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 noneven 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 strips consisting of geometrically isotropic particles arranged in transversely asymmetric arrays. A specific example is the case of 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.