Propagating and evanescent waves associated with inhibited reflection in uniaxial crystals: Extraordinary incidence

Abstract

When an extraordinary wave under inhibited reflection conditions is incident on an interface between a uniaxial crystal and an isotropic medium, the reflected extraordinary wave is evanescent and the polarization of the refracted wave changes from linear to elliptical. In the present paper it is shown that the refracted ray undergoes a shift which is not only longitudinal (as the Goos—Hänchen effect in total reflection in isotropic interfaces) but also transversal. The structure of the evanescent reflected wave is studied and the polarization of the transmitted wave is analysed.     

Reflection of plane waves at the boundary of a pre-stressed elastic half-space subject to biaxial stretch and simple shear

This paper is concerned with the effect of finite pure homogeneous biaxial stretch together with simple shear deformation on the reflection from a plane boundary of elastic waves propagating in a half-space of incompressible isotropic elastic material. This generalizes the previous work in which, separately, pure homogeneous strain and simple shear were considered. For a special class of constitutive law, it is shown that an incident plane harmonic wave propagating in the considered plane gives rise to a surface wave in addition to a reflected wave for every angle of incidence. The amplitude of the surface wave may vanish at certain discrete angles depending on the state of stress, biaxial stretch and simple shear deformation and then specialized to recover results obtained previously. The amplitude of the reflected wave is independent of the pre-stress but does depend upon the magnitude of deformation under consideration. The dependence of the reflected and surface wave behavior on the angle of incidence, amount of shear strain, biaxial stretch and the state of stress is illustrated graphically.     

Reflection and Transmission of Plane Waves at the Planar Interface of a General Uniaxial Medium and Free Space

Abstract

A general uniaxial medium is characterized by its permittivity and permeability tensors having the same preferred axis. The plane wave reflection and transmission characteristics of a planar interface between free space and a general uniaxial medium have been obtained; since application as a polarizer is envisioned, the preferred axis lies in a plane parallel to the interface. Application of the Brewster law, as well as conditions for total reflection are explored.     

Reflection and transmission of ultrasound by a region of damaged material

Reflection and transmission of ultrasonic waves by a layer-like region of distributed microcracks in a bulk material has been investigated. It has been assumed that for sufficiently low frequencies and far away from the damaged layer, the reflected and transmitted waves are plane waves. By applying the Betti reciprocal theorem to a cell containingN cracks, and by choosing one elastodynamic state as the actual wave state and the other as a suitably chosen auxiliary wave state, the reflection and transmission coefficients have been expressed in terms of integrals over theN cracks. Simple expressions have been obtained for the case that all cracks are identical and parallel to each other. For the case that the cracks do not interact with each other, numerical results for the reflection and transmission coefficients are presented for a distribution of penny-shaped cracks. The variation of these coefficients with frequency, relative layer thickness and angle of incidence has been displayed in graphs.     

Reflection of a Beam of Finite Size from a Corrugated Waveguide

Abstract

The paper is concerned with the influence of the finite size of an incident beam upon both the anomalous-reflection spectrum and the shape of the energy distribution in a reflected beam. It is proved experimentally that the use of corrugated waveguides as a laser-resonator selective mirror improves the spatial coherence of radiation.     

Reflection of a weak shock wave from a perforated plug

Summary A plane shock wave is assumed to be incident upon a solid surface that is perforated by a number of closely spaced holes of length L and radius a, where a/L1, and the problem is to determine the character of the reflected wave field. The latter is essentially determined when the rate of inflow from the ambient atmosphere to the perforated plug is known, and the majority of the effort in this paper is devoted to the evaluation of this quantity. The assumption that the incident wave is weak is made throughout. Results show how the reflected wave field depends upon L and a and upon the acoustic-impedance ratio of the ambient air and the air within the slender tubes; the latter may be influenced by the distensibility of the tubes, although this matter is not pursued here. It is theoretically possible for reflected-shock strengths to exceed the solid-wall value for short intervals of time. Qualitative comparisons of the present theory with some existing observations of rather strong-shock reflection from perforated plugs lend support to the predictions, especially in the situation for which viscous effects are slight.     

