  Using the eigen-decomposition 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 participation ratio of the mode
that gives the spatial distribution, and the eigenvalue that is related to the
inverse lifetime of the mode. 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 anti-phase 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.
