Maximal polarization order of random optical beams: reversible and irreversible polarization variations

We discuss the degrees of polarization (DoP) of electromagnetic beams in time and frequency domains. The mean spectral DoP corresponds to the maximal temporal DoP when unitary transformations are applied in frequency domain. We demonstrate that random unitary transformations in frequency domain cannot increase the mean spectral DoP, implying that this quantity is a useful measure of the polarization order of light beams. This leads to a classification of time-domain polarization changes into reversible and irreversible processes.