Cross-spectral purity of nonstationary vector optical fields: A similarity with stationary fields

This study establishes a reduction formula for nonstationary cross-spectrally pure vector light fields with any spectral bandwidth. The formation of a reduction formula, analogous to that for stationary fields, does not apply to the normalized two-time Stokes parameters of a nonstationary field that is cross-spectrally pure. The current formula incorporates time-integrated coherence parameters to ensure cross-spectral purity. The reduction formula derived for nonstationary vector light fields with arbitrary spectral bandwidth shares a similar mathematical structure to that of reduction formulas used for stationary vector fields. Additionally, we examine the requirement of strict cross-spectral purity for using a time-integrated coherence function, which exhibits a mathematical expression similar to that of strict cross-spectral purity in stationary vector fields. This investigation sheds light on the cross-spectral purity of pulse-type fields, which holds potential applications in the field of statistical optics.