The anisotropic effect of hexagonal warping on the transport

In the presence of hexagonal warping (HW), the surface state of a topological insulator (TI) exhibits anisotropic Fermi surface. In this work, we study the transport properties of a TI junction, focusing on the influence of anisotropic effect of the HW on the scattering. We establish general expressions for calculating the scattering with an arbitrary angle between TI surface and the potential step, and find that the transmission probability and conductance have a strong dependence on the angle, making TI junction a promising platform for studying the geometry control of transport. Remarkably, we find that the HW can induce a triple refraction, which gives rise to an anomalous increase of the transmission probability when varying incident angle. The general expressions here for calculating the scattering can be extended to the systems with trigonally and tetragonally warped Fermi surface.     

曲率对有限曲面狭缝阵列传输特性的影响

扩展互导纳法用于研究有限曲面狭缝阵列的传输特性,分析了一维弯曲效应以及单元列数、曲率等因素对磁流分布、散射方向图及频率响应曲线的影响.结果表明,曲面张角是衡量弯曲效应的主要参数. 当曲面张角较大时(120°以上),弯曲效应显著,单元磁流分布剧烈起伏,散射方向图波束展宽且副瓣电平升高,谐振频率、传输带宽及功率透射系数等频率响应特性均发生较大变化.当曲面张角较小时(60°以下),仅边缘附近的单元磁流分布受到曲率影响,散射方向图与传输特性均接近于有限平面阵列,表明此时可近似忽略弯曲效应. 关键词： 频率选择表面 狭缝阵列 传输特性 曲率     

低能Cl^-在Al2O3绝缘微孔膜中的输运过程

研究了10 keV Cl^-离子穿越Al2O3绝缘微孔膜的物理过程,发现穿越的Cl^-其分布中心在初束中心即0°附近,Cl^-离子穿透率下降与几何穿透一致,这是典型的直接几何穿越有一定角发散的微孔导致的结果;而出射的Cl0和Cl^+以微孔轴向为中心分布,Cl^+和Cl0穿透率下降慢于几何穿透.模拟计算发现沉积电荷会使出射粒子中Cl^-占主要成分,并使出射Cl^-角分布中心移动到微孔轴向方向而随微孔膜倾角移动;而在不考虑沉积电荷的情况下,计算结果较好地符合了实验结果.通过分析在不同倾角下散射过程对出射粒子的角分布和电荷态分布的影响,发现绝大部分的Cl0是通过一次和两次散射出射的,其中一次散射出射的Cl0占主要成分,从而导致出射的Cl0沿微孔轴向出射而Cl^+主要是经过一次碰撞出射.这导致了随倾角增大,出射的Cl0穿透率下降速度比Cl^+小,Cl0所占比例相对增大较快,从而导致观测到的Cl^+/Cl0的比例下降.本文结果更仔细地描述了低能离子穿越绝缘体微孔的物理机理,印证了之前实验和理论工作的结果,发现在10 keV以上能区的Cl^-离子穿越绝缘微孔膜的过程中,沉积电荷并未起到主要作用,其主要穿透特征是散射过程造成的.     

Free control of far-field scattering angle of transmission terahertz wave using multilayer split-ring resonators’ metasurfaces

To enhance transmission efficiency of Pancharatnam–Berry (PB) phase metasurfaces, multilayer splitring resonators were proposed to develop encoding sequences. As per the generalized Snell’s law, the deflection angle of the PB phase encoding metasurfaces depends on the metasurface period’s size. Therefore, it is impossible to design an infinitesimal metasurface unit; consequently, the continuous transmission scattering angle cannot be obtained. In digital signal processing, this study introduces the Fourier convolution principle on encoding metasurface sequences to freely control the transmitted scattering angles. Both addition and subtraction operations between two different encoding sequences were then performed to achieve the continuous variation of the scattering angle. Furthermore, we established that the Fourier convolution principle can be applied to the checkerboard coded metasurfaces.     

Enhancement of spectral-angular density of parametric X-rays in Laue geometry due to change in the angle between a target surface and reflecting atomic planes

Coherent X-rays of a relativistic electron crossing a single crystal with a uniform velocity in the Laue scattering geometry are considered in the two-wave approximation of dynamic diffraction theory [1]. Analytical expressions for the spectral-angular distribution of parametric X-rays (PXR) and diffracted transition radiation (DTR) have been obtained. The case when the system of diffracting atomic planes of a crystal is located at an arbitrary angle δ to a crystal surface (asymmetric reflection) is considered. The value δ = π/2 corresponds to the symmetric reflection in the given scattering geometry. The dependence of the PXR and DTR spectral-angular density on the angle δ has been investigated. It has been shown that the PXR spectrum width depends substantially on the given angle, which, in particular, allows one to increase significantly the PXR angular density by decreasing the angle δ.     

Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering

Abstract

The scattering of an electromagnetic wave from a two-dimensional, slightly rough dielectric surface is studied based on the stochastic functional approach. It is shown that in the case of TM(p)-polarized incidence there exists a zero in the incoherent scattering at the angle we call the ‘Brewster scattering angle’, which depends on the incident angle in contrast to the Brewster angle of coherent reflection which is independent of the incident angle, that a ‘quasi-anomalous scattering’ can generally occur in the optically denser medium at the critical angle of total reflection in both TE(s)- and TM(p)-polarized incidence, regardless of which side of the random surface is illuminated, and that the Yoneda peak in the x-ray scattering can be interpreted as a special case of the quasi-anomalous scattering which becomes sharper when the relative refractive index becomes closer to unity as in the x-ray region. Cross-polarized scattering and enhanced backscattering due to the second-order effect are also calculated.     

Pulse-shape distortion in transmission experiments with incoherent phonons in isotropic solids due to elastic scattering

Assuming homogeneously distributed elastic scattering centers in an isotropic dielectric plate, the transmission and distortion of phonon pulses, that are transmitted from a radiator element to a centered detector element at the opposite face, are investigated theoretically. Analytic expressions are derived for the singlescattered phonon signal due to three different phenomenological scattering characteristics: isotropic scattering, preferential forward scattering, and preferential forward/backward scattering. In particular, we find that the asymptotic decay of the scattered phonon signal depends on the associated scattering characteristic. Numerical results are given for the excitation by a delta pulse using all three scattering characteristics. As a special case, the pulse-shape distortion of a rectangular pulse of 100 ns duration is treated in more detail. Parameter is the ratio of phonon mean free path to plate thickness.     

Semiclassical theory of potential scattering for massless Dirac fermions

In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different regimes of scattering. To find the reflection and transmission coefficients in these regimes, we apply the Wentzel–Kramers–Brillouin (WKB), also called semiclassical, approximation. We use the method of comparison equations to extend our prediction to nearly normal incidence, where the conventional WKB method should be modified due to the degeneracy of turning points. We compare our results to numerical calculations and find good agreement.     

由小斜率近似计算空气声经粗糙海面透射至深海中的声场（英文）

The first-order small slope approximation is applied to the problem of the sound transmission from an airborne source into deep ocean through a rough sea surface,and expressions are derived for the transmitted sound field and its coherent component.Numerical calculations are performed.The sea surface is assumed to be random rough with a PiersonMoskowitz spectrum and to have height variations in only one dimension.For the case of the airborne line source,the small slope approximation results are in good agreement with those from integral equations,and show that the mean of sound intensity at observation direction with shallow depression angle increases and approaches a limit as the root-mean-square surface height increases,while the coherent field intensity consistently decreases.For the case of the point source,the small slope approximation results show that the mean of sound intensity depends significantly on the source-receiver bearing angle,but the coherent field intensity is independent of this angle.     

Closed-form expressions for ocean reverberation and signal excess with mode stripping and Lambert's law

Closed-form expressions for two-way propagation and reverberation in variable depth ducts are derived for isovelocity water by using ray invariants and acoustic flux. These expressions include the transition to single mode propagation at long range. Three surface scattering laws are considered: Lambert, Lommel-Seeliger, and angle independent, and these are compared with a point target to give explicit signal-to-reverberation ratios. In particular, there is interesting and sometimes surprising behavior when the propagation obeys mode-stripping (the high angles are preferentially attenuated by bottom losses) whilst the scattering obeys Lambert's law (high angles are preferentially back-scattered). There may be conditions where the signal-to-reverberation ratio is independent of range so that there is no reverberation range limit. Bottom slope dependence of both target echo and reverberation is surprisingly weak. The implications of refraction are discussed. The angle dependence for a point or surface scatterer at a given range can be translated into arrival time, so it is possible to calculate the received pulse shape for one-way or two-way paths. Because the tail is exponential with a range-independent half-life that only depends on bottom reflection properties there is scope for extracting geoacoustic information from the pulse shape alone. This environmental time spread is also of use to sonar designers.     

Microwave Doppler spectra of sea return at small incidence angles: specular point scattering contribution

It is well known that the sea return echo contains contributions from at least two scattering mechanisms. In addition to the resonant Bragg scattering, the specular point scattering plays an important role as the incidence angle becomes smaller (≤20o). Here, in combination with the Kirchhoff integral equation of scattering field and the stationary phase approximation, analytical expressions for Doppler shift and spectral bandwidth of specular point scattering, which are insensitive to the polarization state, are derived theoretically. For comparison, the simulated results related to the two-scale method (TSM) and the method of moment (MOM) are also presented. It is found that the Doppler shift and the spectral bandwidth given by TSM are insufficient at small incidence angles. However, a comparison between the analytical results and the numerical simulations by MOM in the backscatter configuration shows that our proposed formulas are valid for the specular point scattering case. In this work, the dependences of the predicted results on incidence angle, radar frequency, and wind speed are also discussed. The obtained conclusions seem promising for a better understanding of the Doppler spectra of the specular point scattering fields from time-varying sea surfaces.     

