Related papers: Formal uniqueness in Ewald sphere corrected single…
We present a new approach to real-space multiple-scattering theory for molecules and clusters, based on the two-potential (distorted-wave) Lippmann-Schwinger equation formalism. Our approach uses a recently developed form [D. L. Foulis,…
Since the diffraction behavior of a light field is fully determined by its spatial wavefunction, i.e., its spatial complex amplitude (SCA), full characterization of spatial wavefunction, plays a vital role in modern optics from both the…
This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data…
The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of…
Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…
Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by…
The well-known "Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral…
In this paper, we study time-harmonic electromagnetic scattering in two scenarios, where the anomalous scatterer is either a pair of electromagnetic sources or an inhomogeneous medium, both with compact supports. We are mainly concerned…
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…
Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…
The vertical slice transform takes a function on the n-dimensional unit sphere to integrals of that function over spherical slices parallel to the last coordinate axis. This transform arises in thermoacoustic tomography. We obtain new…
The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schr\"odinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is…
SPAD cameras offer single photon detection sensitivity, high frame rates and zero readout noise. They are a core technology for widefield FLIM, but have further potential in ultra-fast imaging applications. However, in practice sensitivity…
Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(\beta,\alpha_0,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely. Here $\alpha_0\in S^2$ is a fixed…
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane…
Since the early 1970s, inversion techniques have become the most useful tool for inferring the magnetic, dynamic, and thermodynamic properties of the solar atmosphere. The intrinsic model dependence makes it necessary to formulate specific…
This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…
Electromagnetic Inverse Scattering Problems (EISP) seek to reconstruct relative permittivity from scattered fields and are fundamental to applications like medical imaging. This inverse process is inherently ill-posed and highly nonlinear,…
We present an NPT extension of Ewald summation with prolates (ESP), a spectrally accurate and scalable particle-mesh method for molecular dynamics simulations of periodic, charged systems. Building on the recently introduced ESP framework,…