Related papers: The resonant nonlinear scattering theory with boun…
We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. This is to our knowledge the first result of scattering for a…
Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous…
Nonlinear processes of light scattering on a two-level system near resonance are considered. The problem is reduced to the emission and absorption of an entangled system, formed by a strong resonant field and a two-level system, having a…
This paper presents a matrix formulation of the scalar laws of radiative transfer. The method applies to coupled mixed boundary condition problems on general domains. Participating media can range from transparent to absorbing, emitting,…
The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a…
The radiation instability in a split-cavity asymmetric resonator is considered for the relativistic case. The space charge of an electron beam is taken into account. In the small-signal approximation, the energy loss by particles passing…
We derive the $\mathcal{T}$-matrix formalism tailored for numerical analysis of second-harmonic (SH) generation from arbitrarily shaped particles made of centrosymmetric optical materials. First, the transfer matrix of a single particle is…
The brightness theorem---brightness is nonincreasing in passive systems---is a foundational conservation law, with applications ranging from photovoltaics to displays, yet it is restricted to the field of ray optics. For general linear wave…
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,…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states,…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the…
A model of the asymmetric coherent scattering process (caused by initial atomic wave-packet splitting in the momentum space) taking place at the large detuning and adiabatic course of interaction for an effective two-state system…
Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…
A consecutive formalism and analysis of exactly solvable radial reflectionless potentials with barriers, which in the spatial semiaxis of radial coordinate $r$ have one hole and one barrier, after which they fall down monotonously to zero…
The backward Compton scattering is a basic process at future higher energy photon colliders. To obtain a high probability of e->gamma conversion the density of laser photons in the conversion region should be so high that simultaneous…
In this article, a novel analytical approach is presented for the analysis of electromagnetic (EM) scattering from radially inhomogeneous spherical structures (RISSs) based on the duality principle. According to the spherical symmetry,…
We develop a quantitative mathematical theory that offers new perspectives on nonlinear harmonic generation in plasmonic structures arising from symmetry breaking. Focusing on second harmonic generation--the most fundamental process and the…
We analytically treat the scattering of two counter-propagating photons on a two-level emitter embedded in an optical waveguide. We find that the non-linearity of the emitter can give rise to significant pulse-dependent directional…
The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic…