Reconstruction of bi-isotropic material parameters using transient electromagnetic fields

Abstract

In this article, a non-iterative method for solving the transient electromagnetic inverse scattering problem for a homogeneous, dispersive bi-isotropic slab is considered. The slab is excited by a normally incident transverse pulse. The inverse scattering problem is to determine (finite time traces of) the susceptibility kernels, i.e., the four integral kernels present in the constitutive relations, given (finite time traces of) the reflection and transmission kernels, which are obtained by deconvolution of the scattered fields. Two numerical examples illustrate the method with noisy data. Finally, the imbedding equations are proved to be uniquely solvable, and the exact solution to the general propagation problem is found. This solution is given as a uniformly convergent series and supports the employed inverse algorithm.

The theory of the propagation of TEM-pulses in dispersive bi-isotropic slabs

“…This fact is used in Ref. 18 to prove that the imbedding equations are also uniquely soluble, and exact solutions to these equations in terms of infinite series were given in the homogeneous case.…”

“…(It ought to be remarked, that, in spite of being of quite different physical origin, the Green functions and the imbedding kernels are intimately related mathematically; specifically, they are obtained from one another by solving Volterra equations of the second kind, see Ref. 18.) The internal fields are obtained by convolution of the Green functions and the incident electric field.…”

“…In recent years, the interaction between electromagnetic pulses and bi-isotropic media has attracted certain attention [4,5,[9][10][11][18][19][20][21]. One interesting line of research within this field is the study of the early time behavior of the signal in these media.…”

“…The accessibility of reliable inverse algorithms is, naturally, of importance for many applications. Specifically, an inverse algorithm using transient TEM scattering data has been developed, and examples of excellent reconstructions with synthetic scattering data have been presented [10,18]. However, unique solubility of this inverse problem has not been proven yet.…”

“…The propagation of transient TEM-waves in dispersive bi-isotropic slabs has been studied extensively using time-domain methods based on the wave splitting technique, see, e.g., Refs 9,10,18,19. In the present article, these studies are developed further.…”