Green's function theory for one-way particle chains

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.