Back-Scattering of Electromagnetic Waves from Spheres and Spherical Shells

Abstract : The classical theory of the scattering of a plane electromagnetic wave by a sphere is reviewed, and the difficulties in getting numerical answers from this formal solution are discussed. It is shown how the computations may be simplified by using suitably defined logarithmic derivative functions and the recurrence formulas due to Infeld. By this method, numerical answers for the scattering amplitude coefficients of any order can be computed exactly, even if the index of refraction is complex. The technique mentioned above has been used to determine the scattering amplitude coefficients and the back-scattering cross section for one special case involving water spheres with sizes comparable to the wavelength. The theoretical results are compared with those obtained experimentally. A rigorous solution is also given for the scattering of a plane electromagnetic wave from two concentric spheres of different dielectric constant. This problem is formulated in a manner similar to that for a single sphere, and the scattering amplitude coefficients are expressed in terms of spherical Bessel functions and the logarithmic derivative functions. The application to a particular physical problem is indicated.