Analytical Methods for Analysis of Electromagnetic Field Behavior at Edges

Kurzfassung

This 25-minutes-long presentation has addressed the problem of singular behavior of electromagnetic fields at places of abrupt changes of geometrical or/and material properties of a reflecting boundary. The presentation has been primarily concerned with a wedge configuration (perfectly conducting, impedance, dielectric) and attention has been focused on the field behavior at the edge of the wedge. In a vicinity of the edge, transverse field components are known to exhibit a power singularity with an exponent which is a function of material and geometrical parameters of the configuration. The ability to predict a precise value of the exponent or, more generally, to construct suitable analytical representations for the electromagnetic field components near the edge of a wedge is of great practical and theoretical interest because this canonical configuration is relevant to a wide variety of practical applications, including reduction of radar cross section of scattering objects, transmission of electromagnetic energy via waveguides and microstrip lines, radiation of waves from antenna apertures, radio communication over irregular terrain features etc. The talk has covered both theoretical and practical aspects of the problem. In particular, it started by introducing basic concepts and techniques (edge conditions, Meixner's method) employed for the analysis of the field behavior at edges. Specific examples of edge behavior in various configurations of practical interest have been given. Then the focus has been on a relatively new technique -- method of edge functions (MEF) -- which is based on eigenfuncion solutions of Maxwell's equations, each correctly satisfying the edge conditions and conditions of continuity of the tangential field components across the wedge faces. The talk concluded with a discussion of possible applications of MEF to semi-analytical solution of canonical problems of high-frequency electromagnetic scattering from wedges.