Monte Carlo simulation of the coherent backscattering of electrons in a ballistic system

We study weak localization effects in the ballistic regime as induced by man-made scatterers. Specular reflection of the electrons off these scatterers causes backscattered trajectories to occur, which interfere with their time-reversed path resulting in weak localization corrections to the resistance. Using a semi-classical theory, we calculate the change in resistance due to these backscattered trajectories. We found that the inclusion of the exact shape of the scatterers is very important in order to explain the experimental results of Katine et al.[Superlattices and Microstructures 20 , 337 (1996)].     

The transmission and reflection of acoustic and optic phonons from a solid-solid interface treated in a linear chain model

A one-dimensional lattice model of a solid-solid interface is presented within which it is possible to calculate the transmission and reflection amplitudes of lattice vibrations at the interface. The model is applied for acoustic and optic phonons with arbitrary wavelength from the Brillouin zone. General expressions for the coefficients of power transmission and power reflection are evaluated. The reciprocity theorem is proved and applications of numerical results are discussed.     

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.     

On the validity and improvement of the ultrasonic pulse-echo immersion technique to measure real attenuation

A fundamental assumption embraced in conventional use of the ultrasonic pulse-echo immersion technique to measure attenuation in solid materials is revisited. The cited assumption relies on perfect and immutable adhesion at the water to sample interface, a necessary condition that allows calculating the reflection coefficient at any interface from elastic wave propagation theory. This parameter is then used to correct the measured signal and obtain the real attenuation coefficient of the sample under scrutiny. In this paper, cases in which the perfectly cohesive interfacial condition is not satisfied are presented. It is shown also that in those cases, the repeatability of the conditions at the interface is always uncertain. This implies that the reflection coefficients are unknown, even when density is known. A new method of simultaneously measuring the reflection coefficients for both exposed interfaces that are normal to the transducer, and the attenuation coefficient of the specimen is developed and is presented here. The robustness of the new method is proven, as we demonstrate that the proper value of attenuation is achieved independently of the continuously varying interfacial conditions of these non-ideal cases.     

Interaction of ultrasonic wave with void-containing layer in solid

Using a general mode for sound reflection from multilayered media,we present in this paper the expressions for sound reflection and transmissioncoefficients on void-containing interface layer in solid and derive the character-istic equation for symmetric and antisymmetric modes of the interface wavesalong the layer.The method for evaluating the effective elastic moduli ofvoid-containing solid is also introduced.The numerical calculation given in thispaper shows the influences of the void volume concentration and layer thick-ness on the sound reflection coefficients and interface wave velocity,providing atheoretical basis for inverse of the mechanical properties of void-containinglayer based on the ultrasonic measurement.     

超声与固体中含气泡层的相互作用

本文利用固体层状媒质声反射模型,给出了固体中含气泡层声反射和透射系数的表达式,并由此导出沿固体中含气泡薄层对称和反对称模式界面波的特征方程式。本文还介绍了含气泡固体有效弹性模量的估算方法,文中给出的数值计算具体说明了气泡体积浓度和气泡层厚度对声反射系数、声透射系数以及反对称模式界面波传播速度的影响,本文的研究为根据声反射系数和界面波的传播速度的测量反演固体间气泡层的力学性能提供了理论依据。 关键词：     

On the boundary conditions to the Ginzburg-Landau equations at the interface of two superconductors with different transition temperatures

The generalized Wiener-Hopf method was used to derive, on the basis of the microscopic BCS theory of superconductivity, the effective boundary conditions to the Ginzburg-Landau equations at the interface of two (including uncommon) superconductors with different transition temperatures in the absence of reflection from the boundary. According to these conditions, the order parameter and its derivative undergo jumps at the interface.     

Multiple scattering by random configurations of circular cylinders: reflection, transmission, and effective interface conditions

In a previous paper, Linton and Martin [J. Acoust. Soc. Am. 117, 3413-3423 (2005)] obtained two formulas for the effective wavenumber in a dilute random array of circular scatterers. They emerged from a study of the problem of the reflection of a plane wave at oblique incidence to a half-space containing the scatterers. Here, their study is extended to obtain formulas for the reflection and transmission coefficients and to investigate the average fields near the boundary of the half-space. Comparisons with previous work are made.     

