Effects of wave propagation anisotropy on the wave focusing by negative refractive sonic crystal flat lenses

<正>In this study,wave propagation anisotropy in a triangular lattice crystal structure and its associated waveform shaping in a crystal structure are investigated theoretically.A directional variation in wave velocity inside a crystal structure is shown to cause bending wave envelcpes.The authors report that a triangular lattice sonic crystal possesses six numbers of a high symmetry direction,which leads to a wave convergence caused by wave velocity anisotropy inside the crystal.However,two of them are utilized mostly in wave focusing by an acoustic flat lens.Based on wave velocity anisotropy,the pseudo ideal imaging effect obtained in the second band of the flat lens is discussed.     

基于蜷曲空间结构的近零折射率声聚焦透镜

研究基于蜷曲空间结构的近零折射率声聚焦透镜.根据近零折射率材料的声波方向选择机理,采用蜷曲空间结构为基本单元进行排列,设计具有特定入射与出射界面的几何结构,对透射声波的出射方向进行调控,实现了平面声波与柱面声波的聚焦效应,并深入讨论了透镜内部刚性散射体对声聚焦性能的影响.在此基础上,改变近零折射率透镜的出射界面,可以精确调控声波阵面的形状与方向.该类型透镜具有单一的单元结构、高聚焦性能及高鲁棒性等优点.研究结果为设计新型近零折射率声聚焦透镜提供了理论指导与实验参考,同时也为研究声波阵面的调控提供了新思路.     

Scattering and Focusing Effect of Stepped Index Luneberg Lens

Focusing effect of the Luneberg lens for wide bandwidth is studied with emphasis on experiment. A model experiment was performed using a stepped index (six-layer) spherical lens. The total electric field amplitude along the propagation axis has the maximum value (focal point) on the surface of the lens. As the size parameter ka (k: wave number, a: radius of the sphere) is larger, the electric field amplitude at the focal point becomes larger. These results correspond with the power of convergence (focusing effect) by the Luneberg lens. The experimental values are in a good agreement with theoretical ones that are calculated using homogeneous multilayered approximate method. They are also in a good agreement with the results using exact solutions for the inhomogeneous dielectric sphere (the ideal Luneberg lens). Therefore, it is found that the six-layer spherical lens has the optimum variation of dielectric constants for the Luneberg lens and maintains focusing effect for wide bandwidth.     

Pink‐beam focusing with a one‐dimensional compound refractive lens

The performance of a cooled Be compound refractive lens (CRL) has been tested at the Advanced Photon Source (APS) to enable vertical focusing of the pink beam and permit the X‐ray beam to spatially overlap with an 80 µm‐high low‐density plasma that simulates astrophysical environments. Focusing the fundamental harmonics of an insertion device white beam increases the APS power density; here, a power density as high as 500 W mm^?2 was calculated. A CRL is chromatic so it does not efficiently focus X‐rays whose energies are above the fundamental. Only the fundamental of the undulator focuses at the experiment. A two‐chopper system reduces the power density on the imaging system and lens by four orders of magnitude, enabling imaging of the focal plane without any X‐ray filter. A method to measure such high power density as well as the performance of the lens in focusing the pink beam is reported.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

基于近零折射率材料的声非对称聚焦透镜

研究基于近零折射率声子晶体的声非对称聚焦透镜。声非对称聚焦透镜的两侧分别为竖直平面与圆弧面结构,由于近零折射率材料的声波方向选择性,当声波从竖直平面一侧入射时,可以通过透镜,实现高性能声聚焦效应;而当声波从圆弧面一侧任意方向入射时,声波无法通过透镜,从而实现同时具有聚焦与非对称传输特性的声学透镜。在此基础上,改变透镜圆弧面的曲率半径,可以调控非对称透镜的正向聚焦焦点位置,且声非对称传输性能保持不变.此外,透镜内部的刚性散射体对声非对称聚焦性能的影响较小。研究结果表明所设计的声非对称聚焦透镜具有多功能、单一结构及高鲁棒性等优点,为设计新型近零折射率声学器件提供相应的理论方案与实验参考.      

Analytical calculation of atom ejection from the Ni (111), Ni (001), and Au (001) surfaces in frames of a three-dimensional model

Atom ejection from lattice sites at the Ni (111) and Ni (001) surfaces in the azimuthal direction toward the center of a lens consisting of two nearest neighboring atoms in the surface plane is calculated using a developed analytical three-dimensional model. The types of scattering of ejected atoms are classified in frames of the constructed model. It is found that the first and second ejection cones are observed in the sputtering pattern in the case of atom ejection from the Ni (111) surface and that the contribution of strongly blocked atoms to sputtering is considerable. The focusing of sputtered atoms at some angle from the surface normal is observed. A maximum of the polar angular distribution of sputtered atoms is shifted nonmonotonically as the energy increases. It is shown that the energy spent by the ejected atom on the recoiling of the lens atoms can be larger than that spent by this atom to overcome the potential barrier. It is found that small changes in the potential hardness and the binding energy at the magnetic phase transition can lead to a qualitative change in the ejection pattern. The expressions for the final ejection angle and energy in the case of Ni in the f-state are found in the form of an expansion in terms of two small parameters. As one passes from the case of atom ejection from the Ni (001) face to the case of atom ejection from the Au (001) face, the interaction cross section increases significantly because of an increase in the atomic number and the effects of blocking and focusing turn out to be considerable.     

