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Fast, high-order accurate algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…
To design a uniaxial anisotropic metamaterial a layered cylindrical metamaterial is introduced for TE polarization. Unlike to the previous work, which the layers were in radial direction, here the layers are in azimuthal direction.…
In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…
We derive a new integral equation that allows the calculation of the scattering or annihilation amplitude of two particles subjected to two potentials when the corresponding amplitude for one potential only is known. We assume that…
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
Freely oriented small anisotropic grains and molecules depolarize radiation both in single scattering and in the process of multiple scattering. Especially large depolarization occurs for resonant scattering corresponding to the electron…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
This paper introduces a high-order accurate surface integral equation method for solving 3D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-M\"uller formulation is leveraged…
Scattering methods make it possible to compute the effects of renormalized quantum fluctuations on classical field configurations. As a classic example of a topologically nontrivial classical solution, the Abrikosov-Nielsen-Olesen vortex in…
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…
We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…
Extremely asymmetrical scattering (EAS) is a new type of Bragg scattering in thick, slanted, periodic gratings. It is realised when the scattered wave propagates parallel to the front boundary of the grating. Its most important feature is…
This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…
In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction…
Recent experiments on inelastic light scattering in a number of insulating cuprates [1] revealed a new excitation appearing in the case of crossed polarizations just below the optical absorption threshold. This observation suggests that…
We consider the unique determinations of impenetrable obstacles or diffraction grating profiles in $\mathbb{R}^3$ by a single far-field measurement within polyhedral geometries. We are particularly interested in the case that the scattering…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…