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This study establishes a reduction formula for nonstationary cross-spectrallypure vector light fields with any spectral bandwidth. The formation of areduction formula, analogous to that for stationary fields, does not apply tothe normalized two-time Stokes parameters of a nonstationary field that iscross-spectrally pure. The current formula incorporates time-integratedcoherence parameters to ensure cross-spectral purity. The reduction formuladerived for nonstationary vector light fields with arbitrary spectral bandwidthshares a similar mathematical structure to that of reduction formulas used forstationary vector fields. Additionally, we examine the requirement of strictcross-spectral purity for using a time-integrated coherence function, whichexhibits a mathematical expression similar to that of strict cross-spectralpurity in stationary vector fields. This investigation sheds light on thecross-spectral purity of pulse-type fields, which holds potential applicationsin the field of statistical optics.

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