Laser cavities and polarization optics for soft X-rays and the extreme ultraviolet

Addressed here are polarization optics for extreme-ultraviolet and soft X-ray wavelengths, especially as relevant to laser cavities. It is pointed out that the whisper-gallery mirrors studied by Vinogradov can serve as weak polarizers and, more importantly, as birefringent elements. The application of multilayer technology to polarizing mirrors and beamsplitters is also considered. It is shown that multilayer beamsplitters can function both as reflective and transmissive polarizers. Their behavior is surprising in some cases, with the same polarization being preferred in both reflection and transmission. Three polarizing cavity schemes are proposed, each incorporating a polarizing beamsplitter as its output coupler. Cavity optimization issues are discussed.     

Design of X-ray super-mirrors using simulated annealing algorithm

An adaptive local search-based simulated annealing (ALSA) algorithm is proposed for the design of the wide band-pass multilayer optical elements operating in the hard and soft X-ray wavelength ranges. At present the SA algorithm has been kept as simple as possible and its performance is being studied before a series of modifications are made to tailor the SA algorithm to optimize super-mirror for particular applications. The algorithm has also been developed with two specific areas in mind: a W/C broad angle super-mirror for hard X-ray applications and a Mo/Si wide band super-mirror operating at normal incidence in the EUV spectral region. The design results show that the ALSA algorithm method has the flexibility to design a wide range of multilayer structures and in comparison to other techniques has good results although computationally more intensive.     

Fabrication and characterization of EUV multilayer mirrors optimized for small spectral reflection bandwidth

Our aim was to produce EUV multilayer mirrors with a small spectral bandwidth ΔE≤3 eV at 70 eV peak energy using UHV electron beam evaporation by varying the thickness ratio (Γ=) between the absorber layer and the bilayer. The deposition process was controlled by in situ soft X-ray reflectometry, and ion-beam polishing as well as substrate-heating methods were applied to reduce the interface roughness. The reflection properties of the Mo–Si multilayer mirrors prepared were characterized by hard and soft X-ray reflectometry and details of the multilayer structure were revealed from cross-sectional transmission electron microscopy. Received: 22 September 2000 / Accepted: 4 October 2000 / Published online: 30 November 2000     

一种有效的色散补偿镜优化设计方法

介绍了一种有效的色散补偿镜优化设计方法.这种方法将广义模拟退火法和最小二乘法结合起来使用.在色散补偿镜的设计过程中,用双啁啾结构作为初始膜系,发现了一些设计双啁啾结构应注意的规律.这种新的优化方法避免了局部陷阱问题,最终结果也比较令人满意.此外,这种优化设计方法还可以应用于设计啁啾光纤光栅.     

Luus-Jaakola optimization procedure for multilayer optical coatings

Designing multilayer optical coatings is a difficult optimization problem because of the huge size of the search space. In the present paper, the Luus-Jaakola (LJ) optimization procedure, a new optimization algorithm, is employed to model multilayer optical coatings in the X-ray domain. With this algorithm it is not necessary to specify initially the number of layers present in a design. Only an upper limit needs to be defined. The algorithm has been used to maximize the reflectivity over a range of incident angles at a fixed wavelength, and over a wavelength range at a fixed incident angle. The results show that the LJ algorithm can be effectively applied to the design of multilayer optical coatings resulting in fewer layers than obtained using alternative optimization methods.     

Fabrication of nested elliptical KB mirrors using profile coating for synchrotron radiation X-ray focusing

This paper describes fabrication methods used to demonstrate the advantages of nested or Montel optics for micro/nanofocusing of synchrotron X-ray beams. A standard Kirkpatrick-Baez (KB) mirror system uses two separated elliptical mirrors at glancing angles to the X-ray beam and sequentially arranged at 90° to each other to focus X-rays successively in the vertical and horizontal directions. A nested KB mirror system has the two mirrors positioned perpendicular and side-by-side to each other. Compared to a standard KB mirror system, Montel optics can focus a larger divergence and the mirrors can have a shorter focal length. As a result, nested mirrors can be fabricated with improved demagnification factor and ultimately smaller focal spot, than with a standard KB arrangement. The nested system is also more compact with an increased working distance, and is more stable, with reduced complexity of mirror stages. However, although Montel optics is commercially available for laboratory X-ray sources, due to technical difficulties they have not been used to microfocus synchrotron radiation X-rays, where ultra-precise mirror surfaces are essential. The main challenge in adapting nested optics for synchrotron microfocusing is to fabricate mirrors with a precise elliptical surface profile at the very edge where the two mirrors meet and where X-rays scatter. For example, in our application to achieve a sub-micron focus with high efficiency, a surface figure root-mean-square (rms) error on the order of 1 nm is required in the useable area along the X-ray footprint with a ∼0.1 mm-diameter cross section. In this paper we describe promising ways to fabricate precise nested KB mirrors using our profile coating technique and inexpensive flat Si substrates.     

