Channeled spectrum in the transmission of phononic crystal waveguides

Waveguiding in a phononic crystal (PC) can be achieved along either linear line defects or a sequence of cavities, for frequencies belonging to a complete bandgap. When waves are coupled inside a PC waveguide, modulations in the frequency transmission are generally observed, leading to the formation of a channeled spectrum. We show that the channeled spectrum results from the interference of forward and backward guided Bloch waves. We first theoretically develop a Bloch wave interference model. Then, we consider the case of linear waveguides and of coupled-resonator waveguides formed in a 2D square PC composed of water cylinders in mercury. The transmission properties of waveguides with different length and defect distribution are examined. In all cases, the observed channeled spectra are well explained by the theoretical model. This work is relevant to the design of new acoustic and elastic wave devices.