Related papers: Quasi-Exactly Solvable Scattering Problems, Exactn…
We provide an exact solution of the scattering problem for the potentials of the form $v(x,y)=\chi_a(x)[v_0(x)+ v_1(x)e^{i\alpha y}]$, where $\chi_a(x):=1$ for $x\in[0,a]$, $\chi_a(x):=0$ for $x\notin[0,a]$, $v_j(x)$ are real or…
For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born…
The discovery of unidirectional invisibility and its broadband realization in optical media satisfying spatial Kramers-Kronig relations are important landmarks of non-Hermitian photonics. We offer a precise characterization of a…
For the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the $N$-th order Born approximation gives the exact solution of…
We use the transfer matrix formulation of scattering theory in two-dimensions to treat the scattering problem for a potential of the form $v(x,y)=\zeta\,\delta(ax+by)g(bx-ay)$ where $\zeta,a$, and $b$ are constants, $\delta(x)$ is the Dirac…
We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations, and discuss its three-dimensional generalization. In particular we construct an infinite class of unidirectionally invisible…
We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
Designing invisible objects without the usage of extreme materials is a long-sought goal for photonic applications. Invisibility techniques demonstrated so far typically require high anisotropy, gain and losses, while also not being…
We outline a method for constructing effectively two-dimensional isotropic optical media that are perfectly and omnidirectionally invisible for both TE and TM waves provided that their wavenumber does not exceed a preassigned value…
A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner…
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…
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…
We give a complete solution of the problem of constructing a scattering potential v(x) that possesses scattering properties of one's choice at an arbitrary prescribed wavenumber. Our solution involves expressing v(x) as the sum of at most…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
We investigate the scattering phenomena in two dimensions produced by a general finite-range nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the…
In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable nonlinear parameter $A$ upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of…
We introduce a nonperturbative approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…