Definition of a second-order degree of polarization in terms of the complex degree of coherence

The classical theory of random electric fields and polarization formalism has been formulated considering the Stokes parameters' auto-correlations. However, in this work, the need to consider the Stokes parameters' cross-correlations to obtain a complete description of the polarization dynamics of a light source is explained. We propose a general expression for the Stokes parameters' degree of correlation using both auto-correlations and cross-correlations, which we derive from the application of Kent's distribution in the statistical study of Stokes parameter dynamics on Poincaré's sphere. Additionally, from the proposed degree of correlation, we obtain a new expression for the degree of polarization (DOP) in terms of the complex degree of coherence, which is a generalization of the well-known Wolf's DOP. The new DOP is tested using a depolarization experiment in which partially coherent light sources propagate through a liquid crystal variable retarder. The experimental results show that our generalization for the DOP improves the theoretical description of a new depolarization phenomenon that Wolf's DOP cannot describe.