Retrieval of the complex reflection coefficient from nano scale thin films by using polarized neutrons and magnetic substrates

A method is proposed for overcoming the famous ‘phase problem’ in neutron specular reflectometry. It is shown that the complex reflection coefficient of any unknown non magnetic layer, with real scattering length density, can be determined by using a magnetic transmitted media and by measuring the polarization of the reflected beam relative to the incident beam. The method follows directly from a recent one which is limited to a one-dimensional neutron polarization. Here, the theory is generalized for a neutron polarization of arbitrary direction. We show that some combinations between the polarization of the incident and reflected beam must be used to determine the reflection coefficient. Also, it is shown that instead of full polarization or reflectivity analysis, some combinations between polarization and reflectivity can be used in the analysis process. The method is supplemented with a schematic example to test the method and its stability in the presence of experimental uncertainties and roughness of the interfaces. PACS 61.12.Ha; 28.20.-v     

涡旋光束在反射中的正交偏振特性研究

本文从角谱理论出发建立了涡旋光束在空气-玻璃界面反射时的傍轴传输模型, 并研究了反射过程中诱导产生的正交偏振效应. 当一水平偏振涡旋光束以不同角度入射时, 反射光束的正交偏振分量呈现出类似于一阶厄米-高斯模式的双峰强度分布, 而水平偏振分量强度分布呈现与入射光束相似的分布, 且只在布儒斯特角附近入射时才现出与正交偏振分量垂直的双峰分布. 对于任意线偏振入射光, 其正交偏振分量的偏振方向不再垂直于入射时的偏振方向, 而是与反射光束的中心波矢垂直, 此时正交偏振分量出现有趣的旋转特性, 其物理原因归结于任意线偏振光入射时所对应的水平与垂直偏振分量的反射系数不同. 最后进行了相关实验验证, 发现实验结果与理论分析符合得较好. 关键词： 正交偏振 涡旋光束 任意线偏振     

Positively and negatively large Goos–Hänchen lateral displacements from a symmetric gyrotropic slab

A detailed study on the lateral displacements of a transverse magnetic (TM) wave transmitted and reflected from a symmetric gyrotropic slab is presented. We give the analytic formulas for the transmission coefficient and the reflection coefficient, as well as the corresponding lateral displacements. It is found that due to the external magnetic field the displacement of a transmitted beam is different from that of reflected one, even for a lossless symmetric configuration. Furthermore, within the chosen frequency band, when the incident angle is near the Brewster angle, the shift of a reflected wave can be large with nonzero reflectance, and can be positive or negative depending on the direction of the applied magnetic field and the incident wave.     

Reflection of neutrons from a magnetic film placed in static and oscillating magnetic fields

Measurements of polarized-neutron reflection from magnetic films placed in a static magnetic field and in an oscillating magnetic field perpendicular to it are described. The process of diffuse neutron scattering involving energy transfer from a RF electromagnetic field to neutrons has been studied. Neutron magnetic resonance has been detected, and splitting of the polarized beam of neutrons reflected from a film has been discovered.     

On the Application of Zeeman Spatial Beam Splitting in Polarized Neutron Reflectometry

Zeeman spatial neutron beam splitting is considered upon reflection from a homogeneous magnetic film placed in an external magnetic field applied at an angle to the surface of a sample. Two ways of applying the Zeeman beam-splitting phenomenon in polarized neutron reflectometry are discussed. One of them is the construction of polarizing devices with a high polarization efficiency. The other is investigations of magnetically noncollinear films at a low spin-flip probability of reflected neutrons. The experimental results are presented for illustration.     

转换反射中光自旋霍尔效应的自旋堆积方向

从理论上和实验上研究了转换反射中光自旋霍尔效应的自旋堆积方向的方法,建立了描述光束在空气-棱镜界面反射的自旋堆积模型,揭示了横移与光束入射偏振角的定性关系。研究发现,当入射角小于布儒斯特角时,随着入射偏振角的逐渐增大,自旋堆积的方向发生反转。而当入射角大于布儒斯特角时,自旋堆积的方向不再随入射偏振角的变化而反转。结果表明,在光束入射角为确定值且小于布儒斯特角的情况下,可以通过调控光束的入射偏振角转换自旋堆积的方向。转换自旋堆积方向的研究为有效调控光自旋霍尔效应提供了新的途径。     

反射光偏振特性分析与物体形状的测量

基于反射光偏振特性,提出了利用图像处理技术测量透明物体三维形状的理论和方法.分析了物体表面反射光的偏振特性,表明自然光在经透明物体表面反射后,反射率随光的振动方向不同而不同,即反射光表现出部分偏振光的特性.研究了强度反射率与入射角以及光强与偏振片方向之间的函数关系,得到了光强大小与入射面方向的关系;根据偏振度概念并结合菲涅耳公式和折射定律,建立了偏振度和入射角之间的表达式,可求得物体表面法线方向,进而得到透明物体的形状.研制了光学实验平台,获得了物体反射光的偏振图像,经过图像处理,获得了被测物体的三维形状.实验结果表明,这种方法对透明物体形状测量是有效和实用的.     

