Related papers: Analytical continuation of two-dimensional wave fi…
We consider a charged particle following the boundary of a two-dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering…
We investigate numerically the scattering of waves on discrete graphs. An efficient algorithm is developed to compute the reflection and transmission (spectral) coefficients. We then explore various configurations of input and output leads,…
Strings propagating along surfaces with Dirichlet boundaries are studied in this paper. Such strings were originally proposed as a possible candidate for the QCD string. Our approach is different from previous ones and is simple and general…
We explore the electrodynamic coupling between a plane wave and an infinite two-dimensional periodic lattice of magneto-electric point scatterers, deriving a semi-analytical theory with consistent treatment of radiation damping,…
Interaction of waves with point and line defects are usually described by $\delta$-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of point defects or parallel line defects…
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,…
An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the M\"uller equations and an impedance boundary condition for a…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
This work presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near "Wood anomaly frequencies". At these frequencies, one or more grazing Rayleigh waves exist, and the lattice sum for…
We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…
The use of Sonic Crystals as environmental noise barriers has certain advantages from the acoustical and the constructive point of view with regard to conventional ones. One aspect do not studied yet is the acoustic interaction between the…
In this article, we develop a new method to prove both global propagation of analyticity and unique continuation in finite time for solutions of semilinear wave-type equations with analytic nonlinearity. It combines control theory…
A method is presented to investigate diffraction of an electromagnetic plane wave by an infinitely thin infinitely conducting circular cylinder with longitudinal slots. It is based on the use of the combined boundary conditions method that…
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…
The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new…
We establish the analytic structure of the S-matrix in the complex-frequency plane for classical wave scattering on a Schwarzschild background in four space-time dimensions. Our argument relies on the analytic continuation of the…
We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set of points in $\mathbb{C}^d$ with all coordinates in the…
We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction…