Planar One-way Guiding in Periodic Particle Arrays with Asymmetric Unit Cell and General Group-Symmetry Considerations

We develop a general theory for one-way optical guiding in magnetized periodic particle arrays. Necessary conditions for a non-even dispersion curves are derived and presented in the context of Frieze symmetry-groups. It is shown, for example, that one-way guiding can be supported in particle \emph{strips} consisting of geometrically isotropic particles arranged in transversely asymmetric arrays. Specific examples consist e.g.~two parallel isotropic particle chains with different periods. The previously studied one-way effect based on the two-type rotation principle is shown to be a special case. In the latter the exclusion of the appropriate Frieze-symmetries is achieved in a single linear chain by associating a geometric rotation to each particle, thus providing the narrowest possible one-way waveguides. It is also shown that nearly any randomly created period may result in uneven dispersion and one-way guiding.