Scattering of a Plane Electromagnetic Wave by Axisymmetric Raindrops

In a recent short note, the authors and Chu 1 gave calculated results of differential attenuation and differential phase shift caused by rain, based on scattering of a plane electromagnetic wave by oblate spheroidal raindrops. These results are of importance in the investigation of cross polarization in radio communications systems. In this paper, we give details of the analytical and numerical procedures used to solve the problem of scattering by a single raindrop, which were only outlined in the note. Although the results given in this paper are for oblate spheroidal raindrops, the procedures are applicable for axisymmetric raindrops that are not too nonspherical, and calculations could be made for raindrops that are more flattened on the bottom than on the top, such as for the shapes determined by Pruppacher and Pitter. 2 Two polarizations of the incident wave, designated I and II, are considered, as depicted in Fig. 1. The factor e~iut has been suppressed. In the first polarization, the electric field is parallel to the plane containing the axis of symmetry of the raindrop and the direction of propagation of the incident wave. In the second polarization, the electric field is perpendicular to this plane. The angle between the direction of propagation and the axis of symmetry is denoted by a. In terrestrial microwave relay systems, a = 90° is of main concern, but other values of a are of interest for satellite systems. 956 THE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1974