Method for measuring the frequency shifts of interference maxima in monitoring of dispersion media: Theory,implementation, and prospects

A theory and implementation of the approach to reconstruction of inhomogeneities in dispersion media, based on measuring the frequency shifts of interference maxima (FSIMs) of wave field, are reported. The possibilities of the new approach are compared with the potential of the conventional technique, which is based on measuring the propagation times of pulsed signals. Specific methods for measuring FSIMs in time-dependent media are described, and the noise immunity of these methods is evaluated. The reconstruction (via FSIM monitoring) of typical oceanic inhomogeneities is described and analyzed. Possible applications of this approach in the infra- and ultrasonic ranges are shown.     

Order and disorder in the microstructure of dielectrically nonlinear heterogeneous materials

The paper deals with the electrical characterisation of dispersions of pseudo-oriented ellipsoids of revolution. We are thus dealing with mixtures of inclusions of arbitrary eccentricity and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. A unified theory covers all the orientational distributions between the random and parallel cases. Each ellipsoidal inclusion is made from an isotropic nonlinear dielectric material described by means of the so-called Kerr nonlinear relation.The electrical averaging inside the composite material is carried out by means of explicit results. We obtain closed form expressions for the macroscopic or equivalent dielectric properties of the overall composite materials. This study affirms that the nonlinear electrical behaviour of such a dispersion of pseudo-oriented particles is completely defined by two specific order parameters, which depends on the given angular distribution. The theory may be applied to characterise media with different shapes of the inclusions (i.e. spheres, cylinders or planar inhomogeneities) yielding a set of procedures describing several composite materials of great technological interest.     

Guided and standing Bloch waves in periodic elastic strips

Elastic waveguiding structures are investigated for guides constructed of periodically alternating media thereby forming a striped waveguide. The guide has finite width with either homogeneous traction-free or clamped boundary conditions on the guide walls, or a combination of these. The band spectrum and associated Floquet–Bloch eigensolutions for these in-plane elastic waveguides are identified. Several features of this guiding structure emerge, and are of interest; in some cases a total stop band at zero frequency is identified providing space for low frequency localized modes: such modes also appear when we create defects in the structured waveguide. The dispersion curves often have maxima and minima of the spectral edges far from the edges of the Brillouin zone and these are related to slow sound or standing waves within the structure. Numerical and asymptotic techniques are developed and discussed, the latter are based on weak contrast, and weak geometric changes, or utilize jump conditions in limits where one medium is thin relative to the other. There are technological applications that could utilize this theory and we demonstrate that imaging is possible using anomalous dispersion.     

Multiscale methods for engineering double negative metamaterials

The approach taken here solves the Maxwell equations inside metamaterial crystals directly and explicitly with no approximations made. The Bloch wave solution and dispersion relation is given by a power series in the ratio between wave number and period. Each term is iteratively defined by the solution of an auxiliary problem depending on the configuration and shapes of the scatterers. The leading order term in the power series for the dispersion relation is given by the complex effective index of refraction. The effective properties and their resonance frequencies depend explicitly on the shape of the scatterers. Double negative behavior is explicitly controlled by the location of resonance frequencies related to spectra intrinsic to the geometric configuration of the multi-phase inclusions. This provides for the rational shape design of inclusions for control of double negative behavior across prescribed frequency ranges.     

An iterative effective medium approximation (IEMA) for wave dispersion and attenuation predictions in particulate composites, suspensions and emulsions

In the present work we deal with the scattering dispersion and attenuation of elastic waves in different types of nonhomogeneous media. The iterative effective medium approximation based on a single scattering consideration, for the estimation of wave dispersion and attenuation, proposed in Tsinopoulos et al., [Adv. Compos. Lett. 9, 193-200 (2000)] is examined herein not only for solid components but for liquid suspensions as well. The iterations are conducted by means of the classical relation of Waterman and Truell, while the self-consistent condition proposed by Kim et al. [J. Acoust. Soc. Am. 97, 1380-1388 (1995)] is used for the convergence of the iterative procedure. The single scattering problem is solved using the Ying and Truell formulation, which with a minor modification can accommodate the solution of scattering on inclusions in liquid. Theoretical results for several different systems of particulates and suspensions are presented being in excellent agreement with experimental data taken from the literature.     

