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.

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.

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

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.

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.