Abstract
The theory for scattering of electromagnetic waves is developed for scattering objects for which the natural modes of the field inside the object do not couple one-to-one with those outside the scatterer. Key feature of the calculation of the scattered fields is the introduction of a new set of modes. As an example, we calculate the reflected and transmitted fields generated by an electromagnetic plane wave that impinges upon a multilayer slab of which the layers are stacked perpendicular to the boundary planes. As this is the geometry of a thick plate with slits our theory encompasses the exact scattering theory of electromagnetic waves by a thick plate with slits.
Highlights
The analysis of scattering- and boundary value problems is a very important branch of physics and it has been extensively explored since the eighteenth century [1, 2]
One of the requisites for the possibility to obtain analytical solutions in closed form for these problems is that the pertinent scalar- or vectorial wave equation admits a potential or refractive index such that this equation separates
Essential for the analytical solution of scattering- and boundary value problems, is that the geometry of the scatterer fits with the geometry of the separable potential or refractive index
Summary
The analysis of scattering- and boundary value problems is a very important branch of physics and it has been extensively explored since the eighteenth century [1, 2]. The exactly solvable boundary value problems in mathematical physics all share one property, namely that the boundaries of the various geometries involved fully coincide with the coordinate surfaces of the various separable coordinate systems for the wave equation. This is the case for the scattering of waves from, for instance, a half-plane, a complete sphere, an ellipsoid or a cylinder filled with a homogeneous medium. A plane wave mode outside the slab couples to an infinity of modes for the layered medium, unlike for the case if the layers had been oriented parallel to the boundary planes of the slab. A survey of the background theory of the mathematical results that have been used in this chapter and can be found in [6], whereas the original theory in full detail can be found in [7]
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