Confluent edge conditions for the electromagnetic wave at the edge of a wedge bounded by material sheets

Abstract

The edge conditions which dictate the asymptotic behaviour of the electromagnetic field near the edges play a crucial role in solving boundary-value problems involving boundaries having edges. In analytical studies they permit one to determine some unknown functions while in numerical investigations they enable one to improve the convergence of some processes by introducing beforehand the edge singularities into the field functions. In spite of its importance, the subject has not yet been studied sufficiently and accurately for new types of boundary conditions which are important for practical applications. This work is devoted to the analysis of wedge configurations bounded by material sheets having different constitutive parameters. The cases where the electric or the magnetic field is parallel to the edge are considered separately. It is shown that for each of these cases 81 physically different configurations are possible. However, from mathematical point of view all these configurations can be reduced only to nine canonical types. These canonical types are investigated in full detail by introducing the confluence concept which permits one to reveal also the logarithmic singularities, if any.