Thermopower of a ballistic nanowire subjected to an in-plane magnetic field in the presence of Rashba and Dresselhaus interactions

Using the single-particle formalism, we calculate the thermopower of conduction electrons in a nanowire considering dispersion relations containing local maxima. At low temperatures, the thermopower exhibits positive and negative peaks that are consistent with Mott's approximation. The peaks are degenerate at a certain direction of the magnetic field defined by the strengths of the Rashba and Dresselhaus interactions. The sign and the height of the peak depend on the number of channels available for conduction.     

Anomalous pulse interaction in dissipative media

We review a number of phenomena occurring in one-dimensional excitable media due to modified decay behind propagating pulses. Those phenomena can be grouped in two categories depending on whether the wake of a solitary pulse is oscillatory or not. Oscillatory decay leads to nonannihilative head-on collision of pulses and oscillatory dispersion relation of periodic pulse trains. Stronger wake oscillations can even result in a bistable dispersion relation. Those effects are illustrated with the help of the Oregonator and FitzHugh-Nagumo models for excitable media. For a monotonic wake, we show that it is possible to induce bound states of solitary pulses and anomalous dispersion of periodic pulse trains by introducing nonlocal spatial coupling to the excitable medium.     

Frequency shifts of sound field maxima in oceanic waveguides

The frequency shifts of sound field maxima that are caused by the variability of the medium in an oceanic waveguide are described. The condition under which the time spectrum of the frequency shifts of interference maxima is proportional to the time spectrum of fluctuations in the dispersion characteristic of the waveguide is determined.     

Localization of nonlinear waves in elastic bodies with inclusions

By the example of the problem of the motion of a semi-infinite string lying on an elastic base, a method for describing wave localization near inclusions is proposed for the case of a cubic nonlinearity of the base. The method applies the perturbation technique to the amplitude of a localized mode. The nature of the divergences is revealed, and the secular terms are found to belong to one of two types: inphase or antiphase with the localized wave. It is shown that a combination of the renormalization method and multiscale method provides a convergence of the solutions, which are sought for in the form of power series in the amplitude of the localized mode. It is found that the localization process is determined by the type of the discrete spectrum, type of the nonlinearity, and type of dispersion. The nonlinearity of the elastic base produces two characteristic effects. First, the frequency of the localized wave becomes dependent on the wave amplitude. Second, the system can generate traveling waves at multiple frequencies, which withdraw energy from the localized wave and cause it to decay. The decay behavior is determined by the minimum frequency of these traveling waves (because it must be higher than the cutoff frequency). The lifetime of the localized wave as a function of the mass of a dynamic inclusion exhibits a number of maxima. In particular, the first maximum corresponds to the minimum amplitude of the traveling wave at the triple frequency.     

A comparative study of the full dispersion relation, Compton dispersion relation, and Raman dispersion relation of a free-electron laser in helical wiggler and guiding magnetic fields

The full dispersion relation obtained for a free-electron laser in the presence of circularly polarized, periodic, static wiggler and guiding magnetic fields by the kinetic approach incorporating the particle trajectories is reduced to Compton and Raman regime approximations in the case of a tenuous electron beam. The temporal growth rate has been compared between the full dispersion relation and the Compton dispersion relation, as well as between the full dispersion relation and the Raman dispersion relation in the microwave region. The results show the maxima of growths in the full dispersion relation and the Compton dispersion relation, as well as the full dispersion relation and the Raman dispersion relation, are at the same locations, but the growth rates in both regimes are enhanced with respect to the full dispersion relation for the same plasma frequency and cavity parameters.     

Collapse of optical vortices

We theoretically and experimentally investigate the self-focusing of optical vortices in Kerr media. We observe collapse to a distinct self-similar profile, which becomes unstable to azimuthal perturbations. We analyze the azimuthal modulational instability for ring-shaped vortices and predict the number of azimuthal maxima solely as a function of power and topological charge. In our experiments, the observed multiple-filamentation patterns are in excellent agreement with our theoretical analysis.     

Modeling the electrical characteristics of periodic dielectric media

The dispersion of the effective permittivities of two inhomogeneous matrix systems with unidirectional fiber inclusions with a square cross section is studied. Interpolation formulas for the effective permittivity as a function of the frequency are obtained, whose range of applicability is determined through physical modeling and comparison with known systems of equations admitting exact solutions. It is established that the effective loss factor exhibits anomalous behavior in the vicinity of the critical concentration of inclusions.     