基于周期结构负反射的远场增强成像研究

远场高分辨率成像是近几年来声学和光学领域的研究焦点之一, 倏逝波无法在介质中传播成为将高分辨率成像带入远场的最大困难.本文提出了一种均匀排列的散射钢柱构成的超构散射体成像方式, 利用周期结构负反射现象将倏逝波信息转化为可传播波来增强成像.有限元数值模拟被用来研究和验证该方案的可行性, 结果显示波长3.4 mm的声波可以在20 cm外的远场获得大约0.6个波长的成像分辨能力. 通过减小散射体的晶格常数有希望达到更高分辨率成像.     

Exciton polaritons in quantum-dot photonic crystals

We present a theory of the photonic band structure of three-dimensional arrays of quantum dots (QDs). A system of Maxwell’s and material equations is solved and the dispersion equation for exciton-polaritons is derived making allowance for a nonlocal dielectric response of quasi-zero-dimensional excitons confined in QDs. The reflection and transmission coefficients are calculated for a single plane, a pair of planes and a stack of equidistant planes of QDs. Two different approaches are proposed to perform a calculation. One of them is based on recurrent equations relating the reflection coefficients for N + 1 and N planes, while in the other approach the Bloch solutions for an infinite QD lattice are used.     

Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light. This revised version was published online in November 2006 with corrections to the Cover Date.     

Waveguiding in surface plasmon polariton band gap structures

Using near-field optical microscopy, we investigate propagation and scattering of surface plasmon polaritons (SPP's) excited in the wavelength range of 780-820 nm at nanostructured gold-film surfaces with areas of 200-nm-wide scatterers arranged in a 400-nm-period triangular lattice containing line defects. We observe the SPP reflection by such an area and SPP guiding along line defects at 782 nm, as well as significant deterioration of these effects is 815 nm, thereby directly demonstrating the SPP band gap effect and showing first examples of SPP channel waveguides in surface band gap structures.     

Approximations to wave propagation through a lattice of Dirichlet scatterers

A scheme of matched asymptotic expansions is used to obtain approximations to the dispersion relation when waves, governed by the Helmholtz equation, propagate through a two-dimensional lattice of scatterers on each of which a homogeneous Dirichlet boundary condition is imposed. The scatterers must be identical, but can be of any shape as long as each is small relative to the wavelength and the lattice periodicity. The results differ from those obtained using homogenisation in that there is no requirement that the wavelength be much longer than the lattice periodicity, and hence it is possible to describe band gaps.     

Resonant tunneling effect in one-dimensional twinned lattice photonic crystal under total reflection conditions

Under total reflection conditions, it typically seems as though light waves will be reflected completely on the interface; in actuality, the waves can penetrate the medium as evanescent waves. In this paper, we present a twinned lattice photonic crystal with a unit cell composed of AB layers and their mirror. We assume that the refractive index n ₀ of the input and output end is equal to n _B and larger than n _A . We first demonstrate the dependence of band structure on the incidence angle and normalized wavelength, in which the resonant tunneling bands are exposed. We then draw a comparison of bands between ABBA and AB. To conclude, we discuss the resonant tunneling effect in the twinned lattice photonic crystal under the total reflection conditions. As incidence angle increases, the resonant tunneling band ultimately vanishes completely.     

Wave reflections from duct terminations

The reflection coefficients and inertial end corrections of several duct terminations, including finite length duct extensions perpendicular to an infinite wall, as well as at a number of angles, curved interface surfaces, and annular cavities, are determined and analyzed in the absence of flow by employing the boundary element method. Predictions for the classical unflanged and flanged circular ducts show good agreement with analytical and computational results available in the literature. The predictions for curved interface surfaces (bellmouth or horn) are also consistent with the available experimental data. In view of its high reflection coefficient, the duct termination with an annular cavity may be suggested for the suppression of noise radiation in a specific frequency band or for an effective wave reflection from the termination.     

