On the theory of X-ray coherent reflection from a rough surface

A solution of the problem of X-ray specular reflection from a statistically rough surface is presented. It is based on using the Green function formalism. The Kirchhoff formula is used to describe the transmission of the wave field through a rough interface. Generally, microscopically exact expressions for the coefficients of transmission through a rough surface and reflection from it are obtained by taking multiple scattering effects into account. Averaging of the obtained expressions over possible realizations of random roughness of the interface between media allows to obtain rigorous expressions for specular reflection and transmission coefficients. The behavior of exact solutions in the limiting case of infinite correlation lengths is studied. It is shown that, in this case, the obtained solution corresponds to the Debye-Waller normalization. Expressions for the reflection and transmission coefficients making it possible to carry out numerical calculations are obtained in the Bourret approximation of multiple-scattering theory.     

一维Hulthén势场中Klein-Gordon粒子的透射共振

用Heaviside函数构造出一维对称的Hulthén势垒,求解了其满足的Klein-Gordon方程. 散射态的精确解可以由超几何函数表示, 透射系数T和反射系数R能由Klein-Gordon 方程满足的边界条件得到.并由流密度守恒推导出低动量粒子发生透射共振的条件. 关键词： Klein-Gordon方程 Hulthén势垒 散射态 透射共振     

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.     

Coherent transmission and reflection of a two-dimensional planar photonic crystal

A method for modeling the radial distribution function for particles of a two-dimensional planar photonic crystal in the form of a monolayer of spatially ordered monodisperse spherical particles is proposed. The coherent transmission and reflection coefficients for layers under normal illumination are calculated in the quasi-crystalline approximation of the multiple wave scattering theory. The dependence of the coherent transmission and reflection of the layer on the degree of ordering of the spherical particles is investigated. The influence of the long-range order on the coherent transmission and reflection coefficients for layers with triangular, square, and hexagonal lattices is estimated. Monolayers of weakly absorbing dielectric and strongly absorbing metallic particles are considered.     

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.     

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.     

利用共振无源腔分析和抑制飞秒脉冲激光噪声的理论和实验研究

理论分析了共振无源腔对飞秒脉冲激光的强度和相位噪声的转化模型,分析表明,通过测量无源腔透射场或者反射场相对于输入场强度噪声的变化,可以间接得到输入场飞秒脉冲激光的相位噪声.在此基础上设计了精细度约为1500、自由光谱区为75 MHz的八镜环形共振无源腔,并测量了钛宝石锁模激光经过该共振无源腔后透射场和反射场强度噪声的变化.实验观察到,飞秒脉冲激光经过无源腔透射后,强度噪声特性得到较好改善,在探测频率2 MHz附近达到散粒噪声极限.同时,结合共振无源腔对激光强度和相位噪声的转化模型,间接给出了钛宝石锁模激光的相位噪声及无源腔对相位噪声的有效抑制作用.     

Normal modes of a poroelastic plate and their relation to the reflection and transmission coefficients

A poroelastic plate that obeys the Biot theory is considered. Compact new forms of its reflection and transmission coefficients, similar to those of the resonance scattering theory for an elastic plate, are derived. A numerical comparison of the reflection coefficient modulus with the plate normal modes, at low frequency, shows that a study of the reflection or transmission coefficient does not provide the same kind of information on the poroelastic plate than an investigation of guided leaky waves propagation.     

Single-Photon Scattering Grating in a Waveguide-Cavity System

We investigate single-photon scattering grating in a one-dimensional waveguide coupled to a cavity embedded with a driven Λ-type three-level atom. The single-photon reflection amplitude and transmission amplitude in the waveguide are obtained via a real-space approach, respectively. By spatially modulating a classical control field to drive the three-level emitter, alternating regions of high reflection and absorption as well as high transmission and absorption of the single photon are generated in both directions of the waveguide, which acts as a kind of scattering grating. The proposed scheme may have the potential for the design of chip-integrated grating.     

Reflection and transmission of SH-waves at a corrugated interface between two semi-infinite anisotropic magnetoelastic half-spaces

An analysis has been carried out for reflection and transmission of a plane SH-wave incident at a corrugated interface between two anisotropic magnetoelastic half-spaces. Rayleigh’s method of approximation is applied to derive the reflection and transmission coefficients for first order approximation of corrugation. The expressions for reflection and transmission coefficients for first order approximation of corrugation are obtained in closed form for a special type of interface. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of magnetoelastic properties of materials of the half-spaces as well as the angle of incidence. Special cases are deduced for anisotropic and isotropic materials for particular case of corrugation. Numerical computations are performed for a specific model of two different anisotropic magnetoelastic media. The effects of anisotropic magnetoelastic coupling parameter, the angle at which wave crosses the magnetic field, frequency factor, wave length of corrugation, and the amplitude of corrugation are shown through figures.     

