Abstract
This paper describes a novel Boundary Source Method (BSM) applied to the vector calculation of electromagnetic fields from a surface defined by the interface between homogenous, isotropic media. In this way, the reflected and transmitted fields are represented as an expansion of the electric fields generated by a basis of orthogonal electric and magnetic dipole sources that are tangential to, and evenly distributed over the surface of interest. The dipole moments required to generate these fields are then calculated according to the extinction theorem of Ewald and Oseen applied at control points situated at either side of the boundary. It is shown that the sources are essentially vector-equivalent Huygens' wavelets applied at discrete points at the boundary and special attention is given to their placement and the corresponding placement of control points according to the Nyquist sampling criteria. The central result of this paper is that the extinction theorem should be applied at control points situated at a distance d = 3s (where s is the separation of the sources) and consequently we refer to the method as 3sBSM. The method is applied to reflection at a plane dielectric surface and a spherical dielectric sphere and good agreement is demonstrated in comparison with the Fresnel equations and Mie series expansion respectively (even at resonance). We conclude that 3sBSM provides an accurate solution to electromagnetic scattering from a bandlimited surface and efficiently avoids the singular surface integrals and special basis functions proposed by others.
Highlights
The theory of electromagnetic waves has been applied most frequently in the field of electrical engineering, where it is central to the understanding of antennas and the design of radar imaging systems
It is noted that the first term in Eq (1) can be identified as the combined field due to magnetic dipoles that are tangential to the surface and have a strength that is proportional to the amplitude of the tangential component of the electric field
In this paper we have presented a straightforward method to compute the electric fields that are scattered and transmitted by the surface at the interface between homogenous media
Summary
The theory of electromagnetic waves has been applied most frequently in the field of electrical engineering, where it is central to the understanding of antennas and the design of radar imaging systems. Under the assumption that multiple scattering is negligible, the Huygens-Fresnel principle allows us to represent coherent scattering as a simple convolution operation and the optical output of measuring instruments to be written as linear filtering operations applied to a “foil” representation of the surface form [5,6]. In this way, we have a useful and conceptionally simple means to characterize the performance of optical surface profiling instruments including coherence scanning interferometers [7] and focus variation microscopes [8] when in normal use. The method is conceptionally simple and provides further insight into electromagnetic scattering from sub-wavelength surface features
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