提出了介质的光学厚度系数成圆形分布的一维光子晶体结构，与周期结构的光子晶体相比，该结构具有禁带展宽特性。同时讨论了起止膜层及膜层的光学厚度对该结构禁带特性的影响，优化出了在所选材料的介电常数所允许的频率范围内，具有完全禁带特征的光子晶体结构。

阐述了一种新的X射线超反射镜的设计方法: 该方法将Frensnel反射系数公式和单纯形调优法相结合，可以设计出满足不同要求的X射线超反射镜。 依据周期多层膜确定膜层数，给出了一种确定超反射镜膜层数的方法。设计了在铜（Cu）的Kα线下，具有不同掠入射角宽度的多种钨（E）F 碳（C）超反射镜：设计中考虑了多层膜结构的界面粗糙度和相互扩散对多层膜反射性能的影响，并做了模拟计算。实验结果表明：用这种方法设计X射线超反射镜优于现有的其他方法。

A method of designing depth-graded multilayer structures with broad angular response for use as coatings in X-ray optics is presented. The design is based on the well-known Fresnel equations and recursive calculation, combined with a merit function plus random variation of the thickness of each layer. This allows the design of multilayer films for different requirements in X-ray optics. Results are presented on the layer thicknesses in depth-graded W/C multilayer films and their reflectivity as a function of the grazing incidence angle for Cu Ka radiation. The required minimum number of bilayers in depth-graded multilayer films depends on the grazing incidence angle, i.e., the saturation effect observed in the design of periodic multilayer films also emerges in the design of depth-graded multilayers. The predicted performances of multilayers designed using this method are superior to those designed using existing methods. All rights reserved.

A systematic method which allows the optimum thickness of each layer in a depth-graded multilayer coating to be determined is described. This enables specific reflectivity responses over broad wavelength bands in the soft X-ray and EUV regions to be calculated. The method is applied to the design of some depth-graded molybdenumrsilicon multilayers for the wavelength range 13-19nm, with average normal incidence reflectivities of about 13% in this range, but it is generally applicable for other material pairs and wavelength ranges. In addition, the effects of layer thickness errors on the performance of depth-graded multilayers can be simulated. The model gives better results than those based on power law variation of the layer thicknesses.

Transmission characteristics are studied for hybrid structures combining defects and multiple heterostructures. It is shown that the nontransmission frequency range can be substantially enlarged and the phenomenon of multiple-channeled filtering can be realized by adjusting the number, position, and size of the defects. One, two, and three channeled filters are considered in the structures. Examples are studied theoretically by transfer matrix methods.

A new method of designing x-ray supcromirrors with broad angular or energy response for use as coatings in x-ray optics is presented. The dcsign is basced on an analytical method with ovcrsimplified analytical and semi empirical fbrmulac, and an cxtensivc numciffcal method is used in the optimization design. A better initial multilaycr is obtained with the formcr mcthod and optimizcd with the lattcr mcthod. Iu the optimization, a good dcsign is achiercd with much less computing time. In addition, the saturation effect due to the intcrfacial roughness in multilaycr also emergcs in the dcsign of x-ray supcrmirrors with definitc pcrformanccs. The reffcctiity of C/W x-ray supermirrosrs as a function of photon cncrgy at the fixed grazing incident angle 0.5

Transmission studies for multiple heterostructures inserted with defects are presented. The results show that the enlargement of the forbidden band and the realization of multiple channeled filtering can be reached simultaneously with these configurations. The frequency, frequency interval, and number of channels can be tuned by adjusting geometric and physical parameters of the defects. Sidebands of the forbidden band can be substantially restricted as compared with that of periodic structures. Experimental fabrication of the designed configurations is carried out with the heterostructures containing TiO2/SiO2 multilayer defects, and the results agree with the calculation very well.

基于分束镜反射率和透射率的乘积为衡量标准的原则！设计了13.9nm软X射线激光干涉测量所需的多层膜分束镜，用磁控溅射法在有效面积达10mm×10mm，厚10nm的氮化硅窗口上镀制Mo/Si多层膜，实现了分束镜制作。用表面轮廓仪实测分束镜面形精度达到nm量级，同步辐射反射率计测试表明，分束镜的反射率和透射率乘积约4%。

介绍了在极紫外波段，利用帽层材料来减少多层膜反射镜因外部环境干扰而造成的反射率降低，使多层膜光学元件能够长时间稳定工作。计算了在13.9nm波长处Mo/Si极紫外多层膜反射镜在表面镀制不同帽层材料时的理论最大反射率，利用单纯形调优法，对帽层和多层膜的周期厚度进行优化，同时把分层理论用于多层膜帽层优化，可使多层膜的反射率得到进一步提高。分析了在加入帽层前后多层膜外层电场强度的分布变化情况。

软X射线干涉测量是通过软X射线激光经过Mach-zehnder干涉仪完成的，是测量临界面附近等离子体状态的重要方法。基于软X射线多层膜的性能特点，指出软X射线干涉测量的干涉仪各光学元件的入射角越接近正入射越好，分束镜的设计应以其反射率和透过率的乘积为衡量标准。用离子束溅射法制作了类镍银13.9nm软X射线激光干涉测量所需的分束镜，实测表明其面形精度达到纳米量级，反射率和透过率乘积大于1.6%。