Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at free space–chiral interface

The scattering of electromagnetic plane wave from a perfect electric conducting strip of finite width is investigated in this study. The strip is placed at the planar interface of free space and chiral medium. The Kobayashi potential method is used to determine the scattering from the strip. The dual integral equations are acquired through the boundary conditions. These equations as well as the edge conditions are satisfied through the properties of Weber–Schafheitlin integrals and the Jacobi polynomials. The projection of the Jacobi polynomials is used to get the matrix equations which are solved numerically to determine the unknown coefficients. Monostatic and bistatic scattering widths are examined in the free space region of the geometry. The far-zone scattered fields are analyzed by changing the values of different parameters, i.e. chirality and incident angle.     

Scattering from topological insulator circular cylinder buried in a semi-infinite medium

The problem of electromagnetic scattering of a plane wave from a topological insulator (TI) cylinder buried beneath a flat interface is undertaken with the method of analysis based on spectral plane wave representation of fields. Saddle point method is employed to evaluate the involved spectral integrals serving as basis functions in the representations of scattered-reflected and scattered-transmitted fields. The distinctions between the scattering pattern for time reversal symmetry TI cylinder and that of time reversal symmetry broken TI cylinder are pronounced. Results are validated through the comparison with the previously available results.     

Scattering from a topological insulator cylinder buried below a slightly rough surface

Electromagnetic scattering from a topological insulator (TI) cylinder buried beneath a rough surface is considered. To account for the interactions of the scattered field and the rough surface, spectral plane wave representation of fields is used along with small perturbation method. Both time-reversal symmetry TI cylinder and time-reversal symmetry broken TI cylinder are considered to evaluate the scattered-transmitted field above the rough surface for different values of the periods of the rough surface and the size of the object. It is observed that co- and cross-polarized field components show a maximum before the time-reversal symmetry is broken. The co-polarized component remains almost constant while the cross-polarized component decreases for time-reversal symmetry broken case.     

Engineering Dirac electrons emergent on the surface of a topological insulator

Abstract

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid ³He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.     

Engineering Dirac electrons emergent on the surface of a topological insulator

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid ³He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.     

Diffraction of a plane wave by a perfectly electromagnetic conducting (PEMC) slot

Using the duality transformations introduced by Lindell and Sihvola, an analytic theory for the electromagnetic diffraction from a perfect electromagnetic conductor (PEMC) slot is developed. Transformations have been applied to the diffracted field of a plane wave from a perfect electric conductor (PEC) slot. The problem was solved by using the Sommerfeld Green’s function and Fresnel integral.     

A note on cylindrical wave diffraction by a perfectly conducting strip in a homogeneous bi-isotropic medium

The diffraction of an electromagnetic wave by a perfectly conducting finite strip in a homogeneous bi-isotropic medium is studied in an improved form. The problem is solved by using the Wiener–Hopf technique and Fourier transform. The scattered field in the far zone is determined by the method of steepest descent.     

Scattering of inhomogeneous plane waves by a truncated cylindrical cap

Scattered fields of the inhomogeneous plane waves from a truncated cylindrical cap are obtained. Also the uniform diffracted fields are performed in terms of the Fresnel functions. Reflected and diffracted fields are obtained by using the physical optics and the geometrical theory of diffraction methods, respectively. All the mentioned results are plotted numerically for various numerical parameters.     

Scattering of electromagnetic spherical waves by a buried spheroidal perfect conductor

We examine the electromagnetic scattering of spherical waves by a buried spheroidal perfect conductor. The proposed analysis is based on the integral equation formalism of the problem and focuses on the establishment of a multiparametric model describing analytically the scattering process under consideration. Both the theoretical and the numerical treatment are presented. The outcome of the analysis is the determination of the scattered field in the observation environment along with its multivariable on several physical and geometric parameters of the system.     

