Scattering by Small Thin Dielectric Particles

In the analysis of electromagnetic scattering by distributions of small dielectric particles an approximation to the scattered field can be obtained by representing the electrical interaction of the particles in terms of the dipole moments of the individual particles. The calculation of the moments necessitates the solution of certain static scattering problems, and this becomes numerically difficult when the particles are thin. An integral equation formulation of the static scattering problem specialized to the case of thin planar dielectric plates is presented, along with an efficient numerical routine. Dipole moments are obtained over a range ofpermittivities for plates with several thicknesses and a variety of cross-sectional shapes, and the shape dependence is discussed. PACS: 42.68.Mj, 77.30. + d The analysis of the scattering and absorption of electromagnetic radiation by distributions of particles is important in the study of aerosols and their effect on the optical properties of the earth's atmosphere. The effect is usually studied by parameterizing the aerosol in terms of the density of the constituent particles as well as the particle shape, size and composition. Most aerosols contain particles with a variety of shapes and orientations, and it would be difficult, if not impossible, to include the precise features of a particle in any scattering calculation. For this reason and to simplify the computational task, the particles are often modelled using equivalent spheres [1]. The use of spheroids has also been suggested [2], but in order to judge the adequacy of these approximations it is important to know how the geometry and material composition of a particle affect its scattering. The particles which are studied in this paper are thin plates having length to thickness ratios ranging from 10:1 to 1000:1. Several simple shapes are examined including a circle, square, 2:1 rectangle, equilateral * Now with the Electrical Engineering and Applied Physics Department, Case Western Reserve University, Cleveland, OH 44106, USA triangle, and a bowtie formed by connecting two equilateral triangles at their vertices. The bowtie, being a reentrant shape, gives results which differ noticably from those for the other (convex) shapes. This is an interesting phenomenon since many aerosols are composed of particles of reentrant shape. To make possible the analysis of these particles, a stable integral equation formulation for the scattered field is presented along with an efficient numerical implementation. The scattered fields for the various shapes are summarized through the calculation of the electric polarizability tensor elements, and these quantities are displayed over a range of permittivities.