Green's functions are an important computational tool for solving a wide range of classical and quantum electromagnetic problems. In arrays, they allow us to understand the influence of defects or inclusions and to model the radiation of a localized source. The Green's function is closely linked to the local density of states, a key quantity in determining the emission rate of quantum emitters placed in or near the structure. In this work, Tan and Tsang present a technique for calculating the Green's function corresponding to a finite source within an infinite two-dimensional array. They are able to overcome the computational problem of poorly converging sums by using a low-frequency extraction, which greatly enhances the convergence.

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