Cross-spectral purity of nonstationary vector fields in space-time and space-frequency domains

We establish the concept of cross-spectral purity for nonstationary electromagnetic fields having any degree of coherence or polarization. The conditions of cross-spectral purity in all Stokes parameters are derived for both space-time and space-frequency domains, which demonstrate that the normalized two-point coherence properties of such fields can be expressed as products of a spatial and a time (or frequency) dependent function. We further determine the condition of strict cross-spectral purity for nonstationary fields, which establishes the equivalence of normalized two-point Stokes parameters governing the spatial factors of the space-frequency and space-time domains. This study may provide interesting aspects of statistical properties of beams obtained from practically available sources such as pulsed lasers, modulated and fluctuating light sources, etc.