Classification of electromagnetic resonances in finite inhomogeneous three-dimensional structures

We present a simple and unified classification of macroscopic electromagnetic resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D structures situated in free space. By observing the complex-plane dynamics of the spatial spectrum of the volume integral operator as a function of angular frequency and constitutive parameters we identify and generalize all the usual resonances, including complex plasmons, real laser resonances in media with gain, and real quasi-static resonances in media with negative permittivity and gain.Comment: 4 pages, 2 figure

Correlations among elastic and inelastic cross-sections and slope parameter

We discuss the unitarity motivated relations among the elastic cross-section, slope parameter and inelastic cross-section of the high energy \textit{pp} interaction. In particular, the MacDowell-Martin unitarity bound is written down in another form to make a relation between the elastic and inelastic quantities more transparent. On the basis of an unitarity motivated relation we argue that the growth with energy of the elastic to total cross-section ratio is a consequence of the increasing with energy of the \textit{inelastic interaction intensity}. The latter circumstance is an underlying reason for the acceleration of the slope parameter growth, for the slowing of the growth of the elastic to total cross-section ratio and for other interesting phenomena, which are observed in the TeV energy range. All of this confirms the old idea that the elastic scattering is a shadow of the particle production processes.Comment: 16 pages, 6 figure

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

Penetration of the magnetic field into the twinning plane in the type I and II superconductors

It is demonstrated that in the type I and II superconductors with low-transparent twinning planes (TP) the penetration of external parallel magnetic field into the region of the twinning plane can be energetically favorable. In the type I superconductors the twinning planes become similar to Josephson junctions and the magnetic field penetrates into the center of the TP in the form of soft Josephson-like vortices. This leads to increase in the critical magnetic field values. The corresponding phase diagram in the parameter plane "temperature - magnetic field" essentially differs from the one obtained without taking the finite value of the magnetic field near the TP into account. Comparison between obtained phase diagrams and experimental data for different type I superconductors can allow to estimate the value of the TP transparency, which is the only fitting parameter in our theory.Comment: 5 pages, 2 figure