Statistics of polarization and Stokes parameters of stochastic waves.

Several theories now exist to describe the probability distribution functions (PDFs) for the electric field strength, intensity, and power of signals. In this work, a model is developed for the PDFs of the polarization properties of the superposition of multiple transverse wave populations. The polarization of each transverse wave population is described by a polarization ellipse with fixed axial ratio and polarization angle, and PDFs for the field strength and phase. Wave populations are vectorially added, and expressions found for the Stokes parameters I , U , Q , and V , as well as the degrees of linear and circular polarization, and integral expressions for their statistics. In this work, lognormal distributions are chosen for the electric field, corresponding to stochastic growth, and polarization PDFs are numerically calculated for the superposition of orthonormal mode populations, which might represent the natural modes emitted by a source. Examples are provided of the superposition of linear, circular, and elliptically polarized wave populations in cases where the component field strength PDFs are the same, and where one field strength PDF is dominant.