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We consider cross-spectral purity in random nonstationary electromagneticbeams in terms of the Stokes parameters representing the spectral density andthe spectral polarization state. We show that a Stokes parameter beingcross-spectrally pure is consistent with the property that the correspondingnormalized time-integrated coherence (two-point) Stokes parameter satisfies acertain reduction formula. The current analysis differs from the previous workson cross-spectral purity of nonstationary light beams such that the puritycondition is in line with Mandel's original definition. In addition, incontrast to earlier works concerning the cross-spectral purity of thepolarization-state Stokes parameters, intensity-normalized coherence Stokesparameters are applied. It is consequently found that in addition to separatespatial and temporal coherence factors the reduction formula contains a thirdfactor that depends exclusively on the polarization properties. We further showthat cross-spectral purity implies a specific structure for the electromagneticspectral spatial correlations. The results of this work constitute foundationaladvances in the interference of random nonstationary vectorial light.

Cross-spectral purity of the Stokes parameters in random nonstationary electromagnetic beams