固-固界面退化特性的超声反射评价方法

提出了一种基于有限宽超声束反射的固-固界面退化特性评价方法,从理论和数值仿真角度进行了分析和计算。将两固体界面间的薄层简化为界面弹簧模型,以界面法向和切向劲度系数表征界面的退化程度。通过数值计算求得有限宽超声纵波束在不同入射角和界面不同退化程度下的反射横波、反射纵波的镜面反射系数。进一步地,通过建立二维有限元模型,仿真研究了有限宽超声纵波束在给定入射角及界面不同退化程度下镜面反射系数的变化规律。结果表明,反射纵波和反射横波的镜面反射系数随有限宽超声纵波束的入射角及界面劲度系数的改变而变化,且存在镜面反射系数随界面劲度系数单调且敏感变化的入射角,据此可准确评价界面的退化程度。     

Applying the phase difference property of polarization angle for measuring the concentration of solutions

This paper proposes a simple method for measuring the concentration of solutions based on the phase difference of internal reflection polarization angle and circularly polarized heterodyne interferometry. For a circularly polarized heterodyne light beam incident on the boundary surface between a hemispherical prism and a test solution, the reflected light passes through a properly oriented analyzer for interference. The phase difference between s- and p-polarized light is sensitive to the solution concentration when the incident angle equals the internal reflection polarization angle. Based on these effects, the resulting phase difference makes it possible to analyze the concentration of solution through heterodyne interferometry. The experiments in this study confirm the feasibility of this method, which provides the advantages of simple installation, ease of operation, and high accuracy.     

Larmor labeling development

The first applications of polarized neutrons were to distinguish magnetic from nuclear scattering amplitudes. Much later the first set-ups for measuring the precession phase of the polarization passing a magnetic field were realized. This phase, determined by the field strength and interaction time, could label magnetic fields, wavelength of the neutrons and length over which the field is present. The latter could be used by proper shaping of the magnetic field to label also the direction of transmitted neutrons. The advantage of this labeling is that high precision measurements are possible without strong confinement of the beam by diaphragms. An overview of the use of Larmor labeling of polarized neutrons is given for applications in magnetism, in inelastic neutron scattering and small angle scattering.     

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.     

On polarized neutron scattering from magnetized samples and the spin echo effect

The scattering of polarized neutrons from magnetized samples is considered in the general case of arbitrary orientation between the incident polarization, the magnetic field of the sample and the polarization of the scattered neutrons. Including both nuclear and magnetic scattering the general expressions for the cross section and the polarization of the scattered beam are derived in the case of small-angle scattering. It is shown that under certain experimental conditions an effect analogous to the Neutron Spin Echo should be observed, which could be used to measure small energy transfers. The contribution arising from the scattering by spin waves is examined in detail.     

Unified theory of total reflection phenomena at a dielectric interface

By utilizing a rigorous plane-wave representation, we investigate the basic wave mechanism that is responsible for both the lateral (Goos-H?nchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium, and the weak radiance that accompanies the reflected beam. We thus find that the complete reflected field contains a geometric-optics component, whose domain is given by the mirror reflection of the incident beam, as well as a lateral-wave component which occupies a much larger domain. Our results show that the near field of the lateral-wave component interferes with the geometric-optics component and thereby produces the Goos-H?nchen shift of the reflected beam. The intermediate and far fields of the lateral-wave, on the other hand, are responsible for the weak radiance that trails the reflected beam. By demonstrating that both the beam shift and the trailing radiance represent two facets of the same wave process, the lateral-wave field is shown to provide a unified interpretation of two effects that have previously been regarded as separate phenomena. The dependence of these effects on beam width, angle of incidence, and polarization are also considered. Portions of this paper were presented orally at the Fall 1971 Meeting of the Optical Society of America, Ottawa, Canada; October 1971.     

电磁波在大面积等离子体片中传播特性的分析

脉冲磁约束线形空心阴极放电形成的大面积等离子体片可应用于等离子体天线、隐身及模拟超音速飞行器表面的等离子体鞘套. 本文首次利用实测等离子体片电子密度时空分布和横向场传播矩阵法, 研究了电磁波在等离子体片中反射率、透射率、吸收率随频率及脉冲放电时间的变化特征. 结果表明: 极化方向平行磁场的电磁波, 在小于截止频率的低频带内具有较高的反射率和吸收率, 增大电流, 反射率增加, 吸收率下降, 在大于截止频率的高频带内反射率和吸收率较低, 增大电流, 透射率下降, 吸收率升高; 极化方向垂直磁场的电磁波在高混杂谐振频率附近存在吸收率明显增强的吸收带, 谐振吸收峰值与放电电流无关; 脉冲放电期间, 电磁波的反射率、透射率与吸收率由不稳定过渡到稳定的时间约为100 μs, 过渡时间随着放电电流的增加而增大, 极化方向垂直磁场、小于截止频率的电磁波在稳定放电阶段谐振吸收较强. 本文的研究成果对利用等离子体片实现对电磁波的稳定高反射作用具有重要意义.     