A desktop X‐ray monochromator for synchrotron radiation based on refraction in mosaic prism lenses

Focusing planar refractive mosaic lenses based on triangular prism microstructures have been used as an alternative approach for wide‐bandpass monochromatization of high‐energy X‐rays. The strong energy dependence of the refractive index of the lens material leads to an analogous energy dependence of the focal length of the lens. The refractive mosaic lens, in comparison with the refractive lens of continuous parabolic profile, is characterized by a higher aperture because of reduced passive material. In combination with a well defined pinhole aperture in the focal plane, the transmittance of photons of an appropriate energy can be relatively high and photons of deviating energy can be efficiently suppressed. The photon energy can be tuned by translating the pinhole along the optical axis, and the bandwidth changed by selecting appropriate pinhole aperture and beam stop. This method of monochromatization was realised at the ANKA FLUO beamline using a mosaic lens together with a 20 µm pinhole and beam stop. An energy resolution of 2.0% at 16 keV has been achieved.     

单层超薄高效圆极化超表面透镜

针对超表面在透镜方面的应用, 本文设计了一种交叉极化透射聚焦超表面, 实现了将圆极化波转化为交叉极化波的同时聚焦电磁波的功能. 设计了一款旋转型单元, 单元为一层且厚度仅为1.5 mm, 分析了旋转型单元提供不同相移的原理并设计了相邻单元相移差为60°的相位梯度超表面, 在中心频率f=15 GHz附近发生奇异折射, 折射角与理论计算结果一致, 验证了设计单元的有效性, 基于该单元设计了尺寸为90 m mm×90 mm、单元数为15×15 的透射型聚焦超表面, 在中心频率f=15 GHz附近, 左旋圆极化平面波照射时, 透射波聚焦于L=40 mm 的实焦点且透射波为照射波的交叉极化波. 该超表面透镜效率高、厚度薄且为单层, 易于加工, 相对于传统透镜, 优势明显, 在操控电磁波、改善透镜性能方面有潜在应用价值.     

Optimized focusing properties of photonic crystal slabs

We propose an optimization procedure for focusing operation in finite two dimensional photonic crystal slabs. The device consists of a triangular lattice air holes etched in a semiconductor matrix at a nanometer scale to operate at 1.55 μm. To reach simultaneously an effective refractive index equal to −1 along with a very high transmission coefficient whatever optical wave incidence, the parameters as the lattice period and/or filling factor are precisely adjusted depending on the slab thickness. The method relies on Fabry-Perot resonances engineering in the air/crystal/air cavity constituting the lens.     

手持式眼底相机光学系统设计

提出一种新型眼底成像系统,结构更加简单、紧凑。系统的成像和调焦投影光路共用调焦镜,调焦投影光路完全嵌入到照明光路。调焦投影光路不再专设照明组件,避免了投影目标和调焦镜之间的机械联动结构。并且充分利用了网膜物镜系统的空间。利用LED光源窄带宽的优势,瞄准和拍照过程共用一个电荷耦合器件相机。采用新的光学结构,设计了一款视场30°、工作距离30mm的眼底相机光学系统,眼光焦度补偿范围-10m-1～+5m-1,物方各视场分辨率为45line/mm,畸变小于5%。     

Diffraction of terahertz waves after passing through a Fresnel lens

The spatiotemporal and spectral characteristics of ultrawide-band terahertz pulses after passing through a Fresnel lens are studied by using the scalar diffraction theory. The simulation shows that the transmitted terahertz waveforms compress with increasing propagation distance, and the multi-frequency focusing phenomenon at different focal points is observed. Additionally, the distribution of terahertz fields in a plane perpendicular to the axis is also discussed, and it is found that the diffraction not only induces focusing on-axis but also inhibits focusing at off-axis positions. Therefore, the Fresnel lens may be a useful alternative approach to being a terahertz filter. Moreover, the terahertz pulses travelling as a basic mode of a Gaussian beam are discussed in detail.     

Combined focusing of an uncharged particle beam by axially symmetric magnetic and electric fields in a vacuum

A way of simultaneously focusing a circular uniform beam of fine uncharged diamagnetic particles in the longitudinal and transverse directions is explored. Focusing is performed by a short magnetic lens and a diaphragm providing a time-dependent electric field. The size of the particles is within the range of 10⁻⁴–10⁻¹ cm.     

