Period asymmetries in particle arrays for one-way and sector-way guiding

A general theory for one-way optical guiding in periodic particle arrays is developed. Conditions on the asymmetry properties of the structure´s period that are necessary to obtain asymmetric dispersion are derived. The two-type rotation principle, presented and studied in previous works on one-way guiding in particle chains, is viewed as a special design that achieves the necessary violation of the period´s symmetries. The recently suggested sector-way metasurfaces are also addressed in the present context. Examples of periodic strips and surfaces that consist of circular particles and support one way and sector-way guiding, are provided.