Evanescent waves and discontinuities

An evanescent wave is a wave disturbance which travels along a direction and attenuates along a different direction. Evanescent waves are typically generated when a plane wave obliquely strikes a boundary between two media possessing different material properties. A detailed analysis of the problem of the oblique incidence shows that plane waves are completely determined by the knowledge of the so-called reflection and transmission coefficients On the contrary the properties of the evanescent waves are summarized by the knowledge of two functions, linearly determined by the amplitude of the incident wave, which are to be chosen as the Hilbert transform of each other; in so doing the evanescent wave exhibits the appropriate behaviour at infinity. A thorough comparison between discontinuity waves and evanescent waves makes it evident that the usual information about discontinuities does not suffice for calculating evanescent waves. This proves that the oblique incidence problem does not admit a consistent answer within the sole framework of discontinuity waves