Related papers: On multiple frequency power density measurements I…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
We consider the high frequency Helmholtz equation with a variable refraction index $n^2(x)$ ($x \in \R^d$), supplemented with a given high frequency source term supported near the origin $x=0$. A small absorption parameter…
We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period $\eta > 0$; we study the behaviour of solutions $(E^{\eta}, H^{\eta})$…
We derive an $H_{0}^{s,p}(\curl;\Omega)$ estimate for the solutions of the Maxwell type equations modeled with anisotropic and $W^{s, \infty}(\Omega)$-regular coefficients. Here, we obtain the regularity of the solutions for the…
A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the…
We study the electric Helmholtz equation $\Delta u + Vu + \lambda u =f$ and show that, for certain potentials, the solution $u$ given by the limited absorption principle obeys a Sommerfeld radiation condition. We use a non-spherical…
In this work, we rigorously derive effective dynamics for light from within a limited frequency range propagating in a photonic crystal that is modulated on the macroscopic level; the perturbation parameter $\lambda \ll 1$ quantifies the…
The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the…
For Hill's equation on [0,infinity) we prove new characterizations of the spectral function rho(lambda) and the spectral density function f(lambda) based on analysis involving a companion system of first order differential equations in…
The method of the optical approximation is used to estimate the high frequency impedances of different vacuum chamber transitions of the European XFEL beam line. The approximations of the longitudinal impedances are obtained in terms of…
The theoretical foundations of quantum mechanics and de Broglie--Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
In this note we construct smooth bounded domains $\Omega \subset \mathbb R^2$, other than disks, for which the overdetermined problem $$ \left\{ \begin{alignedat}{2} \Delta u + \lambda u &= 0 &\qquad& \text{ in } \Omega, \newline u &= b…
We are concerned with an harmonic analysis in Hilbert spaces $L^2(\mu)$, where $\mu$ is a probability measure on $\br^n$. The unifying question is the presence of families of orthogonal (complex) exponentials $e_\lambda(x) = \exp(2\pi i…
We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivity $\varepsilon$ and the permeability $\mu$ take negative…
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…
High Refractive Index (HRI) dielectric particles smaller than the wavelength, isolated or forming a designed ensemble are ideal candidates as new multifunctional elements for building optical devices. Their directionality effects are…
Textbooks state that the successful application of Maxwell's Equations in physical optics problems requires light to interact with matter where any inhomogeneities are spaced by less than or equal to the wavelength of light; the 'dense'…
We show that for optical cavities with any finite dissipation, the term "cavity mode" should be understood as a solution to the Helmholtz equation with outgoing wave boundary conditions. This choice of boundary condition renders the problem…
We deal with the problem of reconstructing interfaces using complex geometrical optics solutions for the Maxwell system. The contributions are twofold. First, we justify the enclosure method for the impenetrable obstacle case avoiding any…
We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In…