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

TL;DR

This paper derives a reduction formula for nonstationary cross-spectrally pure vector light fields, revealing similarities with stationary fields and exploring conditions for cross-spectral purity in pulse-type fields, with implications for statistical optics.

Contribution

It introduces a new reduction formula for nonstationary vector fields with arbitrary spectral bandwidth, extending stationary field concepts to nonstationary cases.

Findings

Derived a reduction formula for nonstationary fields with arbitrary bandwidth.

Showed the mathematical similarity between nonstationary and stationary field formulas.

Analyzed the conditions for strict cross-spectral purity in pulse-type fields.

Abstract

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.