Comparative study of two multipole-based numerical methods for 2D field-translation schemes

Two methods based on multipole expansions for the analysis of the field-translation between two distinct domains are comparatively investigated. Here, domain 1 contains the source of the incident field (a horn antenna) which is solved numerically using a commercial solver. Domain 2 contains the scatterer, here a lossless dielectric cylinder. In both methods, we aim at finding the multipole coefficients of the incident field with respect to domain 2. In the first method, the coefficients of a multipole expansion with respect to domain 1 are found from the computed values of the tangential magnetic field on a circular-cylindrical Huygens surface by exploiting orthogonality. Then, Graf’s addition theorem is applied to express the multipole expansion with respect to domain 2. The second method is based on the dyadic Green’s function directly referred to domain 2. Here both types of tangential fields (electric and magnetic) have to be considered on the Huygens surface of domain 1 which however can have an arbitrary shape in this case. Present work is limited to the 2D TE case. Numerical results show a perfect agreement between the two methods.