Wave transmission through lattices, superlattices and layered media

Wave transmission through periodic and periodic layered structures is studied and the 'average transmissivity' for an incident beam with a bounded uniform spectrum is defined. Both positive and negative delta-function and rectangular potentials are analysed. The phenomenon of the 'resonant transmission', where the wave number is in a permitted band of the central layer and in a forbidden band of the side layers of a three-layer system, is also treated. Consequences of the results, applied to the construction of band pass filters, are discussed.