The edge condition in electromagnetics

The problem of finding the field behavior near a conducting edge in the presence of an arbitrary number of isotropic dielectric wedges is considered. Conditions under which finite and infinite fields can exist are derived. A principal finding is that for four or more dielectrics it is possible to have finite fields at a knife edge. It is shown that the problem is equivalent to finding the fundamental resonance frequency of a resonator formed from a succession of coupled transmission lines.