A Finite-Difference Frequency-Domain (FD-FD) Approach To Electromagnetic Scattering Problems

Abstract

A finite-difference, frequency-domain (FD-FD) approach to electromagnetic wave scattering is presented. This approach evolved from recent progress that features the concept of generalized scattering amplitudes, the application of boundary-fitted curvilinear coordinate systems, and the use of Debye potentials for 3-D obstacle scatterings. The introduction of the radially non-oscillatory generalized scattering amplitudes circumvents the difficulties in dealing with oscillatory field quantities in the infinite exterior scattering region and allows the finite-difference method to be applied to scattering problems in an effective manner. The radiation condition in terms of the generalized scattering amplitude is very simple in form and can be enforced exactly in the far field. For a 3-D scattering problem the formulation in terms of Debye potentials, expressed as functions of body-fitted coordinates, not only decouples the vector scattering problem into a combination of two independent scalar scattering problems but also makes the exact enforcement of obstacle surface condition simple. Specific examples with numerical results validated by the eigenfunction expansion method and the moment method are given to illustrate the salient features of the FD-FD approach.