Green's function theory for one-way particle chains

Abstract

Recently, it has been shown that a new class of particle chains that support the simultaneous interplay of two-type rotations---geometric and electromagnetic---may possess strong nonreciprocity and one-way guiding effects. Here, we use the $Z$ transform to develop a rigorous Green's function theory for these one-way chains. A study of the chain's spectra and its analytic properties in the complex spectral ($Z$) plane, where each and every singularity (e.g., pole, branch cut, etc.) represents a distinct wave phenomenon, reveals all the wave constituents that may be excited. We explore the breach of symmetry of the complex $Z$ plane singularities and their manifestations as the symmetry breaking wave mechanisms that underly the one-way guiding effects. It is shown that this breach of symmetry in particle chains is possible only when both rotations---geometric and electromagnetic---are simultaneously present. It is also shown that the continuous spectrum (e.g., branch singularity) plays a pivotal role in suppressing the radiation into the ``forbidden'' direction.