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Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
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…
We set up the Maxwell's equations and the corresponding classical wave equations for the electromagnetic waves which together with the generating source, a traveling oscillatory charge of zero rest mass, comprise a particle traveling in the…
We present an effective medium description of time-modulated dielectric media. By taking the averaged fields over one modulation period, the relationship between them is derived, defining therefore the different constitutive parameters. In…
We use the fractional integrals in order to describe dynamical processes in the fractal media. We consider the "fractional" continuous medium model for the fractal media and derive the fractional generalization of the equations of balance…
In this overview paper, we investigate the dispersion of electromagnetic waves for dissipative and non-dissipative dielectric-magnetic uniaxial mediums. Changing the sign of one component of dielectric permittivity ({\epsilon}) or magnetic…
It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e.,…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
Frequency upconversion of an electromagnetic wave can occur in ionized plasma with decreasing electric permittivity and in split-ring resonator-structure metamaterials with decreasing magnetic permeability. We develop a general theory to…
Changes in the magnetic moment of an electron near a dielectric or conducting surface due to boundary-dependent radiative corrections are investigated. The electromagnetic field is quantized by normal mode expansion for a non-dispersive…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
The dynamical responses of ferromagnet to the propagating electromagnetic field wave passing through it are modelled and studied here by Monte Carlo simulation in two dimensional Ising ferromagnet. Here, the electromagnetic wave is linearly…
A fractional relaxation equation in dielectrics with response function of the Havriliak-Negami type is derived. An explicit expression for the fractional operator in this equation is obtained and Monte Carlo algorithm for calculation of…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the…
We present a Gupta-Bleuler quantization scheme for the electromagnetic field in time-dependent dielectric media. Starting from the Maxwell equations, a generalization of the Lorentz gauge condition adapted to time varying dielectrics is…
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…