Abstract
The interaction between electromagnetic waves and a sphere is one of the most important problems in scattering theory. Since this problem is exactly solvable, it provides essential insight in dealing with various kinds of scattering problems, although scattering objects in practice are often more complicated than an electromagnetically homogeneous sphere. The exact solution, formulated by expanding electromagnetic fields in vector spherical harmonics, is fundamental to the more complex problems. Despite that this solution is not constructed by Gustav Mie, the theory developed is named after him, who proposed prominent ideas about electromagnetic waves scattering in an attempt to explain light scattering and absorption by gold particles suspended in water [2]. In this report, the problem of electromagnetic waves scattering by a coated sphere will be discussed. Based on the idea of expanding the fields in vector spherical harmonics, a scheme is developed for computing the field coecients of a system with a coated sphere. This scheme can be extended to a system with a symmetric array of spheres. Using these schemes, the field characteristics are studied. Also examined are the variation of the scattering cross section and the scattering eciency with the system parameters including the inner and outer radius of the coated sphere, the refractive index of the core sphere and the coating, the wavelength of the electromagnetic waves and the separation between spheres. To ensure the accuracy of the numerical results, truncation of series computation of vector spherical harmonics is also addressed.