Multiple scattering of electromagnetic waves from two prolate spheroids with perpendicular axes of revolution

A study of multiple scattering from two perfectly conducting prolate spheroids with perpendicular axes of revolution is performed, and new numerical results are given. This study is carried out with rotational-translational addition theorems established by the authors and R. H. MacPhie. In addition, rotational-translational addition theorems for the spheroidal vector wave functions M^r and N^r with a sine or cosine ϕ dependence necessary for this study are also established. The propagation vector of the incident plane wave is in the negative y direction, and consequently, two new expressions of the incident field in terms of series expansions of spherical and spheroidal vector wave functions with respect to the vector r are presented. Finally, multiple scattering polar patterns are shown for two identical prolate spheroids spaced 3.5 times their semimajor axis and this for two values of c, namely c = 2 and c = 5.