The Green function completely encapsulates a system’s linear response to external sources, and plays a central role in optics, electromagnetism, and acoustics. In electromagnetism, a broad range of phenomena are connected to the Green function, including the local density of optical states, superradiance, and the cooperative Lamb shift. Therefore, knowing the Green function is important for progress in fields as diverse as cavity quantum electrodynamics, plasmonics, metamaterials, and photovoltaics. However, experimentally characterizing the full complex Green function is challenging, as it requires amplitude and phase sensitive measurements with deep-subwavelength spatial resolution. Here, we report a method to characterize the full complex Green function with a resolution of $\lambda /100$ by measuring the mutual impedance between two dipoles at microwave frequencies. We apply it to a resonant planar cavity, with both parallel and nonparallel sides, and also explore the effects of modal resonances in a dielectric cube on dipole-dipole interactions. The ability to characterize the Green function with high spatial resolution provides a unique way to investigate cooperative effects in complex photonic systems.

中文翻译：

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复杂环境中的完整电磁二进位格林函数表征-共振偶极-偶极相互作用和协同效应

绿色功能完全封装了系统对外部信号源的线性响应，并且在光学，电磁学和声学中起着核心作用。在电磁学中，格林函数与广泛的现象相关，包括光学状态的局部密度，超辐射和合作的兰姆位移。因此，了解格林函数对于在诸如腔量子电动力学，等离激元，超材料和光伏领域的各个领域取得进展至关重要。但是，对全复杂的格林函数进行实验表征非常具有挑战性，因为它需要对幅度和相位进行敏感的测量，并具有深亚波长空间分辨率。在这里，我们报告了一种方法，该方法可以表征完整的复杂格林函数，其分辨率为$\lambda /100$通过测量微波频率下两个偶极子之间的互阻抗。我们将其应用于具有平行和不平行边的共振平面腔，并且还研究了介电立方体中的模态共振对偶极-偶极相互作用的影响。以高空间分辨率表征格林功能的能力为研究复杂光子系统中的协同效应提供了独特的方法。