Related papers: Shape identification in inverse medium scattering …
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact…
It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always…
Motivated by questions in inverse scattering theory, we develop free boundary methods in obstacle problems where both the solution and the right hand side of the equation may have varying sign. The key condition that prevents the appearance…
We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves, interior transmission eigenfunctions, and their applications to…
A mathematical method for through-wall imaging via wave phenomena in the time domain is introduced. The method makes use of a single reflected wave over a finite time interval and gives us a criterion whether a penetrable obstacle exists or…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
We show that the far--field pattern of a scattered electromagnetic field corresponding to a single incoming plane--wave uniquely determines a bounded supraconductive planar screen. This generalises a previous scalar result of Bl\aa sten,…
Uniqueness is proven for two 3-d inverse problems of the determination of the spatially distributed sound speed in the frequency dependent acoustic PDE. The main new point is the assumption that only the modulus of the scattered complex…
This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
The simplest Lorentz-nonreciprocal medium has the constitutive relations (${\bf D} =\epso {\bf E} -{\bf \Gamma}\times {\bf H}$ and ${\bf B} =\muo {\bf H} + {\bf \Gamma}\times{\bf E}$). Scattering by a three-dimensional object composed of…
In this paper, we adapt the well-known \emph{local} uniqueness results of Borg-Marchenko type in the inverse problems for one dimensional Schr{\"o}dinger equation to prove \emph{local} uniqueness results in the setting of inverse…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…
We consider an inverse spectral theory in a domain with the cavity that is bounded by a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the solutions inside and outside the cavity. The ODE system is connected…
We study time harmonic scattering for the Helmholtz equation in Rn. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission…
In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in ${\mathbb R}^m$, $m=2,3$ from scattering data. In the asymptotic limit as the thickness goes to zero,…
We study the fundamental limit on the localization precision for a subwavelength scatterer embedded in a strongly scattering environment, using the external degrees of freedom provided by wavefront shaping. For a weakly scattering target,…