Scattering from multiple PEC sphere using translation addition theorems for spherical vector wave function

In our manuscript, we are reporting the translation criteria of scattering from Perfect Electric Conductor (PEC) sphere along three-dimensional axes using semianalytical approach.The presented scattering model is based on a generalized Lorenz-Mie theory framework and ensemble with the vector translation Addition Theorem (AT) for the Vector Spherical Harmonics (VSH). Applying extended Mie theory on a sphere leads to a set of an unknown coefficients by the use of translation AT. In the literature, there are many authors reporting different sets of the vector translation coefficients, of which we mention those calculated by Stein, Cruzan and, Mackowski in particular. We have selected the Cruzan formulation of the vector translation coefficients for its structure based on the Wigner 3-j function. As an illustration, we want to present numerical examples than simulations. of total scattered field PEC sphere using vector translation AT. We used advanced computational tools and approaches for mathematical modeling of an observation. During our numerical test, we have deeply investigated generic truncation criteria in scattered electric field using translation AT. However, we have been obtained numerical validation by using computational approach.