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Closed formulas are derived for the field in the focal region of a diffraction limited lens, such that the electric field component in a given direction at the focal point is larger than that of all other focused fields with the same power…
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…
We revisit the problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein-Maxwell system of equations where the matter model is a polytropic gas. We consider a…
Detailed analysis of the coupled Dirac-Maxwell equations and the structure of their solutions is presented. Numerical solutions of the field equations in the case of spherical symmetry with negligible gravitational self-interaction reveal…
The exact solutions of the equation for a composite scalar particle which possesses electric and magnetic polarizabilities are found in an external uniform static magnetic field parallel to the direction of propagation of the quantized…
We describe a non-minimal higher-derivative extension of Einstein-Maxwell theory in which electrically-charged black holes and point charges have globally regular gravitational and electromagnetic fields. We provide an exact static…
We investigate the global properties of black brane solutions of a three-parameter Einstein-Maxwell model nonminimally coupled to a scalar with exponential potential. The black brane solutions of this model have recently been investigated…
The propagation of electromagnetic waves through disordered layered system is considered in the paradigm of Maxwell's equations homogenization. In spite of the impossibility to describe the system in terms of effective dielectric…
We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface \{$t$ = constant\} are spheroidal. The solution of the Einstein-Maxwell system is…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
With the Sturm-Liouville analytical and numerical methods, we investigate the behaviors of the holographic superconductors by introducing a complex charged scalar field coupled with a Power-Maxwell field in the background of $d$-dimensional…
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct…
Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In…
We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R} $$ satisfying Maxwell's equations in a nonlinear medium which is not necessarily…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
An exact solution of the Maxwell equations in Rindler coordinates is obtained. The electromagnetic field represents a wave preserving its shape in a relativistic uniformly accelerated frame. The relation with Airy beams is shown explicitly…
We solve the source free electromagnetic wave equation in Friedmann-Robertson-Walker space-times for curvature $K=0$ and $K=-1$. Deriving a solution expression in the form of spherical means we deduce and compare two properties of the…
We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents a challenging…
This article presents a mathematical framework for solving Maxwell's equations in cylindrical and spherical geometries with continuous angular indices. We extend beyond standard discrete harmonic decomposition to a continuous spectral…
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as…