Green’s function theory for infinite and semi-infinite particle chains

Abstract

A Green's function theory for the excitation of, and scattering from, particle chains is developed. A $Z$ transform is applied to the discrete dipole approximation of the chain, and the chain's spectral properties are explored in the complex $Z$ plane. It is shown that a continuous spectrum may be excited, and the roles of the discrete and continuous spectra in the chain response are studied. The latter may dominate the chain response under lossy conditions. Using the Wiener-Hopf technique, the theory is extended to semi-infinite chains and the chain edge effects are studied. It is shown that edge effects can significantly enhance chain excitation.