Material loss influence on the complex band structure and group velocity in phononic crystals

The influence of material loss on the complex band structure of two-dimensional phononic crystals is investigated. A viscoelasticity model is added to the extended plane-wave expansion (EPWE) method, with viscosity proportional to the frequency. It is found that losses have a stronger influence on the real than on the imaginary part of Bloch waves, in contrast with propagation in homogeneous media. Flat bands, i.e., bands initially showing low group velocity without losses, acquire an enhanced damping as compared to bands with larger group velocities. Losses are also found to limit the appearance of large group slownesses, or conversely small group velocities.