Related papers: Scattering by a collection of $\delta$-function po…
Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long range interactions, whose properties can be tailored by choice of injected laser powers, frequencies and polarizations. We use a…
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the…
We examine harmonic oscillator defects coupled to a photon field in the environs of an optical fiber. Using techniques borrowed or extended from the theory of two dimensional quantum fields with boundaries and defects, we are able to…
The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous…
The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero…
The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…
We consider the elastic scattering of electrons by hydrogen atoms in the presence of a two-color circularly polarized laser field in the domain of moderate intensities below $10^{13}$ W/cm$^2$ and high projectile energies. A hybrid approach…
We present the results of a study of the Poynting vector field generic singularities at the resonant light scattering of a plane monochromatic linearly polarized electromagnetic wave by a subwavelength particle. We reveal the impact of the…
The scattering of wave packets from a single slit and a double slit with the Schr\"odinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region,…
Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``$+\infty$'', and its…
We demonstrate that single scattering of p-polarized waves from uncorrelated surface and volume disorder can lead to perfect depolarization. The degree of polarization is shown to vanish in specific scattering directions that can be…
In this paper, we provide the two-body exact solutions of two dimensional (2D) Schr\"{o}dinger equation with isotropic $\pm 1/r^3$ interactions. Analytic quantum defect theory are constructed base on these solutions and are applied to…
The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the…
The direct and inverse scattering problems on the full line are analyzed for a first-order system of ordinary linear differential equations associated with the derivative nonlinear Schr\"odinger equation and related equations. The system…
Scattering of a time harmonic anti-plane shear wave due to either a pair of crack tips or a pair of rigid constraint tips on square lattice is considered. The two problems correspond to the so called zero-offset case of scattering due to a…
In this work, we study the scattering problem of the general nonlinear finitely many Dirac delta potentials with complex coupling constants (or opacities in the context of optics) using the Green's function method and then find the bound…
Subwavelength atomic arrays are a leading platform for engineering strong light-matter interactions, presenting exciting opportunities for quantum science. However, a full understanding of their multi-excitation dynamics remains a…