Related papers: Electromagnetic Waves in Variable Media
We study the behavior of wave propagation in materials for which not all of the principle elements of the permeability and permittivity tensors have the same sign. We find that a wide variety of effects can be realized in such media,…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…
We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
We find a new set of exact solutions to Maxwell's equations in space--time varying materials, where the refractive index is constant, while the impedance exhibits effective motion, i.e. it is a function of $x-vt$. We find that waves…
A theory of surface electromagnetic waves in gradient media exhibiting arbitrary surface gradients of dielectric permittivity and magnetic permeability has been developed. Novel low-loss propagating surface wave solutions have been found in…
Temporal metamaterials are artificially manufactured materials with time-dependent material properties that exhibit interesting phenomena when waves propagate through them. The propagation of electromagnetic waves in such time-varying…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a…
Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear…
We show that the optical properties of an oblique layered system with two kinds of isotropic materials can be described using the concept of transformation media as long as the thickness of the layers is much smaller than the wavelength.…
Several results concerning active media or metamaterials are proved and discussed. In particular, we consider the permittivity, permeability, wave vector, and refractive index, and discuss stability, refraction, gain, and fundamental…
Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are…
Transformation methods have stimulated many interesting applications of manipulating electromagnetic and acoustic waves by using metamaterials, such as super-lens imaging and cloaking. These successes are mainly due to the form-invariant…
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…
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…