Analysis of multichannel optical soliton collisions with asymmetric energy in strongly dispersion managed transmission networks considering higher-order effects

We study the interaction properties of optical soliton pulses propagating in a two-channel wavelength-division multiplexed strongly dispersion managed communication system. We analyze the effects of third order dispersion, Raman scattering and self-steepening using an ordinary differential equations model obtained by a variational method applied to the Generalized Nonlinear Schrödinger Equation. The validity of the model is assessed against the integration of the full nonlinear partial differential equations. The variational equations are initially solved for a single pulse in order to identify the launching parameters for each pulse in the first DM cell of the system. One pulse per wavelength is then injected in the transmission link. We then systematically study the evolution of multiplexed soliton trains and analyse the transmission system in terms of residual frequency shifts and interchannel interactions as the map strength is varied, focusing on the ratio of dissimilar peak powers in a broad range of dispersion difference values, concluding that the transmission characteristics improve by using specific values of unequal energies and considering higher-order correction terms. The work presented is an extension of previous analysis where isolated intra-channel two-pulse interactions had been addressed considering pulses with dissimilar energies.     

Tunneling interferometry and measurement of the thickness of ultrathin metallic Pb(111) films

Spectra of the differential tunneling conductivity for ultrathin lead films grown on Si(111) 7 × 7 single crystals with a thickness of 9 to 50 ML have been studied by low-temperature scanning tunneling microscopy and spectroscopy. The presence of local maxima of the tunneling conductivity is characteristic of such systems. The energies of maxima of the differential conductivity are determined by the spectrum of quantum-confined states of electrons in a metallic layer and, consequently, the local thickness of the layer. It has been shown that features of the microstructure of substrates, such as steps of monatomic height, structural defects, and inclusions of other materials covered with a lead layer, can be visualized by bias-modulation scanning tunneling spectroscopy.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

Structure of triglycine sulfate embedded in porous aluminum oxide

The X-ray diffraction investigations have been performed for nanocomposite materials based on porous aluminum oxide with inclusions of TGS and TGS, which is doped with L,α-alanine (ATGS). The presence of the TGS and ATGS textures in pores of Al₂O₃ films has been found. It has been established that, under conditions of confined geometry, the broadening of diffraction maxima of the reflection is caused by the size effect. The temperature dependences of the order parameter for porous aluminum oxide with TGS inclusions have been constructed.     

分析布拉格光栅破坏的两纤芯不同的光纤耦合器

进一步推广了描述纤芯不同光纤耦合器的耦合模理论，用于解释被布拉格光栅破坏的两纤芯不同光纤耦合器的耦合现象，理论分析的结果与已报道的实验结果相符，与单独的布拉格光栅所起的反射作用不同,这里布拉格光栅所起的作用主要是引入了强烈的色散，在光栅的频谱范围内使耦合器不再同步，在被布拉格光栅破坏的光纤耦合器的选择性频谱中，其边缘部分出现非常弱的波动，而在其阻带内出现非常强的凹陷。     

Modeling of wave dispersion along cylindrical structures using the spectral method

Algorithm and code are presented that solve dispersion equations for cylindrically layered media consisting of an arbitrary number of elastic and fluid layers. The algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wave numbers of different modes. The advantage of this technique is that it is easy to implement, especially for cases where traditional root-finding methods are strongly limited or hard to realize, i.e., for attenuative, anisotropic, and poroelastic media. The application of the new approach is illustrated using models of an elastic cylinder and a fluid-filled tube. The dispersion curves so produced are in good agreement with analytical results, which confirms the accuracy of the method. Particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies.     

On the applicability of Kramers-Kronig relations for ultrasonic attenuation obeying a frequency power law

In the recent literature concern has been raised regarding the validity of Kramers-Kronig relations for media with ultrasonic attenuation obeying a frequency power law. It is demonstrated, however, that the Kramers-Kronig dispersion relations for application to these types of media are available. The developed dispersion relations are compared with measurements on several liquids, and agreement is found to better than 1 m/s over the experimentally available bandwidth. A discussion regarding the validity of these dispersion relations, in particular how the dispersion relations relate to the so-called Paley-Wiener conditions, forms the conclusion.