Symmetry analysis of large two-dimensional clusters of coupled cavity resonators

A comprehensive symmetry analysis of 2-D clusters with either a square or hexagonal lattice is being performed to determine the dependence of the wave impedance and the propagation constant on the frequency and the azimuthal direction of wave propagation. The boundary conditions for reflection-free, multiport impedance matching around the perimeter of finite clusters are being formally defined. Generalized matrix-algorithms have been derived that formally express the open-circuit impedance matrix of a cluster of finite extent, as seen from the external ports, aligned around the structure perimeter. These algorithms use a multilevel diakoptic approach, by tearing the cluster into progressively smaller subdivisions, while maintaining geometrical similarity, and conserving the translation-, rotation-, and reflection-symmetry of the whole system. Formal expressions have been obtained for the 2-D traveling-wave amplitude and phase patterns generated by any given distribution of mutually coherent excitation sources.<>