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 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.

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。

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.