Analysis of Electromagnetic Waves Scattering by a Finite Size Dielectric and Metal Cylinder in a Rectangular Waveguide

The paper presents a rigorous solution of the scattering problem by a circular dielectric and perfectly conducting cylinders of any radius and any height in the rectangular waveguide oriented perpendicularly to a wall. The method is based on the representation of fields in waveguide and dielectric medium by cylindrical eigenfunctions and application of boundary conditions on surfaces of the cylinder to evaluate the fields inside and outside the cylinder. The reflection and transmission coefficients are expressed through the fields. As an example the reflection and transmission coefficients versus frequency for various dielectric and metallic cylinders are computed. The comparison of numerical with experimental data is presented.     

Reflection of neutrons from a helical system

Analytical expressions have been derived for the reflection and transmission of neutrons from magnetic mirrors with helical magnetization. The reflection curves with and without neutron spin flip are presented. The resonance properties of helical systems have been analyzed.     

Transformation of optical radiation by fast-moving smooth inhomogeneities of a medium

For the problem of the reflection and transmission of monochromatic radiation by a moving smooth inhomogeneity of parameters of a motionless transparent medium, transport equations are derived and an approximate solution to these equations is obtained for the case of weak reflection. Estimates of the effects for quartz in the transparency region are given.     

Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure

We study the fundamental problem of reflection and refraction of a surface polariton as it strikes the interface between two waveguide structures. By making the two waveguide structures match to each other, coupling of surface polaritons to radiating modes is cancelled, and the reflected and transmitted waves consist of only surface modes. The reflection and transmission coefficients are calculated, and negative refraction of surface polaritons is demonstrated. Finite-difference time-domain numerical simulations are also performed to verify the analytical results. As one of the applications of the matched waveguide structure, a square corner reflector for phase-retardation-free reflection of surface polaritons is proposed.     

Plasmons and polaritons in a semi-infinite plasma and a plasma slab

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory behaviour in the transient regime near the surfaces. The propagation of an electromagnetic wave in these plasmas is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved and the reflected and refracted waves are computed, as well as the reflection coefficient. For the slab we compute also the transmitted wave and the transmission coefficient. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient for a semi-infinite plasma exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection). Similarly, apart from characteristic oscillations, the reflection and transmission coefficients for a plasma slab exhibit an appreciable enhancement in the damped regime.     

Analysis of the scattering properties of a nanometric insertion in a film on a substrate

The scattering characteristics of an insertion in a gold film deposited on a glass prism are analyzed using the method of discrete sources. The effect of extreme energy transmission through the film is revealed in the range of total internal reflection.     

基于传输线模型的高阻表面反射相位分析

采用传输线模型对高阻表面表面阻抗进行建模,准确计算垂直入射条件下高阻表面的反射相位.在垂直入射条件下,过孔的影响可以忽略,将高阻表面等效为具有容性的贴片阵与具有感性的介质层的并联,利用传输线原理求得高阻表面的反射系数,再得到其反射相位.计算了不同参数的高阻表面反射相位,传输线模型计算反射相位与数值方法计算结果符合较好.制作了不同参数的高阻表面并测量其反射相位,实验结果表明传输线模型计算反射相位结果与测量结果基本符合,证明了传输线模型的正确性. 关键词： 高阻表面 反射相位 传输线模型     

Acoustic characteristics of a multichannel long line of the flexural type

The properties of an acoustic object represented by a multichannel long line of the flexural type are considered. Analytical formulas are obtained for the basic acoustic characteristics of a multichannel long line with an arbitrary number of flexurally oscillating single lines constituting it: the input impedance, the resonance frequencies, and the reflection and transmission coefficients are determined for an insulating multichannel long line, including the case of a cascade connection. Numerical calculations are performed and the plots are presented for the frequency dependences of the reflection and transmission coefficients for various parameters of the constituting lines. It is demonstrated that the acoustic characteristics of insulating multichannel long lines have certain advantages in comparison with the characteristics of similar objects based on single lines.     

Surface Tamm states in a photonic crystal slab with asymmetric termination

The reflection and transmission spectra of a finite thickness 2D photonic crystal slab (PCS) based on macroporous silicon are investigated. Periodic photonic crystal region is separated from air by homogeneous silicon interfacial layers. These interfacial layers at the silicon/air boundary being defects of the photonic crystal lattice, define the properties of surface Tamm states in the photonic stop‐bands (PSBs). It is demonstrated experimentally and theoretically that the reflection spectra of a structure with different thicknesses of the interfacial layers on both sides of the PCS depend on the illuminated side. At the same time, the transmission spectra are identical for both light directions in agreement with the reciprocity principle. Analysis shows that the dependence of the reflection spectrum on the side of light entrance is due to scattering losses in the real structure. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Acoustical characteristics of a multichannel transmission line

The properties of an acoustic system called by the author ”a multichannel transmission line” (MTL) are considered. Analytical expressions are derived for the following main acoustical characteristics of an MTL consisting of an arbitrary number N of single lines: the input impedance, the resonance frequencies, the reflection and transmission factors for an MTL-insulator, and the reflection factor for an MTL-absorber. For these quantities, numerical calculations are performed, and their frequency dependences are presented for different parameters of the constituent lines in the cases N=2 and 3. It is shown that the acoustical characteristics of MTL-insulators and MTL-absorbers have considerable advantages over the characteristics of similar systems designed on the basis of single lines.