Localization characteristics of two-dimensional quasicrystals consisting of metal nanoparticles

Using the eigendecomposition method, we investigated the plasmonic modes in a two-dimensional quasicrystalline array of metal nanoparticles. Various properties of the plasmonic modes, such as their symmetry, radiation loss and spatial localization are studied. Some collective plasmonic modes are found to be leaky with out-of-plane radiation loss, but some modes can have very high fidelity. To facilitate the analysis on the complex behavior of the collective plasmonic modes, we considered a trajectory map in a three dimension parameter space defined by the frequency of the mode, the eigenvalue that is related to the inverse lifetime of the mode, and the participation ratio of the mode that gives the spatial distribution,. With the help of the trajectory map method, we found that there are modes that are localized in some special ways and the plasmonic mode with highest spatial localization and highly fidelity is found to be a type of antiphase ring mode. In general, different localized modes have very different radial decay behaviors. There is no special relationship between the fidelity of the modes and their spatial localization.