Wave generation at an interface

The problem of wave generation at an interface by an incident wave is fully analyzed with particular attention to the so-called evanescent (or inhomogeneous) waves. After the proof of general results concerning evanescent waves, the paper discusses the properties of evanescent waves in connection with hyperbolicity and dissipative hyperbolicity, the definition of this latter concept being also presented. The main difference is that evanescent waves compatible with dissipative hyperbolicity are allowed to attenuate along the propagation direction whereas, in the case of standard hyperbolicity, they are not. The paper concludes with a detailed discussion about Snell's law