Conservation laws for stochastic electromagnetic free fields

Conservation laws for scalar stochastic free fields propagating in free space are generalized to electromagnetic beam-like fields. New conservation laws are derived for the elements of the cross-spectral density matrix of a stochastic electromagnetic beam, and they can be used to show that some integrated polarization properties, for example, Stokes parameters of a beam, are conserved on propagation in free space. We also show that, unlike integrated Stokes parameters, other polarization characteristics of a beam, for instance, its degree of polarization, are not, generally, conserved on propagation. The theory is illustrated by an example relating to the propagation of single-point and integrated Stokes parameters of an electromagnetic Gaussian Schell-model beam.