A singular integral equation approach to electromagnetic fields for circular boundaries with slots

Abstract

It is shown that for the case of a single cylinder which has any number of axial slots of arbitrary width and infinite length, or for the case of coaxial cylinders where one of the cylindrical boundaries has such slots, the Dirichlet and Neumann problems for the Helmholtz equation (which correspond respectively to E and H waves) can be reduced to that of solving a singular integral equation. It is also shown that the resulting singular integral equation is formally the same for both the Dirichlet and Neumann problems for various kinds of circular boundaries. The exact solution of the integral equation is given and applied to the Dirichlet and Neumann problems. The following three simple cases: (1) a single narrow slot in a cylinder; (2) a single narrow slot in a coaxial cylinder; and (3) narrow circular strips are considered to illustrate the applicability of the method.