Inverse backscattering problem for Maxwell's equations

Abstract

In this paper we consider the inverse backscattering problem for Maxwell's equations in a non‐magnetic inhomogeneous medium, i.e. the magnetic permeability is a fixed constant. We show that the electric permittivity ε is uniquely determined by the trace of the backscattering kernel S(s, −θ, θ) for all s∈ℝ, θ∈S2 provided that it is a priori close to a constant. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.

Uniqueness for the inverse backscattering problem for angularly controlled potentials

“…We think our proof is simpler. Analogous to (b), the articles [SU97], [Wa98], [Wae98], [Wam98], [Wa00], study the inverse backscattering problem but for the acoustic equation, Maxwell's equation or the equations of elasticity and prove injectivity or stability for the problem when the coefficients are close to a constant.…”

Recovery of interior eigenvalues from reduced near field data

“…A classical example of this situation is the backscattering problem. The uniqueness of solution of the inverse problem using the backscattering data can be found in [8], [9], [10], [23], and the recovery of singularities was studied in [24], [31], [22], [26]. In all the papers above, it was assumed that the echo data is available for incident waves coming from all the directions.…”

Inverse scattering for a random potential

“…Other references on inverse backscattering for a time-harmonic Schrödinger equation are [10,37,59]. The backscattering problem has also been studied in the framework of acoustic scattering (see [55,61,62]) and Maxwell equations (see [60]). For a concise treatment of classical inverse scattering, we refer to [17].…”