Surface Plasmon Polaritons in a Class of Quasiperiodic Nanoparticle Gauss Chains

We theoretically consider surface-plasmon (SP) polaritons (SPP) on chains of noncontacting metal nanoparticles (NP) along the z-axis at z=md with m is an element of{0,1,2,...} and d the underlying lattice constant. When m=j(n) for j is an element of{0,1,2,...} and given n is an element of{2,3,4,...} , we term it a Gauss site where such nanoparticles differ in their surface-plasmon frequency from the other nanoparticles. Such Gauss chains are quasiperiodic and may exhibit a self-similar hierarchy of minibands and gaps. Our treat-ment here is carried out within a tight-binding model with the Gauss modulation on the diagonal elements and includes the retarded electromagnetic coupling between all pairs of nanoparticles. The case n=2 exhibits a clear hierarchy of minibands and gaps, and these characteristics are preserved in the presence of long-range retarded dipole-dipole coupling, whereas for n>2 , one observes at most weak features of such self-similar behavior. The special nature of the case n=2 is reflected in the spatial distribution of the SPPs on the Gauss chain compared with n>2