It is shown that, for a 3×3 correlation matrix Wij(r, r, ⍵), (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 ⍵, 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 Wij(r, r, ⍵)=ε*i(r, ⍵)ε j(r, ⍵), where εi(r, ⍵) (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 ⍵ are completely correlated.
© 2004 Optical Society of America
Jeremy Ellis, Aristide Dogariu, Sergey Ponomarenko, and Emil Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field," Opt. Lett. 29, 1536-1538 (2004)