Scattering of inhomogeneous plane waves by a slit formed with impedance and perfectly electric conducting half planes

Scattering of an inhomogeneous plane wave with an arbitrary angle of incidence travelling through a slit made of perfectly electric conducting and impedance half planes is investigated. For the investigation of the scattering phenomena evaluation of the modified theory of physical optics integrals are evaluated asymptotically. An inhomogeneous plane wave is taken into consideration by assuming the incident angle of a homogeneous plane wave as a complex parameter. Uniform asymptotic results will be employed for the correct solution of an incoming inhomogeneous plane wave scattering problem. Asymptotic evaluation is carried out for the reflected and diffracted fields. Diffracted fields are uniformly expressed in terms of the Fresnel functions. To obtain correct plots of the diffracted fields, complex detour parameter decomposition method is applied. Obtained resultant fields are plotted numerically.     

Scattering of electromagnetic pulse from a moving and vibrating perfect plane using characteristic‐based algorithm

Abstract

One‐dimensional numerical simulation results of plane Gaussian electromagnetic pulses reflected from constantly moving and vibrating perfect conductors are provided in this paper. The computational data were obtained using the characteristic‐based algorithm with the aid of relativistic boundary conditions and characteristic variable boundary conditions. Since the perfect conductor can travel and vibrate simultaneously, the size of the grid cell immediately next to the boundary and the corresponding numerical time‐step are time‐dependent. The present numerical method has been shown to accurately handle such problems. In this paper both the reflected electric field intensities and the corresponding spectra are illustrated. The calculated Doppler shifts are found to have good agreement with the theoretical values.     

Scattering of a plane harmonic SH wave by a completely embedded corrugated scatterer

Anti‐plane‐strain model for steady‐state scattering of elastic waves by a rough inclusion or a cavity embedded in a half space is considered by using a direct boundary integral equation method. The roughness of the scatterer is assumed to be periodic with arbitrary amplitude and period. Detailed testing of the numerical results is presented. The motion along the half‐space surface is evaluated for different corrugations, frequencies and impedance contrast of the materials. The importance of the scatterer roughness upon the displacement field is clearly demonstrated. It was shown that larger corrugation amplitudes, shorter corrugation periods and higher frequencies may produce significant change in the displacement field when compared with the corresponding smooth scatterer result. This effect strongly depends upon the impedance contrast of the materials. Copyright © 2008 John Wiley & Sons, Ltd.     

Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surface on a perfect conductor

Scattering of s-polarized electromagnetic planes waves from a film, with a shallow random rough one-dimensional surface, bounded by vacuum and a perfect conductor is calculated. An integral equation that relates the amplitude of the scattered field to the incident wave is found by use of the Rayleigh hypothesis. The integral equation is solved numerically and by use of the perturbation theory, up to the fourth order in the surface profile function. In the angular dependence of the incoherent part of the differential reflection coefficient, the backscattering peak and two additional satellite peaks are observed, owing to two guided waves supported by the film. Analysis of the perturbation solution reveals that the background scattering exhibits minima and maxima as functions of the thickness. By studying the behavior of the scattering as a function of the absorption index of the film, it is shown that the amplitudes of the peaks are low when k ~ 10(-2) and high when k ~ 10(-4).     

带形域内圆柱形夹杂对SH型导波的散射

本文采用波函数展开法建立了带形域内圆形夹杂对稳态SH型导波散射的级数解答。该问题采用镜像法求解,利用圆柱形夹杂边界位移和应力的连续性条件,并借助内域型Graf加法公式将解答归结为一组无穷代数方程组的求解,截断该无穷代数方程组可求得该问题的数值结果。为了便于问题的分析,算例给出了带形域中最低阶对称波型的SH型导波入射时圆柱形夹杂周边的动应力分布情况。结果表明,带形域自由边界的存在以及夹杂的几何位置对动应力集中分布有较大的影响。     

Low-frequency scattering from perfectly conducting spheroidal bodies in a conductive medium with magnetic dipole excitation

