Finite element approach for the numerical analysis and modeling of diffractive and scattering objects

Bernd Lichtenberg; Neal C. Gallagher Jr.

doi:10.1117/12.178062

17 June 1994 Finite element approach for the numerical analysis and modeling of diffractive and scattering objects

Bernd Lichtenberg, Neal C. Gallagher Jr.

Proceedings Volume 2152, Diffractive and Holographic Optics Technology; (1994) https://doi.org/10.1117/12.178062
Event: OE/LASE '94, 1994, Los Angeles, CA, United States

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.

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Bernd Lichtenberg and Neal C. Gallagher Jr. "Finite element approach for the numerical analysis and modeling of diffractive and scattering objects", Proc. SPIE 2152, Diffractive and Holographic Optics Technology, (17 June 1994); https://doi.org/10.1117/12.178062

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