Numerical and analytical study of wave processes in periodic stratified media

We study the behaviour of the solutions of the Cauchy problem with discontinuous initial data for nonstandard linear partial differential equations modeling wave processes in periodic stratified media. Asymptotic formulas at large t are derived. The found asymptotic formulas are in a good agreement with the results of numerical experiments done by using the analytical computation system REDUCE 3.8.     

Degenerate resonant interaction of light with two-photon transition in a periodic medium

The formation of soliton-like structures in a periodic medium containing impurity atoms with resonant two-photon transition degenerate over the magnetic moment projection is studied. For small field amplitudes, the evolution equations are derived and the solutions are obtained, which describe nonlinear polarization effects.     

VUV resonant transition radiation from relativistic electrons

The modified radiator for generation of the resonant transition radiation from relativistic electrons is presented. This radiator consists of a set of small thin foils inclined with respect to the trajectory of an emitting electron. It is shown that the photoabsorption of the emitted photons is almost completely suppressed in the considered scheme. Therefore, the possibility of generating intense beams of quasimonochromatic vacuum ultraviolet (VUV) quanta by the proposed method appears.     

The determination of the relative permittivity of periodic stratified media based on the iterative time-reversal method

In this paper, we present a new method to determine the relative permittivity of periodic stratified media using the iterative time-reversal method. Based on transmission line theory, the focal peak value of iterative time-reversal electro- magnetic waves, which contain information about the periodic stratified medium, is computed in pulse-echo mode. Using the relationship between the focal peak value and the relative permittivity of the periodic stratified medium, the relative permittivity can be obtained by measuring the focal peak value. Numerical simulations are conducted, and the results demonstrate the feasibility of the proposed approach to the measurement of the relative permittivity of a periodic stratified medium.     

Waves in resonant random media

Electromagnetic properties of resonant inhomogeneous media are investigated. A new type of transverse electromagnetic wave arising due to the effective spatial dispersion is studied. It is shown that scattering on the fluctuations of the resonant frequency of the medium shifts the Cherenkov threshold and reduces the intensity of the Cherenkov radiation.     

Waves in resonant random media

Abstract

Electromagnetic properties of resonant inhomogeneous media are investigated. A new type of transverse electromagnetic wave arising due to the effective spatial dispersion is studied. It is shown that scattering on the fluctuations of the resonant frequency of the medium shifts the Cherenkov threshold and reduces the intensity of the Cherenkov radiation.     

Photon localization in resonant media

We report measurements of microwave transmission over the first five Mie resonances of alumina spheres randomly positioned in a waveguide. Though precipitous drops in transmission and sharp peaks in the photon transit time are found near all resonances, measurements of transmission fluctuations show that localization occurs only in a narrow frequency window above the first resonance. There the drop in the photon density of states is found to be more pronounced than the fall in the photon transit time above the resonance, leading to a minimum in the Thouless number.     

Reabsorption of resonant transition radiation

We study reabsorption of resonant transition radiation (RTR) of fast particles in a magnetoactive plasma with random inhomogeneities of electron density. The RTR growth rates are obtained for isotropic and anisotropic distribution functions of fast electrons. The coefficient of radio wave absorption by thermal electrons near the plasma frequency is obtained. It is shown that the RTR instability can be realized in the case of sufficiently strong anisotropy. The properties of such maser transition radiation allow us to distinguish it from other coherent mechanisms of radiation when interpreting laboratory and astrophysical observation results. St. Petersburg State Technical University, A. F. Ioffe Physical and Technical Institute, Russian Academy of Sciences, St. Petersburg, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 8, pp. 941–951, August, 1997.     

Light propagation in stratified anisotropic media

Light propagation in stratified anisotropic media with arbitrary orientation of optic axes smoothly varying from layer to layer is considered. In the WKB approximation, a general expression for the field is obtained. For the case of a uniaxial medium, the normal waves are found and specific features of the light propagation are analyzed. General conditions are obtained that determine the turning points and forbidden zones. It is shown that the developed approach allows one to find trajectories of rays in anisotropic media with arbitrary layered structure.     

Light localization signatures in backscattering from periodic disordered media

The backscattering line shape is analytically predicted for thick disordered medium films where, remarkably, the medium configuration is periodic along the direction perpendicular to the incident light. A blunt triangular peak is found to emerge on the sharp top. The phenomenon roots in the coexistence of quasi-1D localization and 2D extended states. The text was submitted by the author in English.     

Backscattering response from periodic spatial patterns in random media

Abstract

In wave-based remote sensing or radio-location of distant objects in a random medium, a high-frequency electromagnetic wave is scattered by object discontinuities, and portions of the scattered radiation can traverse the same random inhomogeneities as the initial incident field. The statistical dependence of the forward–backward travelling events results in an anomaly in the backscattered intensity pattern that carries information about the scattering object. The quality of this information depends on the ability to resolve the fine-structure elements. In this work we investigate the resolving properties of periodic spatial objects by using the random propagators of the stochastic geometrical theory of diffraction.     

Homogenization for periodic media: from microscale to macroscale

The mathematical tools for the up-scaling from micro to macro in periodic media are considered: the homogenization techniques, the multiscale modelling, etc. The main applications of these tools are the mechanics of composite materials, flows in porous media, and discrete models for nanostructures. The text was submitted by the authors in English.     

Light localization signatures in backscattering from periodic disordered media

The backscattering line shape is analytically predicted for thick disordered medium films where, remarkably, the medium configuration is periodic along the direction perpendicular to the incident light. A blunt triangular peak is found to emerge on the sharp top. The phenomenon roots in the coexistence of quasi-1D localization and 2D extended states.     

Superluminal propagation in resonant dissipative media

We analyse the superluminal propagation of optical narrow-band pulses at resonances in dissipative media. We find that, for a broad class of optical systems holding this type of lossy faster-than-light transmission capability, the output waveform is an attenuated, time-advanced version of the input which can be interpreted as the result of the interference of two scaled replicas of the input having a positive relative delay. This analysis is shown to apply, among other scenarios, both in the propagation in a passive bulk medium at an electronic resonance and in a dielectric waveguide coupled to a lossy micro-ring resonator.