Inductive electromagnetic means that are currently employed in the exploration of the Earth’s subsurface and embedded voluminous bodies often call for an intensive use, primary at the modeling stage and later on at the inversion stage, of analytically demanding tools of field calculation. Under the aim of modeling implementation, this contribution is concerned with some interesting aspects of the low-frequency interaction of arbitrarily orientated (i.e. three-dimensional) time-harmonic magnetic dipoles, with 3-D perfectly conducting spheroidal bodies embedded in an otherwise homogeneous conductive medium. For many practical applications involving buried obstacles such as Earth’s subsurface electromagnetic probing at low-frequency or any other physical cases (e.g. geoelectromagnetics), non-axisymmetric spheroidal geometry approximates sufficiently such kind of metallic shapes. On the other hand, our analytical approach deals with prolate spheroids, since the corresponding results for the oblate spheroidal geometry can be readily obtained through a simple transformation. The particular physical model concerns a solid impenetrable (metallic) body under a magnetic dipole excitation, where the scattering boundary value problem is attacked via rigorous low-frequency expansions for the incident, scattered and total electric and magnetic fields in terms of positive integral powers of (ik), that is (ik)ⁿ for n ? 0, where k stands for the complex wavenumber of the exterior medium. The purpose of the modeling is to contribute to a simple yet versatile tool to infer information on an unknown body from measurements of the three-component electric and magnetic fields nearby. Our goal is to obtain the most important terms of the low-frequency expansions of the electromagnetic fields, that is the static (for n = 0) and the dynamic (n = 1, 2, 3) terms. In particular, for n = 1 there are no incident fields and thus no scattered ones, while for n = 0 the Rayleigh electromagnetic expression is easily obtained in terms of infinite series. Emphasis is given on the calculation of the next two non-trivial terms (at n = 2 and at n = 3) of the aforementioned fields. Consequently, those are found in closed form from exact solutions of coupled (at n = 2, to the one at n = 0) or uncoupled (at n = 3) Laplace equations and they are given in compact fashion, as infinite series expansions for n = 2 or finite forms for n = 3. Nevertheless, the difficulty of the Poisson’s equation that has to be solved for n = 2 is presented, whereas our analytical approach demands the use of the well-known cut-off method in order to obtain an analytical closed solution. Finally, this research adds useful reference results to the already ample library of scattering by simple shapes using analytical methods.     

导波在多损伤板结构中的散射

对导波在含有单个损伤和两处损伤的板结构中时形成的散射波场进行了理论分析,利用附加Bessel理论推导了含两处损伤板的结构中任意一点处的叠加散射位移场。通过数值计算对比了含单损伤板和含两处损伤板以及两处损伤的相对位置变化时散射位移场在损伤周围的分布情况,得到的分析结果是进一步进行多损伤板结构健康监测的基础。     

An optimization approach for the localization of defects in an inhomogeneous medium from acoustic far-field measurements at a fixed frequency

We are interested in the localization of defects in non-homogeneous non-absorbing media, with far-field measurements, generated by plane waves. We present here a way to handle the inhomogeneous background problem by the means of a constrained optimization approach; in the lines of the inf criterion from the factorization method for constant backgrounds. We show that both cost function and constraints present a simple form that is easy to compute. They can thus be treated by many well-known optimization methods, and we numerically illustrate four of them.     

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

In this study, a theoretical method is applied to investigate the multiple scattering of thermal waves and temperature field resulting from a subsurface cylindrical inclusion in a semi-infinite functionally graded material (FGM). The adiabatic boundary condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally graded materials by modulated optical beams. The model includes the multiple scattering effects of the cylindrical thermal wave generated by the line heat source. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented. Numerical calculations illustrate the effect of subsurface inclusion on the temperature and phase change at the sample surface under different physical and geometrical parameters. It is found that the temperature above the conducting cylindrical inclusion decreases because of the existence of the inclusion. The effect of the inclusion on the temperature and phase change at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves, and the distance between the inclusion and the semi-infinite surface. Finally, the effect of the relaxation time of buried inclusion on the temperature and phase change at the surface is examined.     

Decoherence in grazing scattering of fast H and He atoms from a LiF(001) surface

The influence of decoherence on the diffraction during grazing scattering of fast hydrogen and helium atoms from a LiF(001) single crystal surface with projectile energies of some keV, is investigated by two-dimensional angular distributions for scattered projectiles in coincidence with their energy loss and emitted electrons from the target surface. For keV hydrogen atoms, we identify the excitations of electrons and excitons of the target surface as the dominant mechanisms for decoherence, whereas for keV helium atoms these contributions are negligibly small. The suppression of electronic excitations owing to the band gap of insulators plays an essential role for preserving quantum coherence and thus for the application of fast atom diffraction as a surface analytical tool.