Related papers: Introducing a general method for solving electroma…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
Radiative transfer calculations are essential for modeling planetary atmospheres. However, standard methods are computationally demanding and impose accuracy-speed trade-offs. High computational costs force numerical simplifications in…
We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not…
The notion of ``radiating'' and ``non-radiating'' current sources in classical electrodynamics plays an important role in calculations of direct and inverse electromagnetic scattering problems. Such a decomposition of the current is central…
Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the…
We develop an effective computational tool for simulating the scattering of 1D waves by a composite layer architected in an otherwise homogeneous medium. The layer is designed as the union of segments cut from various mother periodic media,…
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic…
Mie theory is one of the main tools describing scattering of propagating electromagnetic waves by spherical particles. Evanescent optical fields are also scattered by particles and exert radiation forces which can be used for optical…
We give a definition of scattering matrices based on the asymptotic behaviors of generalized eigenfunctions and show that these scattering matrices are equivalent to the ones defined by wave-operator approach in long-range $N$-body…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
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…
This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized…
Modal expansion is an attractive technique for solving electromagnetic scattering problems. With the one set of resonator modes, calculated once and for all, any configuration of near-field or far-field sources can be obtained almost…
Electromagnetic fields in bulk bianisotropic media can be represented using plane waves whose k-vectors can be found using the index of refraction operator method and belong to the Fresnel wave surfaces that fall into one of the 5…
The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background…
The algebraic approach to the phase problem for the case of X-ray scattering from an ideal crystal is extended to the case of the neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this…
We report a new analytical method for exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…