Multiple scattering by two PEC spheres using translation addition theorem

An analysis of multiple scattering by two Perfect Electric Conducting (PEC) spheres using translation Addition Theorem (AT) for spherical vector wave functions is presented. Specifically, the Cruzan formalism is used to represent the AT for spherical harmonics, which introduces the translation coefficients for transformation of spherical harmonics from one coordinate to another. The adoption of these coefficients with the use of two PEC spheres in a near zone region makes the calculation of multiple scattering electric fields very efficient. As an illustration, the mathematical formation using advanced computational approaches was inspected. Then, the generic truncation criteria in the scattered electric field by two PEC spheres was deeply investigated using translation AT. However, the numerical validation was obtained using Comsol simulation software. This approach will allow to evaluate the scattering from macro-structures composed of spherical particles, i.e., biological molecules, clouds of airborne particles, etc. An original and fully general solution to the problem using vector quantities is introduced, and the convergence of the solution in several numerical examples is also demonstrated. This approach takes into account the effect of multiple scattering by two PEC spheres for spherical vector function.