A green's function approach to the determination of internal fields

Permittivity Profile Reconstructions Using Transient Electromagnetic Reflection Data

“…This is not true for the sum of the fields E + (z, t) and E − (z, t) in Section 2.3 since the left end point of the slab is varied and thus the physical set-up changed. The representations in (2.22) and (2.23) lead to a very efficient way to calculate the internal field, see [7]. However, calculations of the internal fields are not the main topic of this paper and this matter is, therefore, not pursued here, since the focus is on solving the inverse problem.…”

“…The first algorithm is based upon an imbedding procedure which was suggested originally by Corones, Davison and Krueger [2]. The second algorithm utilizes the Green functions of the problem and this approach was first introduced by Krueger and Ochs [7]. These algorithms and the underlying theory are presented in Section 2.…”

Transient electromagnetic wave propagation in anisotropic dispersive media

“…The equations are obtained by varying the left endpoint of the subsection. Another approach is to introduce Green operators which map the incoming field E + (0, s) to the split internal fields E ± (z, s) at an arbitrary depth z, see Refs [13,16]. The definition of the Green operators, represented in integral form with kernels G ± (z, s ), respectively, are…”

Transient electromagnetic wave propagation in transverse periodic media

“…The propagator maps a split field from one position to another in the waveguide and is represented by a kernel satisfying a hyperbolic equation. The propagator is closely related to the scattering operators used in invariant imbedding techniques, cf [10], [11], [12], and to the operators used in the Green function approach [13]. The Green function approach has recently been applied to transient wave propagation in a homogeneous waveguide [7] and the present paper is partly based upon results in this paper.…”