Proceedings PaperElectromagnetic Inverse Scattering for Stratified Media
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Assume that the permittivity ε and the permeability μ depend on z , i.e. ε= ε6(z) , μ = μ(z). For perpendicular polarization the electric and magnetic fields are determined by Ex , the x-component of the electric field. For this polarization let μ = Ex , μ = μ(z) and c(z) = 1 / /6(z)μ(z) . For parallel polarization the electric and magnetic fields are determined by Hx , the x-component of the magnetic field. For this polarization let μ = Hx and μ = 6(z) and c(z) = 1 / /6 (z)μ (z) Suppose that in the half-space z < 0 both the permittivity and permeability are known, but they are unknown for z > 0. In this paper it is shown how to determine 6(z) and p(z) using the trace method which itself is discussed. The following assumptions are necessary. (1) c(z), μ(z) approach cp1 as z -co and cp1 as z +co where c2'p2 are not known but it must be known that c2 > c1 . (2) certain smoothness assumptions on c(z) and p(z). Suppose a point harmonic source with angular frequency and w is located in the region z < 0 , and suppose p(r,z) is measured at some depth z < 0 for all r for both wi and w2 . Trace methods are then used to recover c(z) and μ(z) for z > 0 , under the assumption that the point source excites only the continuous spectrum. Numerical examples are presented.