Polarization-independent and high-diffraction-efficiency Fresnel lenses based on blue phase liquid crystals

A polarization-independent and high-diffraction-efficiency Fresnel lens is developed based on blue phase liquid crystals (BPLCs). The optically isotropic characteristic of BPLCs is used to produce a polarization-independent Fresnel lens. The small optical phase shift of BPLCs that is induced by the Kerr effect is sufficient for the BPLC Fresnel lens to have high theoretical and experimental diffraction efficiencies of 41% and ～34%, respectively. An electrically erasable memory effect in the focusing diffraction at an electric field E>4.44?V/μm is observed. The electro-optical properties of the BPLC Fresnel lens are analyzed and discussed.     

Determination of the focusing power of flat lenses using the radiovisor

Focusing of electromagnetic radiation of a point source with a wavelength of 3 cm by flat negative-refraction lenses formed by a hexagonal structure of metal cylindrical rods was studied. The spatial distribution of microwave field of H polarization in the lens focal plane was recorded by a radiovisor screen which converts it into a visible image. The full width at half maximum of the focal spot distribution at optimum focusing did not exceed half the emission wavelength.     

Influence of line defects on focusing in a two-dimensional photonic-crystal flat lens

We investigate in detail the influence of line defects on focusing of electromagnetic waves in a two-dimensional photonic-crystal flat lens. Through simulations, we find that a focusing can always be observed when a line defect in the lens is introduced along the light transmission direction and the width of the line defect is less than \lambda /2. However, there appear two focusings when the width of the line defect is more than \lambda /2. When the line defect is introduced along the direction perpendicular to the transmission, there is always one focusing.     

Comparative Features of Electromagnetic Scattering by an Invisible Spherically Symmetric Lens with a Negative Refractive Index

A spherically symmetric lens with a negative refractive index, which can be invisible from the point of view of geometrical optics, is considered. Expressions describing the profile of the refractive index and ray trajectories in the lens, as well as some results of numerical modeling of plane wave scattering by the lens in the rigorous statement of the problem, are presented. It is detected that, unlike in the case of an invisible lens with a positive refractive index, the minima of the radar cross section in the forward direction corresponding to invisibility for the lens with a negative index occur at integer, rather than semi-integer, values of the electric radius, and that their depth is smaller because of the astigmatism associated with focusing of rays on the axis. Some results characterizing influence of losses in the lens on the level of the radar cross-section minima are also presented.     

Theory of an X-ray interferometer in the form of an array of planar compound refractive lenses

The results of theoretical analysis of the interference pattern created by an X-ray multilens interferometer in the case of an arbitrary number of planar compound refractive lenses are presented. The full widths at half maximum of the resonance peaks in the transverse and longitudinal directions relative to the direction of synchrotron radiation are calculated at distances corresponding to the fractional Talbot effect. A relation between the widths is shown to exist that is very close to the width relation in the case of focusing by a single lens. A difference between the fractional and full Talbot effects is discussed, and the necessary conditions for the transverse and longitudinal coherence of radiation are analyzed, the satisfaction of which guarantees that undistorted interference peaks will be observed experimentally.     

Effects of the azimuthal-angle focusing of atoms ejected from the (001) Ni and (001) Au faces

The features of the azimuthal-angle focusing of atoms sputtered from the surfaces of the Ni (001) and Au (001) faces are studied by molecular dynamics using computer simulation. The degree of anisotropy of the azimuthal-angle distribution for atoms sputtered from the (001) Au surface is found to be higher than for atoms sputtered from the (001) Ni face. It is shown that two maxima are observed at comparatively small polar observation angles in the azimuthal-angle distribution in the directions in which Wehner spots are formed, i.e., to the left and to the right of the center of the lens formed by two neighbors closest to the ejected atom. The maxima are shifted from the center with a decrease in the polar observation angle. This feature occurs due to the rainbow scattering effect. The contribution of atoms overfocused with respect to the lens center is studied. All overfocused atoms are found to be strongly blocked. When atoms are ejected from the (001) Au face, the interaction cross section strongly increases due to an increase in the atomic number, and the effects of blocking and focusing appear to be more pronounced.     

Analysis of flexural mode focusing by a semianalytical finite element method

Focusing is one of the most promising techniques for the detection of small defects in pipe works, in which guided waves including longitudinal and flexural modes are tuned so that ultrasonic energy can be focused at a target point in a pipe, and analysis of reflected waves gives information on defects such as location and size. In this paper, the focusing technique is discussed by way of a simulation of guided wave propagation in pipe by a semianalytical finite element method (SAFE). Experiments and SAFE calculations were compared for waveforms transmitted by a single transducer and received at different circumferential positions initially, and then the focusing phenomena were experimentally observed using focusing parameters obtained by calculations. Calculation and visualization were conducted to clarify focusing phenomena in pipe in investigating the potential of the focusing technique. These results show that the time-reversal idea helps in understanding focusing and that resolution of focusing is strongly affected by incident waveforms as well as the number of channels available in an experiment.