Elastic wave propagation along waveguides in three-dimensional phononic crystals

We investigate theoretically using the finite difference time domain method acoustic wave propagation along waveguides in three-dimensional phononic crystals constituted of lead spherical inclusions on a face-centered cubic lattice embedded in an epoxy matrix. The transmission spectra of the perfect phononic crystal for transverse and longitudinal acoustic waves are shown to depend strongly on the direction of propagation. The crystal possesses an absolute band gap. Waveguides oriented along different crystallographic directions, namely the $⟨100⟩$ and $⟨111⟩$ directions, exhibit pass bands in the phononic crystal band gaps for both transverse and longitudinal polarizations.