We establish the concept of cross-spectral purity for nonstationary electromagnetic fields having any degree of coherence or polarization. The conditions of cross-spectral purity in all Stokes parameters are derived for both space–time and space–frequency domains, which demonstrate that the normalized two-point coherence properties of such fields can be expressed as products of a spatial and a time (or frequency) dependent function. We further determine the condition of strict cross-spectral purity for nonstationary fields, which establishes the equivalence of normalized two-point Stokes parameters governing the spatial factors of the space–frequency and space–time domains. This study may provide interesting aspects of statistical properties of beams obtained from practically available sources such as pulsed lasers, modulated and fluctuating light sources, etc.

中文翻译：

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时空和频域非平稳矢量场的跨谱纯度

对于具有任何相干性或极化性的非平稳电磁场，我们建立了跨谱纯度的概念。时空和时空频域都导出了所有斯托克斯参数中的互谱纯度条件，这表明此类场的归一化两点相干特性可以表示为空间和时间的乘积（或频率）相关功能。我们进一步确定了非平稳场的严格交叉谱纯度的条件，这确定了支配时空频域和时空域空间因素的归一化两点斯托克斯参数的等价性。这项研究可能会提供有趣的方面，这些方面的统计信息来自从实际可用的来源（如脉冲激光，