The scattering of electromagnetic radiation by distributions of particles occurs in a variety of circumstances. At radio wave frequencies the operation of radar units is affected by rain and ice crystals suspended within clouds, while at higher, optical frequencies the amount of solar radiation reaching the earth's surface can be affected by pollutants in the upper atmosphere. This study is restricted to particles which are small compared to the wavelength of the illuminating electromagnetic radiation. The particles are assumed to be composed of a homogeneous lossy dielectric, with conductors characterized by large permittivities and lossy materials described by permittivities with relatively large imaginary components. In the investigation of scattering by small particles, it is often convenient and useful to solve for the scattered field in terms of a low frequency expansion (a Taylor series in powers of the maximum dimension of the particle over the wavelength of the incident electromagnetic field). Unfortunately, the usual techniques for computing the low frequency expansion fail if the particle is collapsed to a plate with vanishing thickness. The difficulty arises from an unanswered problem in classical physics, the construction of a vector potential. A solution to this problem is obtained and presented in the context of low frequency scattering. In many cases of low frequency scattering, only the first term of the expansion is necessary to adequately characterize the scattered field. This is obtained by solving a static field scattering problem. Unfortunately, for particles which are very thin (but of finite thickness), existing numerical codes become highly unstable. An algorithm is developed expressly for the thin plate scattering problem which appears accurate over a wide class of thin plates, permitting arbitrarily shaped plates with complex permittivities. The solution is obtained using a finite element method with linear basis functions over triangular elements. The results of the program include the calculation of the dipole moments associated with the plates, and the manner in which these dipole moments affect the electrical properties of the entire distribution is discussed.Ph.D.Electrical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/160357/1/8502863.pd
