Abstract

It is shown that, for a 3×3 correlation matrix Wijr,r,ω,i,j=x,y,z of the electric vector of a random, stationary electromagnetic field to represent a field that is completely polarized at a point r and frequency ω, each element of the matrix must factorize. More precisely, a necessary and sufficient condition for the correlation matrix to represent a fully polarized field at a point r is that the matrix has the form Wijr,r,ω=Ei*r,ωEjr,ω, where Eir,ω i=x,y,z are deterministic functions, i.e., that all pairs of the Cartesian components of the electric field at a point r and frequency ω are completely correlated.

© 2004 Optical Society of America

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