Complex Point Sources For Scattering Of A Homogenous Isotropic Sphere

From the sixties and seventies of last century, complex point sources has received much more attention because of the superior advantage than the real point sources in the scattering of electromagnetic fields. Norris has given a method of complex point-source representation of real point sources in 1986, and other authors, particularly Felsen, have done a lot of research between complex point sources, Gaussian beams, evanescent waves and complex ray, received a number of important results and given the Gaussian beam modes can be represented by multipoles with complex point sources. With the characteristics of paraxial approximation of Gaussian beams, the Gaussian beams scattering from a sphere and cylinder has been a research hot spot.The traditional method to the scattering from a sphere was given by Lorentz and Mie in 1890 and 1908 respectively, descendants call their work together as the Lorentz-Mie theory. It solve the Helmholtz equation with method of separation variables combined with spherical boundary conditions under the spherical coordinate system. However, with the increase of electric size of media, the convergence will be slower and the calculated results may be instability using Lorentz-Mie theory. With complex point sources constructed the expressions of electromagnetic scattering fields can avoid the problems yielded by Lorentz-Mie theory, furthermore, because of the characteristics of paraxial approximation of Gaussian beam, and the Gaussian beam modes can be obtained by multipoles with complex point sources, the results of scattering of electric large objects will be much better.Different with the Gaussian beam as the incident field to calculate the scattering of dielectric spheres, in this paper we use the structure of complex point sources to construct expressions of inside and outside electromagnetic scattering fields of isotropic homogenous sphere, and the corresponding numerical results were given to compared with the results obtained with traditional Lorentz-Mie theory. Firstly, we investigated the electromagnetic scattering from a one-layered homogenous isotropic sphere with complex point sources. Followed, the electromagnetic scattering characteristics of a two-layered homogenous isotropic sphere and a perfectly conduct sphere coated with a homogenous isotropic dielectric layer are investigated. To determined the distribution of electromagnetic scattering fields from the homogenous isotropic sphere, a group of weighted complex point sources are set up inside the sphere. The the continuity of the spherical boundary conditions is used to obtain the weight coefficients of complex point sources. The numerical results is given through calculating the radar cross section (RCS) of the homogenous isotropic sphere. Comparison with the results with Lorentz-Mie theory, we can see that, with complex source points to solve the electromagnetic scattering of the homogenous isotropic sphere is feasible. This article is a good attempt with complex point sources to investigate the electromagnetic scattering of a homogenous isotropic sphere.