Related papers: Singular Modes of the Electromagnetic Field
A new class of generalized solutions related to the essential spectrum of linear Maxwell's equations is presented. The essential modes are given in terms of normalized singular Weyl's sequences, whose square represents Dirac's delta…
Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…
We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. We show that for higher orders, it is more efficient to have fields represented in…
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,…
Electromagnetic waves are described by not only polarization ellipses but also cyclically rotating vectors tracing out them. The corresponding fields are respectively directionless steady line fields and directional instantaneous vector…
We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single…
We consider the strong field asymptotics for the occurrence of zero modes of certain Weyl-Dirac operators on $\mathbb{R}^3$. In particular we are interested in those operators $\mathcal{D}_{B}$ for which the associated magnetic field $B$ is…
We carry out the spectral analysis of singular matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the perturbations, we…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Partial results obtained in a previous paper are completed to represent accurately…
Electromagnetic wave scattering by many parallel infinite cylinders is studied asymptotically as $a\to 0$. Here $a$ is the radius of the cylinders. It is assumed that the points $\hat{x}_m$ are distributed so that…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with…
We prove that the Weyl function of the one-dimensional Dirac operator on the half-line $\mathbb{R}_+$ with exponentially decaying entropy extends meromorphically into the horizontal strip $\{0\ge \mbox{Im}\,z > -\delta\}$ for some $\delta >…
Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator…
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…
In this Letter, we introduce a representation of the electromagnetic field for the analysis and synthesis of the full-wave scattering by a homogeneous dielectric object of arbitrary shape in terms of a set of eigenmodes independent of its…
In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…
We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the $z$-components of the linear…
We obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities, x,…