X-ray focusing with compound lenses made from beryllium

We have measured the intensity profile and transmission of x rays focused by a series of biconcave spherical unit lenses fabricated from beryllium. The use of beryllium extends the range of operation of compound refractive lenses, improving transmission, aperture size, and gain. The compound refractive lens was composed of 160 biconcave unit lenses, each with a radius of curvature of 1.9 mm. Two-dimensional focusing with a gain of 1.5 was obtained at 6.5 keV with a focal length of 93 cm. The effective aperture of the compound refractive lens was measured as 600 mum , with 9% peak transmission.     

Toward one nanometer X-ray focusing: a complex refractive lens design

We report a design for one nanometer X-ray focusing by a complex refractive lens, which is capable of focusing 20 keV X-rays down to a lateral size of 0.92 nm （full-width at half-maximum （FWHM）） and an axial size of 98 nm （FWHM） with intensity gain of 49050. This complex refractive lens is comprised of a series of kinoform lenses, whose aperture is gradually matched to the converging trace of the X-ray beam so as to increase the numerical aperture （NA）. The theoretical principle of the proposed complex refractive lens is presented. The NAs of these lenses are calculated. The numerical simulation results demonstrate that the proposed design can focus the X-ray beam into sub-nanometer while remaining high gain.     

Aspherical lens shapes for focusing synchrotron beams

Aspherical surfaces required for focusing collimated and divergent synchrotron beams using a single refractive element (lens) are reviewed. The Cartesian oval, a lens shape that produces perfect point‐to‐point focusing for monochromatic radiation, is studied in the context of X‐ray beamlines. Optical surfaces that approximate ideal shapes are compared. Results are supported by ray‐tracing simulations. Elliptical lenses, rather than parabolic, are preferred for nanofocusing X‐rays because of the higher peak and lower tails in the intensity distribution. Cartesian ovals will improve the gain when using high‐demagnification lenses of high numerical aperture.     

An exact theory of imaging with a parabolic continuously refractive X-ray lens

A theory is developed of image formation with an X-ray lens that consists of a large number of elements. Each element has a biconcave parabolic profile and weakly refracts an X-ray beam. Since such a lens can have a relatively large length comparable to the focal length, the thin-lens approximation is inapplicable. An exact expression for the propagator of a continuously refractive lens is derived that describes the transfer of radiation through a refractive parabolic medium. We calculate the image propagator that describes the focusing of a parallel beam and the image transfer (the focusing of a microobject), as well as the Fourier transform of the transmission function for a microobject with a lens, is calculated. The effective aperture of an X-ray lens is completely determined by the absorption of radiation and does not depend on its geometrical cross-sectional sizes. If we write the complex refractive index as n=1? δ+iβ, then the beam diameter at the focus is approximately a factor of 0.8β/δ smaller than the diameter of the effective aperture, with the index depending only slightly on the wavelength. A continuously refractive lens has no aberrations in the sense that all of the rays that passed through the lens aperture are focused at a single point. The lens can focus radiation inside it and has the properties of a waveguide; i.e., it can reconstruct the beam structure for some lengths to within the absorption-caused distortions. Nonuniform X-ray absorption in the lens leads to the interesting visualization effect of transparent microobjects when their image is focused. In this case, the phase shift gradient produced by the microobject is imaged. We discuss the properties of the Fourier transform pertaining to the absorption of radiation in the lens.     

聚焦法测量塑料光纤折射率分布的可行性研究

结合理论分析和实验验证,探讨了聚焦法测量塑料光纤纤芯的折射率分布的可行性。结果表明,对GI-POF而言,聚焦法是一种简单可行的技术.但是对SI-POF,由于入射光线在光纤边界处发生交叉,聚焦法不能精确测量其折射率分布.     

Refractive microlens array for wave-front analysis in the medium to hard x-ray range

We report an alternative approach to x-ray wave-front analysis that uses a refractive microlens array as a Shack-Hartmann sensor. The sensor was manufactured by self-assembly and electroplating techniques and is suitable for high-resolution wave-front analysis of medium to hard x rays. We demonstrate its effectiveness at an x-ray energy of 3 keV for analysis of x-ray wave-front perturbations caused by microscopic objects. The sensor has potential advantages over other methods for x-ray phase imaging and will also be useful for the characterization of x-ray beams and optics.     

