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

Abstract

This study establishes a reduction formula for nonstationary cross-spectrally pure vector (or electromagnetic) light fields with any spectral bandwidth. In general, for nonstationary cross-spectrally pure electromagnetic fields, the reduction formula of the two-time Stokes parameters normalized by the corresponding usual Stokes parameters is not similar to the one for stationary fields since the correlation properties for nonstationary fields depend on two-time instants t1 and t2, in addition to their time difference. Here, we derive a reduction formula by including time-integrated correlations that share a similar mathematical structure to that of reduction formulas used for stationary vector fields if the normalized spectra of the interfering fields are identical. Additionally, we examine the requirement of strict cross-spectral purity for nonstationary electromagnetic fields using a time-integrated coherence function, which exhibits a mathematical form 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 statistical optics.