Angular Momentum Balance on Light Reflection

Abstract

It was pointed out by Holbourn in 1936 that there is an apparent breakdown of angular momentum conservation on reflection of circularly polarized light at the plane interface between two lossless dielectrics. The analysis presented in this paper shows that this discrepancy does not arise provided that: (a) the intensities of the incident, reflected, and transmitted beams vanish at large distances from their axes, and (b) the angular momentum of each beam is calculated from first principles.     

Resonant Excitation of Surface Electromagnetic Waves: An Analogy between Metallic Films and Gratings

Abstract

We show that near the resonant excitation of surface electromagnetic waves the amplitude of the reflected wave in a metallic film admits formally the same approximation as applies for gratings. Using this approximation it is easy to show that the phase exhibits different behaviour when the film thickness is above or below the critical value corresponding to the absorption of the reflected wave.     

Optics for Neutral Atomic Beams: Reflection and Diffraction of Sodium Atoms by Evanescent Laser Light Fields

Abstract

Realization of the analogues of optical components for the manipulation of atomic de Broglie waves has recently become possible through the use of laser-based techniques. The strong fields generated by laser light have already been used to reflect atoms using travelling evanescent waves, and to diffract atomic beams through small angles using transmission gratings formed by a standing laser light wave in vacuo. Present experiments aim to combine these techniques to produce a reflection diffraction grating formed by a standing evanescent laser-light field, and to exploit the larger diffraction angles made possible theoretically by such a scheme.     

Reflection/transmission Measurements of Anisotropic Films with One of the Principal Axes in the Direction of Columnar Growth

Abstract

In depositing crystalline thin films, anisotropy may be induced by the texture structure of the film. Generally one of the principal axes of this anisotropy is in the direction of columnar growth, which may be neither normal nor parallel to the film surface. In this paper we have developed a general method for characterizing thin films with this kind of anisotropy. Propagation of plane waves in media with the above mentioned crystalline structure has been studied. The reflectance and transmittance of a plane wave from the films with the structure-induced anisotropy have been calculated. By comparing calculations with measurements, we could determine optical properties and thicknesses of the films with the columnar-structure-induced anisotropy.     

Reflection of an electromagnetic wave by a layered superconductor-dielectric structure

An analysis is made of the propagation of an electromagnetic wave through an infinite periodic superconductor-dielectric structure consisting of alternating layers of dielectric and thin layers of type II superconductor. The presence of thin layers of superconductor is taken into account by introducing a suitable boundary condition. It is observed that the reflection coefficient depends abruptly on the angle of incidence of the wave, the thickness of the superconducting film, and the external magnetic field. Pis’ma Zh. Tekh. Fiz. 24, 9–12 (January 12, 1998)     

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.     

Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media

The paper analyzes the reflection and refraction of a plane wave incidence obliquely at the interface between piezoelectric and piezomagnetic media. The materials are assumed to be transversely isotropic. Numerical calculations are performed for BaTiO₃/CoFe₂O₄ material combination. Four cases, incidence of the coupled quasi-pressure (QP) and quasi-shear vertical (QSV) wave from BaTiO₃ or CoFe₂O₄ media, are discussed. The reflection and transmission coefficients and energy coefficients varying with the incident angle are examined. Calculated results are verified by considering the energy conservation. Results show that the reflected and transmitted wave fields in the sagittal plane consist of six kinds of waves, i.e. the coupled QP and QSV waves, evanescent electroacoustic (EA) and magnetic potential (MP) waves in the piezoelectric medium (BaTiO₃), evanescent magnetoacoustic (MA) and electric potential (EP) waves in the piezomagnetic medium (CoFe₂O₄), among which the EA, MA, MP and EP waves propagate along the interface. The most amount of the incident energy goes with the waves that are the same type as the incident wave, while the energy arising from wave mode conversion occupies a less part of the incident energy. The electric energy in BaTiO₃ is higher than the magnetic energy in CoFe₂O₄; they both attain their maximum values at/before the critical angle. Critical angles have little effect on evanescent waves except when the total reflection takes place. These results would provide useful complementary information for magnetoelectric composite materials.     

