36 = 0.361 (2018) - Q2 - T2 Categ. JCR: OPTICS rank: 28 / 95 = 0.295 (2018) - Q2 - T1 Factor impacto SCIMAGO: 1.268 - Atomic and Molecular Physics, and Optics (Q1)