Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch

The finite-difference time-domain method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional (2D) phononic lattices, i.e., periodic solid-solid, solid-liquid, and solid-vacuum composites, for which the conventional plane-wave-expansion method fails or converges very slowly. Numerical examples are developed for 2D structures with polyethylene, mercury, and vacuum cylinders forming a square lattice in an aluminum matrix. The implication of the calculated dispersion relations for ultrasound transmission experiments is discussed.