Kinoform单透镜的硬X射线聚焦性能

Kinoform单透镜可以高效聚焦硬X射线至纳米量级, 在X射线纳米显微学和纳米光谱学领域有着重要的应用前景. 基于衍射光学和傅里叶光学理论, 给出了X射线经由Kinoform单透镜聚焦的物理模型, 基于数值模拟, 研究了不同材料、光子能量、台阶数量和顶点曲率半径对Kinoform单透镜聚焦性能的影响. 结果表明, 孔径为1 mm的Kinoform单透镜对30 keV的X射线聚焦, 可以得到14 nm焦斑、62 μm焦深, 且可实现4个量级的光强增益和大于30%的光强透过率.     

双环径向偏振涡旋光束经介质界面的深聚焦

基于矢量德拜理论,研究了双环径向偏振涡旋光束经介质分界面的深聚焦特性。当选取适当的入射光束拦截比时（即透镜孔径半径与入射光束的束腰半径的比）,在聚焦场中可以得到一个极小的局域空心光束。局域空心光束的大小不仅与透镜的数值孔径有关,还与聚焦场介质的折射率有关。另外,还研究了透镜的数值孔径、入射光束的拦截比以及探测深度对聚焦光束实际焦点位置的影响。通过对聚焦光束的实际焦点位置的计算发现：当选取一定的光束拦截比时,聚焦光束存在一个焦点开关。     

双环径向偏振涡旋光束经介质界面的深聚焦

基于矢量德拜理论,研究了双环径向偏振涡旋光束经介质分界面的深聚焦特性。当选取适当的入射光束拦截比时(即透镜孔径半径与入射光束的束腰半径的比),在聚焦场中可以得到一个极小的局域空心光束。局域空心光束的大小不仅与透镜的数值孔径有关,还与聚焦场介质的折射率有关。另外,还研究了透镜的数值孔径、入射光束的拦截比以及探测深度对聚焦光束实际焦点位置的影响。通过对聚焦光束的实际焦点位置的计算发现:当选取一定的光束拦截比时,聚焦光束存在一个焦点开关。     

Limits for superfocusing with finite evanescent wave amplification

Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provides extreme subwavelength focusing by "amplifying" evanescent wave components that are usually lost. This Letter provides a relation between the achievable focus spot size, the amplification available, and the focal length. This may be considered as a revised version of Abbe's diffraction limit for focusing systems that have evanescent wave amplification. It is useful in comparing the amplification achieved in various subwavelength focusing implementations as well as determining when it is better to use existing near-field techniques, such as simple diffraction from an aperture or slit, than to attempt complicated superfocusing.     

Nanometer linear focusing of hard x rays by a multilayer Laue lens

We report on a type of linear zone plate for nanometer-scale focusing of hard x rays, a multilayer Laue lens (MLL), produced by sectioning a multilayer and illuminating it in Laue diffraction geometry. Because of its large optical depth, a MLL spans the diffraction regimes applicable to a thin Fresnel zone plate and a crystal. Coupled wave theory calculations indicate that focusing to 5 nm or smaller with high efficiency should be possible. Partial MLL structures with outermost zone widths as small as 10 nm have been fabricated and tested with 19.5 keV synchrotron radiation. Focal sizes as small as 30 nm with efficiencies up to 44% are measured.     

Liquid-crystal adaptive lenses with modal control

We report on a novel approach to the realization of nematic liquid-crystal (LC) phase correctors to form spherical and cylindrical wave fronts. A LC cell with a distributed reactive electrical impedance was driven by an ac voltage applied to the cell boundary to yield the desired spatial distribution of the refractive index. The two-dimensional function of the phase delay introduced into the light beam depends on the frequency of the ac control voltage, the geometry of the boundary electrode surrounding the LC cell, and the electrical parameters of the cell. We realized a cylindrical adaptive lens with a clear aperture of 15 mm x 4mm and a spherical adaptive lens with circular aperture of 6.5 mm. Both devices are capable of focusing collimated light in the range infinity...0.5 m.     

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.     

FDTD方法对固体浸没透镜的光场分析

采用二维时域有限差分(2D-FDTD)方法研究了高斯光束通过固体浸没透镜(SIL)的光场分布特性.模拟结果表明,SIL的折射率越大,底面出射的光斑越小,但随离底面距离的增大光束很快展宽;当只有入射角大于全反射临界角、具有高空间频率的部分高斯光束聚焦到SIL底面金属膜中心的微孔时,针对不同直径的微孔,模拟了出射光场的分布,发现微孔直径在某一特定值时,出射光斑半径在距SIL底面近半个波长范围内无明显改变,该结果为增大SIL和存储介质间距的方案提供了理论依据.     

