Peculiarities of Acoustic Wave Reflection from a Boundary or Layer of a Two-Phase Medium

A mathematical model is presented for determining the oblique incidence of an acoustic wave at both a boundary and layer of a gas–drop mixture or a bubbly liquid of finite thickness. The basic wave reflection and transmission patterns are established for the incidence of a low-frequency acoustic wave at an interface between a pure gas and a gas–drop mixture, as well as between a pure and bubbly liquid. A range of varying volume fractions for a drop is determined, for which the zero value of the reflection coefficient is possible for low frequencies at oblique incidence. It is shown that the reflection coefficient will never be zero at angles of incidence above 24.5° from a gas–drop mixture at a pure gas boundary; however, when a wave is incident from a pure gas at a gas–drop mixture boundary, a zero reflection coefficient is possible for nonzero angles of incidence and the volume fraction of inclusions. The results of calculating reflection of an acoustic wave from a two-phase layer of a medium with a finite thickness are presented. It is established that the minimum reflection coefficient is possible depending on the perturbation frequency for a certain range of angles of incidence for the boundary or the layer of the gas–drop mixture, which is governed mainly by difference in densities between it and the pure gas.     

Resonant reflection of Bose-Einstein condensate by a double delta-function barrier within the Gross-Pitaevskii equation

Resonant reflection of a Bose-Einstein condensate by a double delta-function barrier has been considered analytically using the Gross-Pitaevskii approximation for nonlinearity. The reflection coefficient has been derived taking into account a weak nonlinearity of the Schrödinger equation produced by the interaction between cold alkali atoms. Nonlinear term is given in the limit of asymptotically weak interaction and zero temperature. The one-dimensional potential is approximated by two repulsive delta-function barriers. The analytical solution was obtained for the reflection coefficient using a multiple-scale analysis in order to remove secular terms. The most interesting case corresponds to the condensate energies for which reflection is absent without nonlinear term. Thus, reflection is determined only by the nonlinearity. The reflection coefficient is derived in the first order on the nonlinearity parameter.     

Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

We study dynamical behaviors of a Bose-Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R_s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R_s~cos[λ(θ-π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitive width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.     

Reflection of a pulse by multiple-dielectric layers

The reflection of a pulse by multiple-dielectric layers is treated theoretically. The reflected wave is obtained by expanding the reflection coefficient of an elementary plane wave in a series, including the special case for which total reflection occurs. The pulsed waves reflected by two-dielectric slabs are considered in detail both analytically and numerically. The effect of a carrier frequency of a pulse-modulated carrier wave on the reflected wave form is also discussed.     

Analysis of a Microwave Reflection System for Breast Cancer Detection

A method is investigated for early detection of breast cancer through microwave reflection measurement of a bilayered biological tissue. The permittivity difference between the tumor and the normal breast tissue could be detected through microwave reflection measurement. The reflection characteristics of the tumor have been analyzed. Numerical results showed that the reflection coefficient is very sensitive to the tumors.     

Temperature elevation generated by a focused Gaussian ultrasonic beam at a tissue-bone interface

When a focused Gaussian ultrasonic beam in soft tissue normally impinges on the boundary of a contiguous bone, reflection and transmission occur. Taking account of the reflection, the steady-state temperature elevation along the beam axis for this case was calculated. The effect of perfusion is also included.     

Effective Reflection Area of a Cube Corner Retroreflector

The effective reflection area of a cube corner retroreflector is defined. It is testified for a cube corner retroreflector (CCR) that the ray reflected from a CCR is not parallel with the ray incident on the CCR undersurface. The effective reflection area of CCR is calculated when the ray incident on the CCR undersurface vertically, and the effective reflection area of a CCR is two thirds of the CCR undersurface.     

Electromagnetic-wave reflection from a nonlinear dielectric plate in a waveguide

The interaction of opposing TE-waves in a nonlinear cubical dielectric located in a waveguide of arbitrary cross-section is examined. It is shown that the propagation constants of the interacting waves are functions of the combination of the amplitudes of those waves. Wave reflection and refraction in a nonlinear plate are investigated. A formula for the reflection coefficient and a “trnasillumination” condition of the nonlinear plate are obtained.     

