Cross-spectral purity of the Stokes parameters in random nonstationary electromagnetic beams

TL;DR

This paper investigates the cross-spectral purity of Stokes parameters in nonstationary electromagnetic beams, revealing how spectral and polarization properties influence coherence and spectral correlations, advancing understanding of vectorial light interference.

Contribution

It introduces a new formulation of cross-spectral purity aligned with Mandel's original definition, incorporating intensity-normalized coherence Stokes parameters and revealing a third polarization-dependent factor.

Findings

Cross-spectral purity relates to a specific reduction formula for normalized coherence Stokes parameters.

The reduction formula includes a polarization-dependent factor beyond spatial and temporal coherence.

Cross-spectral purity constrains the structure of spectral spatial correlations in electromagnetic beams.

Abstract

We consider cross-spectral purity in random nonstationary electromagnetic beams in terms of the Stokes parameters representing the spectral density and the spectral polarization state. We show that a Stokes parameter being cross-spectrally pure is consistent with the property that the corresponding normalized time-integrated coherence (two-point) Stokes parameter satisfies a certain reduction formula. The current analysis differs from the previous works on cross-spectral purity of nonstationary light beams such that the purity condition is in line with Mandel's original definition. In addition, in contrast to earlier works concerning the cross-spectral purity of the polarization-state Stokes parameters, intensity-normalized coherence Stokes parameters are applied. It is consequently found that in addition to separate spatial and temporal coherence factors the reduction formula contains a third factor that depends exclusively on the polarization properties. We further show that cross-spectral purity implies a specific structure for the electromagnetic spectral spatial correlations. The results of this work constitute foundational advances in the interference of random nonstationary vectorial light.