Related papers: Determination of electromagnetic medium from the F…
We study Maxwell's equations on a 4-manifold where the electromagnetic medium is modelled by an antisymmetric (2, 2)-tensor kappa with real coefficients. In this setting the Fresnel surface is a fourth order polynomial surface in each…
We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each…
Geometrical optics describes, with good accuracy, the propagation of high-frequency plane waves through an electromagnetic medium. Under such approximation, the behaviour of the electromagnetic fields is characterised by just three…
The propagation of light through bianisotropic materials is studied in the geometrical optics approximation. For that purpose, we use the quartic general dispersion equation specified by the Tamm-Rubilar tensor, which is cubic in the…
Within the framework of generally covariant (pre-metric) electrodynamics, we specify a local vacuum spacetime relation between the excitation $H=({\cal D},{\cal H})$ and the field strength $F=(E,B)$. We study the propagation of…
It is proved that the equality $\Delta\ln|\kappa-\lambda|=6\kappa$, where $\kappa$ is the Gaussian curvature of a metric tensor g on a 2-dimensional manifold is a sufficient and necessary condition for local realizability of the metric as…
Magnetic permeabilities derived for infinite, periodic media are used in the Fresnel equation to calculate the reflection from corresponding semi-infinite media. By comparison to finite-difference-time-domain (FDTD) simulations, we find…
We study the {\em propagation of electromagnetic waves} in a spacetime devoid of a metric but equipped with a {\em linear} electromagnetic spacetime relation $H\sim\chi\cdot F$. Here $H$ is the electromagnetic excitation $({\cal D},{\cal…
It is shown that in polar geometry and normal incidence the 2x2 matrix technique - as discussed in detail in a preceeding paper [Phys. Rev. B 65, 144448 (2002)] - accounts correctly for multiple reflections and optical interferences, and…
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, ${\cal K}^{ijkl}$. This tensor density is, by definition,…
It is shown that the dominant decay mode of $\vec\omega \to \pi^+ \pi^- \pi^0$ can be employed to determine the Fano statistical tensor $t^2_0$ of $\vec \omega$ with respect to the quantization axis normal to the decay plane. In $pp \to pp…
The optical reflection coefficient of a dielectric medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a…
We present a systematic theory connecting the nonlocal response kernel of a homogeneous medium to its effective surface susceptibilities for an arbitrary curved interface. Starting from the most general tensorial nonlocal constitutive…
We show show that the singularities of the Fresnel surface for Maxwell's equation on an anisotrpic material can be accounted from purely topological considerations. The importance of these singularities is that they explain the phenomenon…
We formulate a general framework for describing the electromagnetic properties of spacetime. These properties are encoded in the `constitutive tensor of the vacuum', a quantity analogous to that used in the description of material media. We…
It is known that the Fresnel wave surfaces of transparent biaxial media have 4 singular points, located on two special directions. We show that, in more general media, the number of singularities can exceed 4. In fact, a highly symmetric…
The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) $\ff_\alpha$ of order $\alpha>-1/2$. Roughly speaking, if we denote by $PW_\alpha(b)$ the Paley-Wiener…
We solve time-harmonic Maxwell's equations in anisotropic, spatially homogeneous media in intersections of $L^p$-spaces. The material laws are time-independent. The analysis requires Fourier restriction-extension estimates for perturbations…
We start from a local and linear spacetime relation between the electromagnetic excitation and the field strength. Then we study the generally covariant Fresnel surfaces for light rays and light waves. The metric and the connection of…
The Fermi surface topology in the two-dimensional Hubbard model is particularly relevant for the high-temperature superconductors, whereas its theoretical research encounters with the difficulty of the analytical continuation problem. To…