On the existence of branch points in the eigenvalues of the electric field integral equation operator in the complex frequency plane

Baum (1978), and Pearson and Wilton (1981) have speculated upon the existence of branch-integral constituents in the singularity expansion method (SEM). The present investigation is concerned with the presentation of specific examples that eigenvalues of the electric field integral equation (EFIE) operator for finite extent objects in lossless media can have branch points in the complex frequency s-plane. A formal solution of the EFIE is considered, and the validity of the eigenmode expansion method (EEM) is discussed. The SEM expansion for the current density on an object is derived, and some of the theoretical aspects of this representation is considered. Branch points in circuit and transmission line problems are examined, taking into account lumped circuits and a distributed two-port example. Aspects of scalar scattering from a prolate spheroid, and TM scattering from an elliptic cylinder are also explored.