Abstract
It is shown that the elements of the cross-spectral density matrix in any cross-sectional plane z = constant > 0 can be expressed in a unique tensor form when the stochastic electromagnetic beam propagates in a uniaxial crystal whose optical axis coincides with the x-axis. The distributions of the spectral degree of polarization of the uniformly polarized stochastic electromagnetic beam passing through a rutile crystal and a diamond crystal are illustrated and compared by numerical examples. Necessary analyses are given to theoretically explain the physical phenomena.