| Multilayer-coated gratings realize the high spectral resolution of diffraction gratings and the high normal-incidence reflectivity of multilayer coatings in a single optical element, so they are widely used in extreme-ultraviolet (EUV) astronomical spectrometers, EUV lithography systems, and so on. Diffraction efficiency, which is the key performance parameter of a grating, depends largely on the grating's groove shape. Gratings with a rectangular groove shape (laminar gratings) have been used in most EUV applications, for the rectangular groove shape can be accurately controlled. A blazed grating with a triangular groove shape has higher theoretical diffraction efficiency than a laminar grating. However, the required blaze angle of a EUV blazed grating is so small (typically < 3°) that it is difficult to control precisely the groove profile. As a result, the measured efficiency of a blazed grating is much less than the theoretical prediction. Researchers are now focusing on improving the fabrication technique so as to get higher efficiency. This dissertation mainly reports our investigation on EUV blazed gratings, which includes efficiency calculation, grating fabrication, and efficiency measurement and analysis. Some other types of EUV gratings are also studied.For efficiency calculation, a computer code based on the differential theory was written, which takes the actual groove shape and the surface and interface roughness into account. The calculated results are in good agreement with the measured results. This computation program is useful for analyzing the relationship between diffraction efficiency and groove parameters.A simple and practical method to make high-quality EUV blazed gratings is developed. This method uses an argon and oxygen mixed-gas ion-beam to directly etch the fused silica substrate through a rectangular-profile photoresist mask. A corresponding theoretical model is built to analyze the etching process. This method is characterized by its use of rectangular photoresist masks and oxygen as an etchant ingredient. With oxygen added, it is easy to obtain small blaze angles of 0.5-3°. The etch model based on rectangular mask is concise, and the etch process can be precisely controlled. Experimental results confirm the convenience of the method and the effectiveness of the model. With this fabrication technique, blazed gratings with sharp edges can be reproducibly fabricated, and the control precision of the blaze angle is±10%.A typical multilayer-coated blazed grating was measured with synchrotron radiation and has a peak efficiency more than 30%, which approaches or is even slightly higher than the best results published to date. Besides, a group of blazed gratings with different groove parameters were fabricated and measured for comparing their measured efficiencies and with theoretical calculation. The influences of different groove parameters on the efficiency are quantitatively assessed. The error margins of all parameters are found, which might be a guide for making EUV blazed gratings.In addition, a multilayer-coated laminar grating was made; its peak efficiency is larger than 20%, which is comparable with the efficiencies of pratical laminar gratings. Besides, a grating with broad wavelength bandwidth was designed and fabricated. Its efficiency is ~10% in a 2.8 nm-wide wavelength range that is almost 3 times more than that of a multilayer grating not designed for broad band applications.
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