Al Lakki Mohammad, Friberg Ari T, Setälä Tero
Opt Lett. 2021 Apr 1;46(7):1756-1759. doi: 10.1364/OL.420573.
Despite a wide range of applications, the coherence theory of random, nonstationary (pulsed or otherwise) electromagnetic fields is far from complete. In this work, we show that full coherence of a nonstationary vectorial field at a pair of spatiospectral points is equivalent to the factorization of the cross-spectral density matrix, and full pointwise coherence over a spatial volume and spectral band leads to a factored cross-spectral density throughout the domain. We further show that in the latter case, the time-domain mutual coherence matrix factors in the spatiotemporal variables, and the field is temporally fully coherent throughout the volume. The results of this work justify that certain expressions of random pulsed electromagnetic beams appearing in the literature can be called coherent-mode representations.
尽管随机、非平稳（脉冲式或其他形式）电磁场的相干理论有广泛应用，但其仍远未完善。在这项工作中，我们表明非平稳矢量场在一对时空谱点处的完全相干等同于交叉谱密度矩阵的因式分解，并且在空间体积和频谱带内的完全逐点相干会导致整个域内的交叉谱密度因式分解。我们进一步表明，在后一种情况下，时域互相关矩阵在时空变量中因式分解，并且场在整个体积内是时间上完全相干的。这项工作的结果证明了文献中出现的某些随机脉冲电磁束的表达式可称为相干模表示。
