<title>Finite element approach for the numerical analysis and modeling of diffractive and scattering objects</title>

Abstract

A Finite Element Method (FEM) for open region scattering problems with arbitrarily shaped outer boundary is considered to model diffractive objects. In open region problems it is necessary to introduce an artificial boundary to limit the area of computation. Therefore, boundary conditions are implemented to absorb the outgoing waves with as little reflection as possible. It is desirable to use Absorbing Boundary condition (ABC) which can truncate the region conformal to the geometry of the scatterer. Thus, a smaller computational domain and a more efficient numerical solution are achieved. In this talk a local ABC for arbitrarily shaped outer boundaries is used which preserves the sparsity of the resulting matrix after discretization. The second order ABCs are implemented to solve the Helmholtz equation numerically in the frequency domain. Different two-dimensional scatterers are considered. First, a study of Fresnel zone plates is conducted. The intensity and distribution of the focal points for different orders and thicknesses is discussed. Next some reflection gratings are studied and verified by comparing the results to theoretical derivations. Last a two-dimensional hologram is modeled.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.