Combined-method for designing broadband dispersion mirror based on local optimization approach and needle optimization technique

A combined-method based on local optimization and needle optimization is proposed to design broadband dispersion mirrors. The broadband dispersion mirrors are designed by using needle optimization combined with cross application of local optimization and changing high refractive index materials. We combine high efficiency of the local optimization and accuracy of needle optimization. This method can efficiently prevent optimizing process from being captured in a local minimum and obtain higher reflectivity and more smooth group delay dispersion (GDD) curves. The designed dispersion mirrors have a few numbers of layers, which do not have the thin layers that are not easily deposited.     

软X光激光用多层膜反射镜的设计与性能模拟计算

介绍在研制软Ｘ光激光用多层膜反射镜中发展起来的一套设计方法。给出了这类反射镜在现阶段所研究的部分Ｘ光激光波长下的设计结果。利用波动光学迭代方法模拟计算了反射镜的性能，并讨论了膜厚控制误差、表（界）面粗糙度等对性能的影响。     

Advances in Hard X-ray Focusing Optics

Focusing and imaging components, such as lenses and mirrors, are necessary in a wide range of optical systems. For the visible light region, such components are readily available, but they are still in the research and development stage for the hard X-ray region. The extremely short wavelengths of hard X-rays require unprecedented accuracy in the manufacture of focusing devices. For many years, a large amount of research carried out at synchrotron facilities has focused on the theory, fabrication, evaluation, and application of X-ray focusing elements.     

Multilayer X-ray mirrors based on La/B<Subscript>4</Subscript>C and La/B<Subscript>9</Subscript>C

Multilayer X-ray mirrors that are based on La/B₄C and La/B₉C and intended for the reflection of X-ray radiation in the spectral region near λ = 6.7 nm are prepared and studied. Reflection coefficients at a level of 40–60% are achieved for mirrors with various periods. The difference in the interlayer roughnesses reconstructed from the data measured in the hard and soft X-ray spectral regions is explained using a structural model with an asymmetric permittivity profile in a mirror period. A proximate technique is developed to estimate the permittivity profile in a multilayer-structure period using reflectometry data. The effect of antidiffusion Sn, Cr, and Mo barriers on the reflection coefficient of multilayer La/B₄C structures is studied experimentally     

Hybrid approach for the design of mirror array to produce freeform illumination sources in immersion lithography

Source and mask optimization (SMO) has emerged as a key resolution enhancement technique (RET) for 45 nm technology node and below in lithography. The design method of freeform illumination sources predicted by SMO is significant for the scanner development. We present a hybrid approach combining simultaneous and sequential approaches to optimize the tilt angles of the mirrors to produce multi target freeform illumination sources accurately and quickly. The size of spot reflect by plane mirror can be easily controlled by changing different microlens arrays with appropriate focal length, which reduce the complexity of the system and makes it more flexible to produce the specific freeform sources compared to curving the mirrors used in previous work. The relationship between the tilt angles of plane mirrors and the positions of the spots in the pupil is obtained by chief ray tracing. Using the hybrid approach the freeform illumination sources required by SMO can be designed by merely adjusting the tilt angles of mirrors without changing other parameters of optical elements, which is most effective for both lithography tool manufacture and its applications. The real ray tracing results demonstrate that our design method is capable of creating multi freeform illumination sources with high transmittance, and confirm that the effectiveness of the hybrid approach for optimized design and control of mirror array in immersion lithography system.     

基于模拟退火算法的宽角度X射线超反射镜设计研究

应用于硬X射线波段的宽带多层膜光学元件———宽角度X射线超反射镜的设计可以归结为一个连续变量的多维多极值的全局优化问题。缺少一种有效的全局优化方法是阻碍解决这一难题的一个关键。模拟退火算法是一种简单而且通用的全局优化算法。结合光学多层膜的设计原理提出了利用模拟退火算法来进行宽角度X射线超反射镜设计的新方法。结合已有的方法选择了W和C作为膜层的膜对材料,设计出Cu的Kα线处角度范围0.9°~1.1°反射率达到20%的宽角度X射线超反射镜。并在此基础上采用改进的自适应模拟退火算法实现了Cu的Kα线处宽角度X射线超反射镜的理想设计结果。设计结果表明了模拟退火算法在多层膜最优化设计领域的正确性和有效性。     

High resolution hard X-ray photoemission using synchrotron radiation as an essential tool for characterization of thin solid films

Recently, we have shown that hard X-ray photoemission spectroscopy using undulator X-rays at SPring-8 is quite feasible with both high resolution and high throughput. Here we report an application of hard X-ray photoemission spectroscopy to the characterization of electronic and chemical states of thin solid films, for which conventional PES is not applicable. As a typical example, we focus on the problem of the scatter in the reported band-gap values for InN. We show that oxygen incorporation into the InN film strongly modifies the valence and plays a crucial role in the band gap problem. The present results demonstrate the powerful applicability of high resolution photoemission spectroscopy with hard X-rays from a synchrotron source.     

