Changes in the state of polarization of a random electromagnetic beam on propagation

We show that the state of polarization of the polarized portion of a random, statistically stationary, electromagnetic beam may change on propagation, even in free space. We derive analytic formulas for the orientation angle and for the magnitudes of the major and of the minor axes of the polarization ellipse in terms of the elements of the 2 × 2 cross-spectral density matrix of the electric field. We also obtain conditions for the invariance of the state of polarization on propagation. We illustrate the results by a numerical example relating to an electromagnetic Gaussian Schell-model beam.