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.

Planar one-way guiding in periodic particle arrays with asymmetric unit cell and general group-symmetry considerations

“…There are also two intersections with the light-line cone corresponding to the so called "light-line modes". The latter are practically unexcitable in SDC-type structures, whether reciprocal [31,38], or non-reciprocal [44]. Hence only −x propagating mode can be excited, as seen in the response in Fig.…”

“…Since it incorporates geometrical rotation and Faraday rotation simultaneously, it is termed as the two-type rotation principle. We refer the reader to [43,44] for examples of planar chains. Hence, in the context of the present study, the two-type rotation principle can be viewed as a method to generate p1 or p1m1 structures systematically, using only a single chain.…”

“…In [42][43][44] a family of magnetized plasmonic SDC's one-way waveguides, based on the 'twotype rotation" principle was proposed for oneway guiding and optical isolation. As has been shown there, exposing a conventional spherical particles SDC to external magnetic bias may formally create non-reciprocity due to the Faraday rotation induced in the plasmonic particles.…”

“…The interplay between the field polarization rotation due to the gyrotropy of the resonant particles and the structural chirality is utilized in order to enhance non-reciprocity and create uneven dispersion. Significant optical isolation and one-way guiding are then obtained at operation points near the light-cone -see [42][43][44]. These structures have two main advantages over other one-way schemes.…”

Formation of nonreciprocal bands in magnetized diatomic plasmonic chains

“…Furthermore, for simplicity, simple lossless Drude model is used [19], and bands related to p z k;σ , the z component of p k;σ , are not shown. It is because B is in z direction, so p [10,20,21]. Figure 2(a) shows a case with non-reciprocal (asymmetric) bands.…”