Scattering of a plane electromagnetic wave by axisymmetric raindrops

This paper gives details of the analytical and num$eLrical procedures used to solve the basic problem of the scattering of a plane electromagnetic wave by an axisymmetric raindrop. A nonperturbative solution is obtained by expanding the scattered and transmitted fields in terms of spherical vector wave functions, so that Maxwell's equations are satisfied exactly in the regions exterior and interior to the raindrop, and by combining point matching with least-squares fitting to satisfy the boundary conditions on the surface of the raindrop with sufficient accuracy. Numerical results are presented for scattering by oblate spheroidal raindrops, with eccentricity depending on (and increasing with) drop size, for two orthogonal polarizations of the incident wave. The calculations were made at 4, 11, 18.1, and 30 GHz, in the case in which the direction of propagation of the incident wave is perpendicular to the axis of symmetry of the raindrop, which is of interest for terrestrial microwave relay systems. At 30 GHz, the calculations were also made for the case in which the angle between the direction of propagation and the axis of symmetry is 70° and 50°, since different elevation angles are of interest for satellite systems. These basic results were summed earlier over the drop-size distribution to calculate the differential attenuation and differential phase shift caused by rain, which are of importance in the investigation of cross polarization in radio communication systems.