Next: Numerical Solution of Up: EM Scattering from Previous: EM Scattering from

Impedance Boundary Conditions for Scattering from a Conducting Body with a Thin Lossy Dielectric Coating

In this section, the scattering of a plane electromagnetic wave by a 3-D perfectly conducting body with a dielectric material coating is studied by the parametric method of moments described in the previous chapter with an impedance boundary condition. The problem can be formulated in terms of various integral equations derived from the Leontovich [58] impedance boundary condition (IBC). There are many papers on IBC [63][62][61][60][59]. This approximation makes integral equation formulations of the problem nearly as simple as those for perfectly conducting bodies without coating. When using IBC, one can take advantage of the derivation in the previous chapter for using IBC.

Let S denote the closed surface of a three-dimensional perfectly conducting body with an infinitely thin layer of lossy dielectric material coating shown in Figure 3.1 where is the outward unit vector normal on and () are incident fields which are produced by some impressed sources in the absence of the scatterer. The material coating on the perfectly conducting body is characterized by a pair of complex parameters , where is the permittivity and is the permeability. The space outside the scatterer is filled with the homogeneous material with permeability and permittivity .

In solving the problem, it is often useful to apply the equivalence principle (Chapter 3, [47]) using equivalent electric and magnetic surface currents to represent the scatterer. If the task is to find the exterior field only, an exterior equivalent problem can be shown in Figure 3.2, where the fields external to the scatterer can be considered equivalent (to those of the original problem) due to the electric () and magnetic () surface current densities on which are given by

where is the external surface of the dielectric coating.

Although the exterior fields must be unique, there are many sets of equivalent currents and interior fields which will give rise to the correct exterior fields in general scatterers. It is natural to let the interior field be the null field, since the perfectly conducting body is inside . The Leontovich impedance boundary condition on implies that only the electric and magnetic fields external to the scatterer are relevant and their relationship is a function of the material constitution (here, surface impedance) of the scatterer. As shown in Figure 3.2, the electric and magnetic fields are zero inside , and the electric and magnetic fields outside are related by [63]

The dual form of the IBC is

where is the intrinsic impedance of free space which is given by ; is the relative surface impedance.

The total electric field is the vector sum of the incident electric field and the scattered electric field. The scattered electric field produced by the surface currents can be expressed in terms of the magnetic and electric vector potentials and the electric scalar potential, and the total electric field is given by

where and are the magnetic vector potential and the electric scalar potential, respectively, given by () and () in the previous chapter. is the electric vector potential given by

where is the free space Green's function given in the previous chapter. Substituting () and () into () yields

Either of the boundary conditions in () and () the following simple relationship between the electric surface current and the magnetic surface current

With given by (), () is the so-called electric field integral equation when the impedance boundary condition exists. In the next section, we will apply the parametric method of moments to solve for the electric current.



Next: Numerical Solution of Up: EM Scattering from Previous: EM Scattering from


xshen@
Sat Dec 3 17:51:03 EST 1994