Front Propagation in Evanescent Media

We investigate the time evolution of waves in evanescent media generated by a source within this medium and observed at some distance away from the location of the source. The aim is to find a velocity which describes a causal process and is thus, for a medium with relativistic dispersion, limited by the velocity of light. The wave function consists of a broad frequency forerunner generated by the onset of the source, and of a monochromatic front which carries the oscillation frequency of the source. For a medium with Schrödinger-like dispersion the monochromatic front propagates with a velocity which is in agreement with the traversal time, and in the relativistic case the velocity of the fronts is limited by the velocity of light. For sources with a sharp onset, the forerunners are not attenuated and in magnitude far exceed the monochromatic front. In contrast, for sources which are frequencyband limited, the forerunners are also attenuated and become comparable to the monochromatic front: like in the propagating case, there exists a time at which a broad frequency forerunner is augmented by a monochromatic wave. PACS numbers: 05.45.+b, 72.10.Bg, 72.30.+q Typeset using REVTEX