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.