Covariance operators, Green functions, and canonical stochastic electromagnetic fields

In this paper, we show that for a large class of lossless reciprocal configurations, a “canonical” stochastic electromagnetic field can be defined such that its spatial covariance is proportional to the real part of the Green tensor function of the configuration. This result generalizes some relations between stochastic plane waves and free space Green functions which are well known in theoretical physics. A special application of the ideas presented here is elaborated for the configuration of a semi-infinite, short-circuited waveguide. It is shown that the canonical stochastic electromagnetic field in that case is a pseudoisotropic plane wave corresponding to a very special stochastic linear combination of propagating modes only. This has important consequences for the electromagnetic theory of so-called mode-stirred chambers.