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

Abstract

Abstract.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.

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

“…For given incident electric fields, E ± i0 , at the boundaries z = ∓d/2, the direct problem (1.8) has a unique solution. This is a consequence of the vacuum wave splitting, which transforms the scattering problem defined by (1.8) into (1.27) subject to the boundary relations (1.26), for which there is a theory available [22]. The solution of (1.8) can be written in the form…”

“…It should be pointed out that also the direct problem defined by these matrix equations is uniquely solvable [22].…”

“…owing to the identity 22) which reflects the fact that the vectors n ⊥ andẑ × n ⊥ constitute a linear basis for vectors in the x-y plane. The eigenoperators are, where…”

Theory of inversion of dispersive bi-isotropic slab parameters using TEM pulses

“…The smooth input guarantees that there exists a unique TEM solution of Maxwell's equations in the space of continuous functions [17]. The solution is given explicitly below.…”

Electromagnetic Signal Propagation in a Lorentz Dispersive Medium

“…The issues of uniqueness, causality and regularity of a pulse propagating in a dispersive, nonuniform medium are discussed in [7]. Detailed analysis of dispersive propagation is given in two monographs, [8] and [9].…”