14.1 What are Wave Guides?

Wave guides are cylindrically shaped objects of metal (almost ideal conductors) which are open at both ends. Resonators, also called resonant cavities, differ from these in being closed at both ends. The interior of such objects is filled with some homogeneous material with electromagnetic constants ?, ?; alternatively the interior can be composed of layers of different materials. We have seen before, that the larger the conductivity ? of a medium or the frequency of the incident electromagnetic wave, the smaller the skin depth, i.e. the depth of penetration of the radiation into the conducting medium. This follows from the dispersion relation that we encountered several times earlier, i.e.

together with the plane wave ansatz

The square root of k ² is

Here we have to choose the physically relevant sign. For instance for the wave exp( ikz) and a medium extended indefinitely in the direction of z, the sign has to be chosen such that the wave is damped, so that the current density j = ? E cannot grow arbitrarily (which would be nonsensical). It is because of this skin effect that it is possible to confine radiation in hollow bodies or to use them for the propagation of waves (ideal conductors with ? = ? do not permit any penetration of radiation into the walls). The radiation is fed into the wave guide or resonator with a sender or emitter. We assume...