Partially coherent fields are abundant in many physical systems. While the propagation of partially coherent light undergoing diffraction is well understood, its evolution in the presence of coherent diffusion (i.e., diffusion of complex fields) remains largely unknown. Here we develop an analytic model describing the diffusion of partially coherent beams and study it experimentally. Our model is based on a diffusion analog of the famous Van Cittert–Zernike theorem. Experimentally, we use a four-wave mixing scheme with electromagnetically induced transparency to couple optical speckle patterns to diffusing atoms in a warm vapor. The spatial coherence properties of the speckle fields are monitored under diffusion and are compared to our model and to the familiar evolution of spatial coherence of light speckles under diffraction. We identify several important differences between the evolution dynamics of the spatial coherence under diffraction and diffusion. Our findings shed light on the propagation of partially coherent fields in media where multiple scattering or thermal motion lead to coherent diffusion.

中文翻译：

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部分空间相干的相干扩散

在许多物理系统中，部分相干的领域非常丰富。尽管人们很好地理解了部分相干光经过衍射的传播，但在相干扩散（即复杂场的扩散）存在下其演化过程仍是未知之数。在这里，我们建立了一个描述部分相干光束扩散的解析模型，并进行了实验研究。我们的模型基于著名的Van Cittert–Zernike定理的扩散模拟。在实验上，我们使用具有电磁感应透明度的四波混合方案，将光学散斑图样耦合到扩散热蒸气中的原子。散斑场的空间相干性在扩散条件下进行监测，并与我们的模型以及衍射下光斑的空间相干性的演化进行了比较。我们确定了衍射和扩散下空间相干性的演化动力学之间的几个重要区别。我们的发现揭示了部分相干场在介质中的传播，介质中多次散射或热运动导致相干扩散。