Efficient generation of Xe K-shell x rays by high-contrast interaction with submicrometer clusters

The interaction between a 25 TW laser and Xe clusters at a peak intensity of 1 × 101? W/cm2 has been investigated. Xe K-shell x rays, whose energies are approximately 30 keV, were clearly observed with a hard x-ray CCD at 3.4 MPa. Moreover, we studied the yield of the Xe K-shell x rays by changing the pulse duration of the laser at a constant laser energy and found that the pulse duration of 40 fs is better than that of 300 fs for generating Xe K-shell x rays.     

A novel probe for an evanescent wave fibre-optic absorption sensor

A novel, highly sensitive probe consisting of a uniform region sandwiched between two linear tapers for an evanescent wave fibre-optic absorption sensor is proposed. The diameter of the uniform region is chosen to be equal to the minimum allowed diameter of the taper's output end. The first taper is used to bring the angles of the rays in the input fibre close to the critical angle of the sensing region while the second taper reconverts the angles into their initial values so that they can propagate in the output fibre. It has been shown that the sensitivity of the sensor depends on the length of the uniform region of the probe, the refractive index of the fluid and the numerical aperture of the fibre. The sensitivity increases with increase in the length of the uniform region and also with decrease in the numerical aperture of the fibre. In addition, the sensitivity of the proposed probe can be further increased by launching the selected rays into the input fibre.     

Quenching electron runaway in positive high-voltage-impulse discharges in air by laser filaments

Strong hard (ε>100 keV) x rays being observed from impulse atmospheric discharges with maximal voltages from U=0.5 to 0.9 MV just before the breakdown were completely stopped with the use of femtosecond-laser-filament plasma. Runaway electrons generating such x rays and being estimated to achieve their maximal energy, ε~U, near the positive electrode disappear if a laser filament plasma is ignited perpendicularly to the runaway near the positive electrode. A preheating mechanism for formation of the electron runaway in air is proposed.     

Divergence and aperture angle of conical light guides

Relations derived for the angle of divergence and the aperture of hollow metallic or dielectric cones may not directly be assigned to dielectric core/cladding light guides. The accurate results for the angle of aperture and divergence are stated here under consideration of the total internal reflection at the junction of the core to the surroundings. Furthermore the full angle of the conical element, the geometrical length and the varying diameters, the refractive indices and non-axial ray entrance are considered. All derivations are made by means of geometrical optics for meridional rays.     

抛物面型X射线组合折射透镜聚焦性能的理论与实验研究

结合衍射理论和矩阵光学方法得出抛物面型X射线组合折射透镜的光学性能指标(包括其焦距的严格表达式、薄透镜近似的判定准则、透过率和有效孔径,以及极限聚焦光斑尺寸等).采用X射线深度光刻技术实际制作了PMMA材料抛物面型X射线组合折射透镜并给出了工艺测试结果.最后在北京同步辐射装置(BSRF)上,实际构建了基于3种不同结构参数的PMMA材料抛物面型X射线组合折射透镜的微束聚焦实验系统.并实际测试了其聚焦性能,均获得了良好的聚焦效果,给出实测结果并对实测结果进行了分析和讨论.     

级联式平面抛物面型X射线组合折射透镜的设计与制作

X射线组合折射透镜(CRL)已逐步成为同步辐射光源下X射线聚焦光学器件的标准配件之一,它具有结构紧凑、易调节校准、适用光子能量范围大等优点.本文设计了一种级联式平面抛物面型CRL,它将N1个具有较大抛物面几何孔径(R0)的折射单元I与N2个具有较小抛物面顶点曲率半径(R)的折射单元II级联,以解决常规CRL设计过程中焦斑尺寸与透过率的矛盾.采用PMMA材料,利用LIGA技术制作了一组级联式平面抛物面型CRL,其中折射单元I的主要结构参数为N1=15,R1=200μm,2R01=564μm;折射单元II的主要结构参数为N2=20,R2=50μm,2R02=140μm.在上海光源同步辐射线束上,所制作的级联式平面抛物面型CRL实现了对初始光斑尺寸为200μm×100μm的入射X射线的一维聚焦,测试得到的焦距为1.052 m,横向焦斑尺寸为24.9μm@8 keV,透过率为2.19%.