Waves on chains: Periodic, clustered, and quasi-periodic arrangements

Linear arrays of electrically small resonating particles may support trapped optical modes, leaky waves, and continuous-spectrum (“lateral”) waves. We discuss the generalization of traditional perfectly-periodic Bravais chains to structures arranged as clustered periodic non-Bravais crystals, and to a new type of almost-periodic arrays. Although the latter can be viewed as a special case of non-Bravais lattice whose period is extended to infinity, its analysis is based on a new formulation borrowed from the theory of almost-periodic sequences. The wave spectra and modal features of these structures are presented and discussed.