Influence of periodicity on the reflection properties of finite periodic media

The dispersion relation of periodic systems, the well-known bands structure, gives the information about the propagating modes inside the media. These bands reveal both propagating and non-propagating ranges of frequencies. It is well known that the transmission properties, with relation to the propagating modes, can be characterized by both the bands structure and the equifrequency contours. Oppositely, in finite systems, one should consider the reflection properties on the interface defined by the host and the periodic media in order to know the spatial distribution of the reflected field. In this work, we analyze the reflected acoustic field by a periodic system. An experimental set up is proposed in this work to analyze the reflection properties of a periodic media. From the exploitation of the properties of both the interface and the inner periodicity of the crystal, fundamental and applied questions can be discussed using this media.