Stabilizing a single integral equation for transverse electric wave scattering by dielectric cylinders

A single integral equation (SIE) for the scattering of transverse electric waves by a system of multiply-connected dielectric cylinders has been presented. The SIE overcomes the stability problem associated with the "magnetic current only" SIE formulation by employing a layer of combined electric and magnetic current having a single unknown density. Corresponding numerical results presented for the case of a single homogeneous circular dielectric cylinder are considerably improved. However, the optimum ratio of electric current to magnetic current is not predicted by the theory; rather, it must be determined experimentally.