A Rapid Numerical Procedure for Determining Axisymmetric Transverse Electric Electromagnetic Fields Via Boundary Integrals

Abstract : An important engineering problem is the determination of the electromagnetic fields in microwave systems, for example tapered waveguides, horns, scatterers, close cavities, and open resonators. Consider the case of axisymmetric transverse electric modes. Such problems for monochromatic radiation can be reduced to consideration of an elliptic partial differential equation similar to the Helmholtz equation. Methods have been developed for the direct numerical solution of the partial differential equation. Variational principles have been used to optimally determine approximate values of object of interest like reflection and transmission coefficients. An alternative approach is the reduction of the problem to consideration of an integral equation defined on the metallic walls defining the object (the boundary integral method). These have been solved for the case of scalar fields described by the Helmholtz equation. The boundary integral equation method is feasible when the Greens function is known in a computationaly convenient form, and is very often much more computationaly efficient than its competitors, particularly when the geometry is complex. The theory and effective numerical implementation are described of such a boundary integral equation approach for the case of an axisymmetric transverse electric electromagnetic field. The technique is readily generalizable to arbitrary axisymmetric fields.