Detection of nano scale thin films with polarized neutron reflectometry at the presence of smooth and rough interfaces

By knowing the phase and modules of the reflection coefficient in neutron reflectometry problems, a unique result for the scattering length density (SLD) of a thin film can be determined which will lead to the exact determination of type and thickness of the film. In the past decade, several methods have been worked out to resolve the phase problem such as dwell time method, reference layer method and variation of surroundings, among which the reference method and variation of surroundings by using a magnetic substrate and polarized neutrons is of the most applicability. All of these methods are based on the solution of Schrödinger equation for a discontinuous and step-like potential at each interface. As in a real sample there is some smearing and roughness at the boundaries, and consideration of smoothness and roughness of interfaces would affect the final output result. In this paper, we have investigated the effects of the smoothness of interfaces on the determination of the phase of reflection as well as the retrieval process of the SLD, by using a smooth varying function (Eckart potential). The effects of the roughness of interfaces on the same parameters have also been investigated by random variation of the interface around its mean position.     

Effect of size quantization of the reflection coefficient of an electron beam incident on a thin heteroepitaxial film

The effect of size quantization of the reflection coefficient of electrons incident on a thin single-crystal film located on a substrate has been theoretically predicted. Two methods for observing this effect experimentally are proposed. In the first method, the variation in the intensity of the beam of specularly reflected electrons can be measured by varying the small glancing angle α of the electron beam with a particle energy on the order of 10 keV. In the second method, intensity oscillations of the diffracted beam as a function of the variation in the reflection angle β are measured in the case of a small fixed glancing angle α (on the order of 1°–3°). Thus, the second variant corresponds to studying the intensity distribution along streaks (reflexes) in the case of electron diffraction on a smooth surface. In the second case, the appearance of elastically scattered electrons along the streaks between diffraction reflexes is predicted. Their number (the beam intensity) varies periodically as a function of the angle β.     

A reflective surface-relief two-layer grating for splitting beams with the polarization-selective property

A polarization-selective beam splitter is presented based on a reflective surface-relief two-layer grating with a metal slab. The grating is composed of two dielectric layers and a metal slab on the substrate. For TE polarization, efficiencies of 97.58% can be diffracted into the reflective −1st order. For TM polarization, two-port output of 47.55% and 47.11% can be split into the 0th order and the −1st order, respectively. Such a polarization-selective beam splitter can be fulfilled by one grating in reflection. The grating depths of two layers are optimized by using rigorous coupled-wave analysis with the given duty cycle of 0.6 and period of 1100 nm. The performance for different incident conditions is investigated when the incident wavelength and angle deviate from the central wavelength and the Bragg angle, respectively. For TM polarization, good uniformity can still be achieved within the given incident wavelength and angle regions. For TE polarization, the reflective polarization-selective beam splitter can have merits of wideband for different incident wavelengths.     

光波p分量在单轴晶体表面反射和折射的相位特性

根据单轴晶体的双折射和双反射性质,通过数值计算研究了光轴在入射面内并与晶体界面成任意角时光波p分量在单轴晶体表面反射和折射的相位特性.结果表明,光轴取向对相位变化有较大影响,光从光疏各向同性介质射入单轴晶体时,光轴方向改变反射光p分量的相位突变点,但对折射光p分量相位无影响.光从光密各向同性介质射入单轴晶体未发生全反射时,光轴方向同时影响p分量反射光和折射光的相位突变|发生全反射后,光轴方向影响反射光p分量的相位变化曲线.从单轴晶体出射到光疏各向同性介质未发生全反射时,光轴方向改变反射光p分量的相位跃变规律,折射光p分量在光轴方向和晶面成小角度时在布儒斯特角附近发生相位突变|发生全反射后,反射光p分量的相位变化曲线随光轴方向的改变发生较大变化.     

任意偏振态光束全反射时的侧向和横向位移

光束在电介质界面发生全反射时,实际反射光束会在入射面内相对于几何反射光束产生一侧向位移,在垂直于入射面的方向产生一横向位移。利用改进的能流法研究了任意偏振态光束发生全反射时的侧向和横向位移特性。研究表明,侧向位移的大小与入射光束的两组成部分———TE和TM偏振光的相位差无关,而与两组分的光强比密切相关,且该位移可以表示为TE和TM偏振光束各自的位移按光强的加权平均。横向位移的大小不仅与入射光束两组分的光强比相关,还与组分的相位差密切相关。另外,反射光束不仅在椭圆偏振态入射的情况下会产生横向位移,而且在TE和TM偏振态之外的其他线偏振态入射时,也会产生横向位移。