Binary sinusoidal single-order multilayer gratings for tender x-ray region

We propose and theoretically analyze a single-order diffractive optical element, termed binary sinusoidal multilayer grating (BSMG), to effectively suppress high-order diffractions while retaining high diffraction efficiency in the first order. The key idea is to integrate sinusoidal-shaped microstructures with high-reflectivity multilayer coatings. The dependence of the high-order diffraction property on the microstructure shape and multilayer coatings is investigated. Theoretical calculation reveals that the second-, third-, fourth-, and fifth-order diffraction efficiencies are as low as 0.01%. Strikingly, we show that first-order relative diffraction efficiency (the ratio between the intensity of the first diffraction order versus that of the reflected light) as high as 97.7% can be achieved. Thus, the proposed BSMG should be highly advantageous in future development and application of tender x-ray spectroscopy.