Spectral and polarization properties of stochastic electromagnetic beams propagating in gain or absorbing media

Based on the generalized Huygens–Fresnel diffraction principle and on the unified theory of coherence and polarization of light, the analytical expressions for the cross-spectral density matrix of a class of stochastic electromagnetic beams in linear, deterministic media with gain or absorption, in which the wave number is generally complex, has been derived. In particular, through numerical examples based on our analytical formulas the behavior of the spectral density, and of the degree of polarization of the Electromagnetic Gaussian Schell-model is analyzed. It is demonstrated how these statistical properties of the beam propagating in such media depend on the properties of the source and on the wave number of the medium. Numerical examples relate to two model sources: with uncorrelated and partially correlated mutually orthogonal transverse components of the electric field. The results will impact potential applications involving natural absorbing media, such as oceanic waters, and man-made media such as active lasers, for instance.