Evanescent Bloch waves and the complex band structure of phononic crystals

The complex band structure of a phononic crystal is composed of both propagating and evanescent Bloch waves. Evanescent Bloch waves are involved in the diffraction of acoustic phonons at the interfaces of finite phononic crystal structures. They are shown to arise both because of band gaps, where they directly measure the exponential decrease upon transmission, and because of the frustrated nature of higher-order diffracted waves at low frequencies. These diffracted evanescent Bloch waves become propagative as the frequency increases thus populating higher frequency bands. These results should apply as well to any periodic medium supporting the propagation of waves.