Wave transmission trough inhomogeneous chain of transparent obstacles

We investigate the resonance and guiding properties of a chain of inhomogeneous transparent obstacles. Pass and stop bands are studied. Approximate expressions for the first waveguiding frequencies and phase velocities of the wave-guiding modes in a transparent periodic structure consisting of two different media (chain of transparent obstacles) are found. It is shown that the length of a guided wave in a chain of transparent obstacles can exceed considerably the transparent obstacle sizes. The phase velocity of a guided wave can be smaller than wave velocities in both media in the event that the interaction between neighbouring transparent obstacles is taken into account. The influence of inhomogeneity of transparent obstacle sizes on the first wave-guiding frequencies of a chain of transparent obstacles is investigated. The resonance phenomena in periodical non-homogeneous chains of transparent obstacles for sources localized or distributed in space are investigated. As a result of the analysis, new physical phenomena are reported: 1. Resonance growth of amplitude in the neighbourhood of a source, and 2. Travelling wave resonance. Conditions of realization of the mentioned phenomena are obtained.