The Stokes decomposition theorem for three-dimensional stationary fields

Paraxial approximation defines the electric field of an optical beam at each point as a two-dimensional vector orthogonal to the direction of propagation. The Stokes decomposition theorem asserts that “any light beam is equivalent to the sum of two lights, one of which is polarized and the other unpolarized”. In a modern framework of random stationary processes, the theorem needs more accurate statements. In this paper, we study three-dimensional fields, and we prove that the decomposition problem has at most two solutions (except for an undetermined argument) which are characterized by well determined circuits of LIF (Linear Invariant Filters).