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。

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 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.