Design and performance of two-channel EUV multilayer mirrors with enhanced spectral selectivity

In this paper, we present a study on two-channel multilayer mirrors which can operate at two wavelengths in Extreme Ultraviolet (EUV) spectral range. We propose a new method to design two-channel EUV multilayer mirrors with enhanced spectral selectivity. The mirror structure is a stack of two periodic multilayers separated by a buffer layer. We have defined the main parameters which allow adjustment of the distance between different order Bragg’s peak and of wavelength positions of reflectivity minima. Two mirrors have been designed and deposited for solar EUV telescope applications by using this method. The first mirror reflects Fe IX–X line (17.1 nm) and Fe XVI (33.5 nm) lines with attenuation of the He II line (30.4 nm). The second mirror reflects Fe IX–X and He II lines with attenuation of Fe XV (28.4 nm) and Fe XVI lines. Measurements with synchrotron radiation source confirm that, in both cases, for these mirrors, we are able to adjust reflectivity maxima (Bragg peak position) and minima. Such multilayers offer new possibilities for compact design of multi-wavelength EUV telescopes and/or for high spectral selectivity.     

Design and fabrication of low-cost X-ray mirrors

Traditional X-ray mirrors made from Zerodur and silicon carbide are quite expensive because of the fabrication cost involved in achieving a very high surface finish of the order of 15 Å or better. The cost of X-ray mirrors can be greatly reduced by using replication methods for producing the grazing-incidence type mirrors. This paper presents the optical and optomechanical design for a Wolter type I mirror and its mount, and the fabrication method used to produce a low-cost replicated nickel mirror. The finite element analysis results for this mirror are also presented. The design and fabrication steps for the aluminium master mandrel used for replication are also discussed. A surface finish of better than 15 Å was achieved for a such an electroformed mirror with a wall thickness of only 1 mm.     

X-ray spectroscopy of cooling clusters

We review the X-ray spectra of the cores of clusters of galaxies. Recent high resolution X-ray spectroscopic observations have demonstrated a severe deficit of emission at the lowest X-ray temperatures as compared to that expected from simple radiative cooling models. The same observations have provided compelling evidence that the gas in the cores is cooling below half the maximum temperature. We review these results, discuss physical models of cooling clusters, and describe the X-ray instrumentation and analysis techniques used to make these observations. We discuss several viable mechanisms designed to cancel or distort the expected process of X-ray cluster cooling.     

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.     

场共轭数值模拟研究

给出了一种考虑光源的强度分布后用两个变形镜头实现场共轭的算法,并对高斯光束进行了数值模拟,结果表明这种算法是有效的。变形镜平滑的表面可以剔除相位局部跳变,明显改善光强分布。对高斯光束,发射面相位面形状十分简单,易于用变形镜构造。本文还讨论了两变形镜之间距离的影响,最后指出如何改进现有算法。     

Theoretical modeling of hard X-ray surface modes in a periodic multilayer

The excitation of hard X-ray surface modes of a periodic multilayer is studied with the help of theoretical modeling. It is found that a hard X-ray surface mode can appear in a specific periodic multilayer coated with a high-density reflecting layer. The generation of the hard X-ray surface modes is shown to be effective only at a certain set of the structural parameters of the multilayer. A method for the calculation of the propagation (attenuation) length of the surface mode running in the periodic multilayer is described. The excitation of the hard X-ray surface modes is compared with that of optical surface modes in photonic crystals. The relationship between the surface modes and guided modes of periodic multilayers is discussed.     

Design of multi-mirror optics for industrial extreme ultraviolet lithography

We develop a new method for multi-mirror optics design. The system includes several mirror groups that will be designed separately to fulfil the designer’s needs. The elements of individual mirror group are all spherical mirrors. The radii and separations of the all spherical mirror groups can be calculated by three conditions: the pupil-stop condition, the non-obstruction condition and the conjugate condition. The connected mirror groups could be optimized as a whole optics by gradual optimization process, and the final optics includes high order aspheric mirrors. The all sphere structure design method is effective to reduce the load of calculation and evaluation of the configurations. The gradual optimization method can help the objective achieve high imaging performance smoothly. Finally we got a NA 0.3 EUVL objective, and the mean wavefront error of 0:0287λ (RMS) is reached.