Scattering of longitudinal waves (sound) by defects in fluids. Rough surface

The classical theory of scattering of longitudinal waves (sound) by small inhomogeneities (scatterers) in an ideal fluid is generalized to a distribution of scatterers and such as to include the effect of the inhomogeneities on the elastic properties of the fluid. The results are obtained by a new method of solving the wave equation with spatial restrictions (caused by the presence of the scatterers), which can also be applied to other types of inhomogeneities (like surface roughness, for instance). A coherent forward scattering is identified for a uniform distribution of scatterers (practically equivalent with a mean-field approach), which is due to the fact that our treatment does not include multiple scattering. The reflected wave is obtained for a half-space (semi-infinite fluid) of uniformly distributed scatterers, as well as the field diffracted by a perfect lattice of scatterers. The same method is applied to a (inhomogeneous) rough surface of a semi-infinite ideal fluid. A perturbation-theoretical scheme is devised, with the roughness function as a perturbation parameter, for computing the waves scattered by the surface roughness. The waves scattered by the rough surface are both waves localized (and propagating only) on the surface (two-dimensional waves) and waves reflected back in the fluid. They exhibit directional effects, slowness, attenuation or resonance phenomena, depending on the spatial characteristics of the roughness function. The reflection coefficients and the energy carried on by these waves are calculated both for fixed and free surfaces. In some cases, the surface roughness may generate waves confined to the surface (damped, rough-surface waves).     

Concentric layered Hermite scatterers

The long wavelength limit of scattering from spheres has a rich history in optics, electromagnetics, and acoustics. Recently it was shown that a common integral kernel pertains to formulations of weak spherical scatterers in both acoustics and electromagnetic regimes. Furthermore, the relationship between backscattered amplitude and wavenumber k was shown to follow power laws higher than the Rayleigh scattering $k^2$ power law, when the inhomogeneity had a material composition that conformed to a Gaussian weighted Hermite polynomial. Although this class of scatterers, called Hermite scatterers, are plausible, it may be simpler to manufacture scatterers with a core surrounded by one or more layers. In this case the inhomogeneous material property conforms to a piecewise continuous constant function. We demonstrate that the necessary and sufficient conditions for supra-Rayleigh scattering power laws in this case can be stated simply by considering moments of the inhomogeneous function and its spatial transform. This development opens an additional path for construction of, and use of scatterers with unique power law behavior.     

Reflection and transmission of phonons at a planar interface between two dissimilar solids

Two semi-infinite dissimilar crystals with, however, the same crystal structure and lattice parameter are in contact at a planar interface. Using a simple force constant model, restricted to near-neighbour interaction reflection and transmission coefficients for sound waves propagating along one solid are calculated. At low frequencies the reflection and transmission coefficients are determined solely by the force constants and the atomic masses in the two media. At high frequencies the transmission coefficient becomes small if the force constant at the interface between the two media is weak. Information of the local force constant in the interface region can be gained at least in principle, by measuring the reflection and transmission coefficients at high frequencies.     

Diffusion in lattice Lorentz gases : Nearest scatterers approximation

The expressions for diffusion coefficients and for velocity autocorrelation functions of lattice Lorentz gases are derived both in the nearest scatterers and Boltzmann approximations. The results are obtained for linear chain, square, triangular, simple cubic, body centred cubic, face centred cubic and face centred hyper cubic lattices. The diffusion coefficients are compared with those from the effective medium approximation for the square lattice and with computer simulation results for triangular, simple cubic and body centred cubic lattices.     

Intrinsic anisotropy of the effective acoustic properties in metafluids made of two-dimensional cylinder arrays

Within a unified theoretical framework, we extract the omnidirectional effective acoustic parameters for the metafluid consisting of isotropic fluid cylinders embedded in an isotropic fluid background. Besides the analytical formulas for the effective parameters reported previously, i.e., the bulk modulus and the mass density perpendicular to the cylinders, we also derive a simple expression for the effective mass density parallel to the cylinders. As expected, these two effective mass densities are not identical and constitute an anisotropic density tensor. Such intrinsic anisotropy can be engineered much stronger than the pure in-plane anisotropy induced by either anisotropic lattices or anisotropic scatterers.