Related papers: Optimal Focusing for Monochromatic Scalar and Elec…
In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces…
The present study deals with total internal reflection of a plane electromagnetic wave at an infinite plane boundary between a transparent medium and an amplifying or attenuating lower-index medium. Solutions of Maxwell's equations are…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
A technique is given to generate coupled scalar field solutions in colliding Einstein - Maxwell (EM) waves. By employing the Bell - Szekeres solution as seed and depending on the chosen scalar field it is possible to construct nonsingular…
It is now wellknown that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group-velocities (0 < v_g < infinity). Some of them, which are rigidly moving and have been called localized solutions, attracted large…
In order to analyse classical electromagnetism in a medium at finite temperature we introduce `an optical density operator', and reformulate Maxwell's equations with the operator, starting from the Dirac-equation-like formulation of…
A general method is presented for determining the maximum electric energy in a bounded region of optical fields with given time-averaged flux of electromagnetic energy. Time-harmonic fields are considered whose plane wave expansion consists…
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical…
In this paper we extend for the case of Maxwell equations the "X-shaped" solutions previously found in the case of scalar (e.g., acoustic) wave equations. Such solutions are localized in theory, i.e., diffraction-free and particle-like…
We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld…
Using techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasi-energies is obtained, which shows…
We consider Maxwell's equations in a 3-dimensional material, in which both, the electric permittivity, as well as the magnetic permeability, fluctuate in space. Differently from all previous treatments of the disordered electromagnetic…
Maxwell's equations are solved when the amplitude and phase of the electromagnetic field are determined at all points in space. Generally, the Stokes parameters can only capture the amplitude and polarization state of the electromagnetic…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an…