Single-Integral-Equation Method for Three-Dimensional Scattering
The fields scattered by a homogeneous dielectric or finitely conducting object can be obtained from two tangential vector fields, the components of the electric and magnetic fields, on the interface. We have adapted the single-integral-equation method for gratings to the time-dependent Maxwell equations, which reduce to a singular integral equation for a single tangential vector field. For monochromatic fields, the integral equation is equivalent to the Maxwell equations plus the outgoing wave condition. We use the scalar Green function for the wave equation, which is less singular than the dyadic Green function. The integral equation can then be solved by an approximate method such as point matching. The decrease in computer memory requirements can be significant, especially for scattering by three-dimensional dielectric objects. Exact solutions of scattering problems are useful in the resonance region, where the dimensions of the scatterer are comparable to the wavelength, and to estimate the accuracy of approximate methods in other cases. The single-integral-equation has also been derived using the equivalence principle. Once the boundary functions are computed, the fields at an arbitrary location, as well as the far fields, can be found by integration.