Reflection and refraction of light at saturating active boundaries

Abstract

This study deals with the topic of reflection and refraction of light from the boundary of a high-gain saturating laser amplifier. Expressions for the electric field and intensity reflection and transmission coefficients are obtained for the case of a wave in a uniform dielectric that is incident normally on a nonlinear saturating active medium. Bistability effects are predicted even for the simplest case of zero frequency detuning from the line centre of the saturating transition.     

Peculiarities of reflected shock wave bifurcation on a needle

The axisymmetric bifurcation of a reflected shock wave interacting with the boundary layer on a 79-mm-long needle with a diameter of 1.1 mm has been studied. The needle, oriented in counterflow direction, was mounted at the axis on the end wall of a shock tube with 98 × 98-mm section. Experimental data on the parameters of reflected shock wave bifurcation are presented for CO₂ at an initial pressure of 4 kPa and Mach number M = 2.5 of the incident shock wave. The obtained data are compared to experimental parameters of the reflected shock wave bifurcation on side walls of the shock tube. Experimental data were obtained by schlieren imaging of flow patterns and high-speed photography with a DICAM-Pro camera in the double-frame recording mode.     

Conversion of the polarization of an electromagnetic wave under cyclotron resonance in a two-dimensional electron system

A theoretical analysis is made of the conversion of the polarization of an electromagnetic wave when cyclotron resonance is excited in a two-dimensional electron system. It is shown that the greatest conversion of the polarization can be achieved in the reflected wave. At high electron concentrations the effect remains very appreciable even in the presence of electron scattering. In this case, the wave polarization conversion effect can be used to obtain information on electron relaxation in a two-dimensional system. Pis’ma Zh. Tekh. Fiz. 25, 21–26 (November 12, 1999)     

光纤布拉格传感器兰姆波检测的反射谱分析

传统的兰姆波多采用压电陶瓷换能器激发和接收。建立了新的超声兰姆波无损检测系统,其基本思想是采用布拉格光纤传感器作为兰姆波的接收器。光纤光栅传感的基本原理是通过检测光栅反射的中心波长移动实现对外界参量如超声的测量。超声作用下光纤光栅的反射谱发生变化,对超声作用下光纤光栅的反射谱变化进行了数值分析,结果表明,超声对光栅反射谱的影响与超声波长与光栅长度的比值是高度相关的。只有当这个比值相当大时,反射谱的形状才不会变化而中心波长发生偏移,此时光纤传感器可用来探测兰姆波。这个结论为利用新的兰姆波无损检测系统在布拉格光栅长度的设计和兰姆波波长的选择方面提供了有用的工具。     

Reflection and transmission of nonlinear waves from arterial branching

In this work, treating the arteries as a prestressed thin walled elastic tube and the blood as an inviscid fluid, we have studied the reflection and transmission of nonlinear waves from arterial branching, through the use of reductive perturbation method. The reflected and the transmitted waves at the bifurcation point are calculated in terms of the incident wave. The numerical results indicate that the reflected wave is comparatively small whereas the transmitted waves in branches are comparable with the incident wave. This result is quite consistent with the experimental measurements [N. Sergiopulos, M. Spiridon, F. Pythoud, J.J. Meister, On wave transmission and reflection properties of stenosis, J. Biomech. 26 (1996) 31-38].     

有限声束在固体板表面的声反射

采用将有限声束分解为一系列平面波的方法，对有限声束在液体－固体板－液体结构中的声反射问题进行了分析和计算。当有限声束以平面波反射系数相位为１８０°时的入射角入射时，在固体板表面反射的声束沿板表面存在显著的移动和展宽现象。本文的有关结果，对进一步研究有限声束在板状结构表面的声反射具有积极意义。     

平面S波在非饱和土自由边界上的反射问题研究

运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性,分析了平面S波在非饱和土层自由边界上的反射问题。根据边界条件,分别导出了在非饱和土自由边界上的四种反射波：反射P1波、反射P2波、反射P3波及反射S波的振幅反射率及能量反射率的理论表达式,并在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射率及能量反射率受平面S波入射角度及土层饱和度变化的影响情况。计算结果表明：各反射波的振幅反射率及能量反射率不仅与入射角有关,也受到饱和度变化的影响,这些结论对土动力学的理论研究以及相关工程地震勘探具有一定指导意义。