Stationarity, homogeneity and isotropy in the coherence theory of the electromagnetic fields

Abstract

The concepts of stationarity, homogeneity and isotropy are introduced in terms of the invariance of certain expectation values under time translations, under space translations and under space rotations respectively. Some consequences of homogeneity and isotropy on the forms and relations among second-order correlation tensors of the electromagnetic field are derived. It is shown that, if the second-order correlation tensors are invariant under space translations, they are also invariant under time translations. Further it is also shown that in such cases the trace of the electric correlation tensor is identical to the trace of the magnetic correlation tensor. General forms of the second-order electromagnetic correlation tensors are derived for fields which are both isotropic and homogeneous. Both quantum and classical descriptions of coherence are considered and the restrictions which stationarity, homogeneity or isotropy impose on the density operator in quantum description and on the probability distributions in classical description are deduced.