About the Stokes decomposition theorem of waves

The Stokes decomposition theorem deals with the electrical field E→=X,Y of a light beam. The theorem asserts that a beam can be viewed as the sum of two differently polarized parts. This result was recently discussed for light in the frame of the unified theory of coherence. We study the general case of an electromagnetic wave which can be in radio, radar, communications, or light. We assume stationary components with any power spectrum and finite or infinite bandwidth. We show that an accurate definition of polarization and unpolarization is a key parameter which rules the set of solutions of the problem. When dealing with a “strong definition” of unpolarization, the problem is treated in the frame of stationary processes and linear invariant filters. When dealing with a “weak definition”, solutions are given by elementary properties of bidimensional random variables.