由小斜率近似计算空气声经粗糙海面透射至深海中的声场

采用一级小斜率近似方法处理空气声经粗糙海面透射至深海中的声场问题,导出了透射场及其相干分量的表达式。假定海面高度一维变化且频谱满足PM谱,采用小斜率近似方法计算了相应的透射场。对于空气中的线源,小斜率近似与积分方程方法结果一致。当水下测量点距离较远且深度较浅时,平均声强随海面均方根高度增加而增加至一极限值,相干声强则随海面均方根高度增加而一致减小。对于空气中的点源,小斜率近似计算表明,水下平均声强还依赖于测量点相对于声源的方位,而相干声强则与测量点的方位无关。      

Oblique incidence properties of locally resonant sonic materials with resonance and Bragg scattering effects

A locally resonant sonic material (LRSM) is an elastic matrix containing a periodic arrangement of identical local resonators (LRs), which can reflect strongly near their natural frequencies, where the wavelength in the matrix is still much larger than the structural periodicity. Due to the periodic arrangement, an LRSM can also display a Bragg scattering effect, which is a characteristic of phononic crystals. A specific LRSM which possesses both local resonance and Bragg scattering effects is presented. Via the layered-multiple-scattering theory, the complex band structure and the transmittance of such LRSM are discussed in detail. Through the analysis of the refraction behavior at the boundary of the composite, we find that the transmittance performance of an LRSM for oblique incidence depends on the refraction of its boundary and the transmission behaviors of different wave modes inside the composite. As a result, it is better to use some low-speed materials (compared with the speed of waves in surrounding medium) as the LRSM matrix for designing sound blocking materials in underwater applications, since their acoustic properties are more robust to the incident angle. Finally, a gap-coupled LRSM with a broad sub-wavelength transmission gap is studied, whose acoustic performance is insensitive to the angle of incidence.     

Phonon coupling in inelastic atom-surface scattering

Inelastic scattering of a thermal He beam from a LiF surface has been observed in terms of velocity and intensity distributions as a function of scattering angle. The results allow a correlation with theoretical predictions assuming single Rayleigh phonon coupling for both phonon creation and annihilation processes. A marked decrease of inelastic intensities with momentum or energy transfer is demonstrated, which depends strongly on the temperature of the scattering surface.     

光学元件亚表面缺陷偏振双向反射分布函数

 利用琼斯散射矩阵,借助右手正交基组来表示入射场和散射场,推导出光学元件亚表面缺陷或微粒在不同偏振状态下的双向反射分布函数的表达式。给出了亚表面缺陷在不同入射角条件下,不同偏振状态下的双向反射分布函数与散射方位角之间的关系,以及不同入射角下p偏振入射产生的p偏振双向反射分布函数的3维散射图。结果表明:p偏振入射产生的p偏振双向反射分布函数强烈依赖于入射角、散射角和方位角,且随着入射角的增加,其最小值点所对应的方位角逐渐减小。     

Ballistic electron transport in wrinkled superlattices

Inspired by the problem of elastic wave scattering on wrinkled interfaces, we studied the scattering of ballistic electrons on a wrinkled potential energy region. The electron transmission coefficient depends on both wrinkle amplitude and periodicity, having different behaviors for positive and negative scattering potential energies. For scattering on potential barriers, minibands appear in the electron transmission, as in superlattices, whereas for scattering on periodic potential wells the transmission coefficient has a more complex form. Besides suggesting that tuning of electron transmission is possible by modifying the scattering potential via voltages on wrinkled gate electrodes, our results emphasize the analogies between ballistic electrons and elastic waves even in scattering problems on non-typical configurations.     

On the role of scattering and absorption edges in waveguide collimation of X-rays

The role of incoherent scattering in damping of transmitted radiation is studied on the basis of the statistical theory of X-ray scattering in a narrow rough collimator. Approximate expressions for the damping coefficients of waveguide modes are obtained, and damping associated with scattering is found to be proportional to the product of a root-mean-square amplitude of roughnesses by the correlation length. The effect of a considerable suppression of scattering near the absorption edges due to dispersion is predicted; this can also be observed from a decrease in the back-scattered beam intensity. The roughnesses not only reduce the radiation transmission by diffractive filters, but also adversely affect the selectivity of radiation filtering. The analytic expressions for the damping coefficients of waveguide modes make it possible to generalize the results to collimators with various properties of the surfaces.     

Coherent Transmission and Reflection by a monolayer of discrete scatterers

Coherent transmission and reflection of a plane wave through a monolayer of discrete particles are considered on the basis of simple and physically transparent formulae for the single scattering approximation (SSA) corrected by introducing a multiple scattering permittivity factor. This factor allows for multiple scattering of Waves between monolayer particles, opposite to the SSA. The multiple scattering permittivity factor is considered on the basis of the quasi-crystalline approximation (QCA) via ? matrix formalism. The multiple scattering permittivity factor and parameters for obtaining coherent transmission and reflection coefficients (the effective extinction coefficient and the transmission and reflection coefficients due to rescattering) are calculated within the scope of QCA and plotted for comparison with SSA results. The expressions for these values are simplified for small Rayleigh particles to simple analytical formulae.     

Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.