Complex space multipole expansion theory with application to scattering from dielectric bodies

Classical multipole theory valid for radiation from sources with small dimensions is extended to complex space. It is shown that by locating the multipole in complex space, the first terms in multipole series can be made more dominating than when restricting to real space. Expression for the complex location is derived to minimize the effect of the second-order multipole term. With an example, radiation from a phased cubic source it is seen that the radiating characteristic is an order of magnitude better for the dipole approximation when the dipole is in complex space instead of being at the center of the cube. Simultaneously, it is demonstrated that the validity of the dipole approximation is extended from to about , being the measure of the source. Complex location for the electric dipole approximating a dielectric spherical scatterer is found through integral equation analysis corresponding to a linear approximation of the inner field of the scatterer.