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The collective modes of two-dimensional ordered atomic arrays can modify theradiative environment of embedded atomic impurities. We analyze the role of thelattice geometry on the impurity's emission linewidth by comparing theeffective impurity decay rate obtained for all non-centered Bravais latticesand an additional honeycomb lattice. We demonstrate that the lattice geometryplays a crucial role in determining the effective decay rate for the impurity.In particular, we find that the minimal effective decay rate appears inlattices where the number of the impurity's nearest neighbours is maximal andthe number of distinct distances among nearest neighbours is minimal. Wefurther show that, in the choice between interstitial and substitutionalplacement of the impurity, the former always wins by exhibiting a lower decayrate and longer photon storage. For interstitial placements, we determine theoptimal impurity position in the lattice plane, which is not necessarily foundin the center of the lattice plaquette.

Optimized geometries for cooperative photon storage in an impurity coupled to a two-dimensional atomic array