Higher-order polarization in coherent optics

We introduce a definition of 2N-order polarization and apply this definition for analysis of general effects of the anisotropy of optical radiation. As an initial definition, we use a set of polarization matrices of order 2N, which are considered as statistical means of the Kronecker N-fold second-order tensors: g([1,1])= E+circle times E. Evidently, this set contains all paired mixed moments of polarization components, thus determining all possible polarization properties of the above-defined field. Furthermore, any unitary (non-depolarizing) transform in Jones vector space corresponds to the unitary transform of polarization matrix of higher orders, and therefore does not change polarization of any order. This notion allows us to determine a degree of polarization P-[N] for higher order using invariants of unitary transforms of a corresponding polarization matrix. The concept of higher order polarization is applied to the problems of photon counting, intensity interferometry and nonlinear optics.