Investigation of single-source surface integral equations for electromagnetic wave scattering by dielectric bodies
Swatek, David R.
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The problem of wave scattering by systems of homogeneous, multiply-connected dielectric cylinders is formulated, directly, in terms of a combined layer of electric and magnetic surface current enjoying only a single unknown surface density. The relative contributions of the electric and magnetic current are manipulated so that the integral equation enjoys a unique solution at all frequencies. A new criterion is proposed for the numerically stable moment method solution of this single source surface integral equation. The problem of electromagnetic wave scattering by heterogeneous dielectric cylinders is formulated, in a recursive manner, by organizing their homogeneous subregions into hierarchical multiply-nested structures. The composition of each multiply-nested body is completely accounted for by a pair of surface operators that yield the field components tangent to the outer surface exclusively in terms of a single unknown electric current density distributed on that same surface. Such an equivalent outer-surface representation is independent of external material and illumination, and is invariant under rotation and translation. In this manner, the problem of wave scattering by heterogeneous dielectric bodies is reduced to a scattering problem over their outermost surfaces in terms of only a single unknown current density. For a large number, ' N', of different homogeneous dielectric subregions within such a heterogeneous cylinder, the proposed method has a computational complexity of 'O '('N'1.5). Having solved the scattering problem, the fields at any interior points are recovered by a fast backward recursion. This method is applied to fields at any interior points are recovered by a fast backward recursion. This method is applied to arbitrary cylinders containing conducting surfaces and pockets of general, inhomogeneous material.