A Numerical Alternative for 3D Addition Theorems Based on the Bilinear Form of the Dyadic Green's Function and the Equivalence Principle

A numerical method based on the equivalence principle and the dyadic Green's function is presented. It can be used to compute the spherical-multipole amplitudes with respect to an origin in a subdomain 2 due to sources in a distinct subdomain 1. As an example, consider that subdomain 1 contains a horn antenna that is solved numerically using a commercial full-wave simulator. The radiated field serves as the incident field for subdomain 2 which contains the scatterer, in our example a lossless dielectric sphere. The proposed method is based on the equivalence currents on a Huygens surface enclosing the antenna and uses the free-space dyadic Green's function to compute the electric and magnetic fields on a sphere enclosing the scatterer. From this electromagnetic field on the spherical surface, the spherical-multipole amplitudes of the incident field with respect to the center of the sphere enclosing the scatterer are obtained numerically and can be further processed. The results obtained with this method are compared to the results solely computed by the numerical full-wave simulator.