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

Abstract

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.