Reconstruction of bi-isotropic material parameters using transient electromagnetic fields

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

Modes of propagation of electromagnetic pulses in open dispersive slab waveguides

As a preparatory study of electromagnetic pulse propagation in open waveguides, the modes of propagation of pulses in open slab waveguides are investigated systematically. Core and cladding both consist of simple (linear, homogeneous, isotropic), dispersive materials modeled by temporal convolution with physically sound susceptibility kernels. Under these circumstances, pulses cannot propagate along the guide unless the sum of the (first) initial derivatives of the electric and magnetic susceptibility kernels of the medium in the core is less than the corresponding sum for the medium in the cladding. Only a finite number of pulse modes can be excited, and relevant temporal Volterra integral equations of the second kind for these modes are derived

Time-domain direct and inverse scattering for bianisotropic slabs at oblique incidence

Using the Cayley-Hamilton theorem and unique solubility of scalar Volterra convolution equations of the second kind, the inverse problem of determining the four time-dependent susceptibility dyadics of a linear, homogeneous, bianisotropic slab from generic scattering data at oblique incidence is shown to be well posed. An explicit formula for the crucial step is given

Theory of Inversion of Dispersive Bi-Isotropic Slab Parameters using TEM-Pulses

A new method of reconstructing the causal susceptibility kernels of a homogeneous, temporally dispersive, bi-isotropic medium from generic scattering data at normal incidence is presented. This inverse problem is shown to be well posed in the space of continuous functions furnished with the maximum norm, C[0, T]. A numerical example is given

The Theory of the Propagation of TEM-Pulses in Dispersive Bi-Isotropic Slabs

A survey of the theory of propagation of transient transverse electromagnetic waves in temporally dispersive, bi-isotropic slabs is given, and a novel wave splitting, which completely separates right-going and left-going waves in the dispersive medium, is proposed. The new approach leads to a simple scattering relation in terms of wave propagators and single-interface scattering operators only. These temporal integral operators are related to the four timedependent susceptibility kernels of the medium through non-linear Volterra equations of the second kind. In a subsequent article, the corresponding inverse scattering problem is addressed on the basis of the new results

Existence, Uniqueness, and Causality Theorems for Wave Propagation in Stratified, Temporally Dispersive, Complex Media

A mixed initial-boundary value problem for a nonlocal, hyperbolic equation is analyzed with respect to unique solubility and causality. The regularity of the step response and impulse response (the Green functions) is investigated, and a wave front theorem is proved. The problem arises, e.g., at time-varying, electromagnetic, plane wave excitation of stratified, temporally dispersive, bi-isotropic or anisotropic slabs. Concluding, the problem is uniquely solvable, strict causality holds, and a well-defined wave front speed exists. This speed is independent of dispersion and excitation, and depends on the nondispersive properties of the medium only

Modes of propagation of electromagnetic pulses in open dispersive circular waveguides

Modes of propagation of electromagnetic pulses in open circular waveguides are investigated systematically. Core and cladding both consist of simple (linear, homogeneous, isotropic), dispersive materials modeled by temporal convolution with physically sound susceptibility kernels. Under these circumstances, pulses cannot propagate along the guide unless the sum of the (first) initial derivatives of the electric and magnetic susceptibility kernels of the medium in the core is less than the corresponding sum for the medium in the cladding. Only a finite number of pulse modes can be excited, and relevant temporal Volterra integral equations of the second kind for these modes are derived. A theory of functions of integral operators is developed in order to obtain the results

One-dimensional pulse propagation in temporally dispersive media - exact solutions versus numerical results

One-dimensional pulse propagation in temporally dispersive dielectrics is analyzed using a scalar, causal fundamental solution of the dispersive wave operator (a single, retarded Green’s function). A number of exact solutions for normal incidence on dispersive half-spaces are given, and these solutions are compared to time-domain numerical results and to forerunners (precursors)

The inverse scattering problem for a homogeneous bi-isotropic slab using transient data

Transient wave propagation in a finite bi-isotropic slab is treated. The incident field impinges normally on the slab, which can be inhomogeneous wrt depth. Dispersion and bi-isotropy are modeled by time convolutions in the constitutive relations. Outside the slab the medium is assumed to be homogeneous, non-dispersive and isotropic, and such that there is no phase velocity mismatch at the boundaries of the slab. Two alternative methods of solution to the propagation problem are given—the imbedding method and the Green function approach. The second method is used to solve the inverse problem and the first to generate synthetic data. The inverse scattering problem is to reconstruct the four susceptibility kernels of the medium using a set of finite time trace of reflection and transmission data

One-way wave operators for nonstationary dielectrics

Propagation of transient electric and magnetic (TEM) pulses in nonstationary, linear, homogeneous, and isotropic dielectric and magnetic materials is investigated using an exact wave splitting. Key intrinsic properties are the index of refraction and the relative admittance, which are both temporal integral operators with kernels that depend on two time variables. In addition, the Sommerfeld forerunners in dispersive nonstationary materials are derived. A numerical example — a single-resonance Lorentz model with time-dependent plasma frequency — is presented