Phonon transport and waveguiding in a phononic crystal made up of cylindrical dots on a thin homogeneous plate

We present a theoretical analysis of the phonon transport and guiding of acoustic waves in a phononic crystal made up of a square array of cylindrical dots, which is deposited on a thin homogeneous plate. With appropriate choice of the geometrical parameters, this structure can display several gaps, one of them being well below the Bragg gap. With the help of the finite difference time domain method, we calculate the transmission coefficient vs the frequency and demonstrate a good agreement with the dispersion curves. We show the possibility of guided modes inside an extended linear defect created either by removing one row of cylinders or by changing the height or the materials constituting the dots in a row. The wavelengths of the waves transmitted in the low-frequency gap are about ten times larger than the width of the waveguide. We discuss the transmittivity of each confined mode appearing in the band gap as well as the conversion in the polarization of the transmitted waves which can occur more or less significantly.