Related papers: A generalized Debye source approach to electromagn…
The Debye source representation for solutions to the time harmonic Maxwell equations is extended to bounded domains with finitely many smooth boundary components. A strong uniqueness result is proved for this representation. Natural complex…
Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their…
The well-known "Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral…
In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out, and also by getting absorbed within the medium. We analyze the leaky modes of solid dielectric spheres by examining solutions…
The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative…
Closed expression for the Green's function of the stationary two-dimensional Schrodinger equation for an electron in group-VI dichalcogenides in the presence of a magnetic field is obtained in terms of the Whittaker functions. The resulting…
Dissipative effects in electromagnetism on macroscopic scales are examined by coarse graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by…
A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…
It is well-known that electromagnetic dispersive structures such as metamaterials can be modelled by generalized Drude-Lorentz models. The present paper is the first of two articles dedicated to dissipative generalized Drude-Lorentz open…
We develop a framework for the multiple scattering of a polarized wave. We consider particles with spin propagating in a medium filled with scatterers. We write the amplitudes of each spin eigenstate in a local, mobile frame. One of the…
Graphene's structure bears on both the material's electronic properties and fundamental questions about long range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multi-layer…
We discuss the numerically stable, spectral-domain computation and extraction of the scattered electromagnetic field excited by distributed sources embedded in planar-layered environments, where each layer may exhibit arbitrary and…
In this paper, we establish new results for the uniform far-field asymptotics of the two-layered Green function (together with its derivatives) in 2D in the frequency domain. To the best of our knowledge, our results are the sharpest yet…
An integral equation-based numerical method for scattering from multi-dielectric cylinders is presented. Electromagnetic fields are represented via layer potentials in terms of surface densities with physical interpretations. The existence…
When a set of charged or dyonic objects scatter and subsequently disperse, the process generically emits electromagnetic radiation. The classical soft photon theorem constrains the constant term and leading power-law fall-off of the emitted…
We prove decay with respect to some Lebesgue norms for a class of Schr\"odinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space…
A general theory of the interaction of the quantized electromagnetic field with atoms in the presence of dispersing and absorbing dielectric bodies of given Kramers--Kronig consistent permittivities is developed. It is based on a…
We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…
In this work, we develop a potential-based formalism for Maxwell's equations in isotropic media with weak spatial dispersion within the electric quadrupole-magnetic dipole approximation. We introduce an operator form of the constitutive…
In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for…