Waveguide and anomalous properties of circular disk periodic chain embedded in 3D space

Anomalous and waveguide properties of a periodic chain of circular disks are studied. The existence of waveguide and anomalous properties are proved to be independent of the chain period and the disk size. Classification of the waveguide modes according to the symmetry groups of problem are given. The number of waveguide modes and the dependence of waveguide frequencies on the geometric parameters is investigated.