  We investigated the plasmonic modes in a two-dimensional quasicrystalline
array of metal nanoparticles. The polarization of the modes is in the array
plane. A simplified eigen-decomposition method is presented with the help of
rotational symmetry. Two kinds of anti-phase ring modes with radial and
tangential polarizations are of highest spatial localizations among all of
plasmonic modes. For the leaky characteristic of the anti-phase ring modes, the
highest fidelity mode is found to be tangential polarized mode in the
quasicrystal array, whereas normal-to-plane polarized mode in the solo ring.
The leaky characteristics and spatial localizations of other plasmonic modes
are also studied, for example, collective vortex mode that may be potentially
useful to form negative responses in plasmonic device, and collective radial
mode that may be used to generate light sources with radial polarizations.