Effective Reflection Area of a Cube Corner Retroreflector

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Explicit results for wave scattering and transmission through a rough fluid-fluid interface

This paper describes an analysis of reflection and transmission of acoustic waves from an imperfectly reflecting, rough fluid-fluid interface within the Kirchhoff approximation. It presents the results of calculations of the coherent and diffuse field. This work is motivated by the fact that few explicit results of the characteristics of the scattered and transmitted wave field exist in the literature for this problem. For the problem of interest, the surface reflection coefficient depends at each point upon the local angle between the incident wave and the rough surface. For surfaces with statistically independent local surface position and gradient, coherent field calculations show that the correction to constant reflection coefficient analyses is simply a multiplicative factor that depends upon the statistical characteristics of the surface gradient, sound speed and density ratio across the surface. This multiplicative factor is interpreted as an average reflection or transmission coefficient, <R> and <T>, respectively. The principle differences between these results and constant reflection coefficient analyses occur when waves impinge upon regions with higher sound speeds, where total internal reflection may occur. While the wave characteristics of smooth or constant reflection coefficient surfaces change abruptly in the vicinity of the angle of total internal reflection, the average reflection coefficient exhibits a much smoother dependence upon angle of incidence or sound speed ratio for rough surfaces. It is also shown that the direction of maximum diffuse scattering moves relative to its value were the reflection coefficient constant.     

Influence of the adiabatic index on switching between different types of shock wave reflection in a steady supersonic gas flow

A comprehensive pattern of different types of shock wave reflection in a steady supersonic gas flow is analytically constructed with regard to a new wave configuration found by the authors-negative-angle irregular reflection. A double Mach reflection with a negative reflection angle in a steady supersonic gas flow is numerically obtained for the first time.     

Reflected image of a strongly focused spot

We describe the reflection of a strongly focused beam from an interface between two dielectric media. If the beam is incident from the optically denser medium, the image generated by the reflected light is strongly aberrated. This situation is encountered in high-resolution confocal microscopy and data sampling based on solid immersion lenses and oil immersion objectives. The origin of the observed aberrations lies in the nature of total internal reflection, for which there is a phase shift between incident and reflected waves. This phase shift displaces the apparent reflection point beyond the interface, similarly to the Goos-H?nchen shift.     

Reflection spectrum of a cholesteric liquid crystal with structural defects

An expression is obtained for the reflection coefficient of circularly polarized light normally incident on the film of a cholesteric liquid crystal with a variable helix pitch. It is shown that, in the case of a single defect (local change in the helix pitch), the spectrum of light reflection from a cholesteric acquires a dip corresponding to the defect mode. New qualitative features appear in the reflection spectrum of a cholesteric with two defects as the distance between them varies.     

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.     

Penetration of a symmetric light pulse through a wide quantum well

The reflection, transmission, and absorption of a symmetric electromagnetic pulse whose carrier frequency is close to the frequency of the interband transition in a quantum well are calculated. The energy levels in the quantum well are assumed to be discrete, and one excited level is taken into account. Consideration is given to the case of a sufficiently wide quantum well when the pulse wavelength corresponding to the carrier frequency is comparable to the quantum well width and when allowance should be made for the dependence of the matrix element of the interband transition on the photon wave vector. The calculations are performed with due regard for the difference between the refractive indices of the material of the quantum well and the barrier at an arbitrary ratio of the reciprocal radiative to nonradiative lifetimes of the excited level of the electronic system. It is demonstrated that the inclusion of the spatial dispersion and the difference in the refractive indices most strongly affects the reflection of the electromagnetic pulse, because the reflection due to interband transitions in the quantum well is accompanied by an additional reflection from the quantum well boundaries. Compared to the previously considered model, the most radical changes in the reflection are observed in the case when the reciprocal nonradiative lifetime of the excited state is substantially longer than the reciprocal radiative lifetime.     

Nonlinear Amplitude-Phase Effects in Selective Reflection from a Resonance Gas

Selective reflection of a laser wave from a resonance gas is considered for arbitrary intensity, polarization, and angle of incidence on the interface. Variations of the reflection spectra nonlinear in the wave amplitude are studied taking into account the nonlinear increment of the optical phase upon reflection. The result of this increment is a quadrature component of the reflected wave shifted by a quarter period, which may be observed using the homodyning technique (optical mixing). The regularities studied are of interest both for spectroscopy and for nonlinear transformations in the quantum statistics of reflected light.     

立方角锥棱镜的有效反射区

定义了立方角锥棱镜的有效反射区 ,证明了立方角锥棱镜底面角部区域 (即非有效反射区 )入射光与出射光不平行 ,并且在入射光垂直棱镜底面入射情况下计算得有效反射区的面积为底面的三分之二。     

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.     

Reflection of a spherical wave from a plane surface

A simple approach to the reflection of a spherical sound wave from a locally reacting plane surface is developed. The theory is based on a generalization of the method of images, and expresses the reflected wave as a series in terms of the reciprocal of distance from the image source. Although no general proof that this form for the reflected wave satisfies the surface boundary condition to all orders is available, it has been shown that the first five terms of this solution does satisfy the boundary condition, and agrees with the existing exact solutions for this type of reflection.