Soft X-ray and Extreme Ultraviolet (EUV) radiation (defined as light with wavelength in the 1 to 100 nm range) has been playing a growing role in major scientific and industrial applications over the last 20 years: astrophysics and solar physics, materials sciences, biology, semiconductor industry, plasma diagnostics. Especially the emergence of novel EUV/X-ray sources with unprecedented brightness and coherence (4th generation synchrotrons, free-electron lasers, tabletop lasers, high-harmonic generation and attosecond sources) has ushered a new era in the fields of materials science, chemistry, plasma physics, biology and life sciences. Several scientific and technological breakthroughs have been achieved recently. X-ray radiation from the SPRING-8 synchrotron light source in Japan has been focused on a spot with diameter smaller than 10 nm; this constitutes the smallest spot of light ever produced and could enable studies with the most exquisite spatial resolution. The generation of ultrashort EUV pulses with a duration less than 0.1 femtosecond (= 100 attosec-onds) made it possible for the first time to observe electron orbitals in molecules. Photolithography scanners based on EUV light have entered the world of semiconductor manufacturing in order to produce the next generation of computer chips. In 2007, the EUV telescopes aboard NASA's Solar Terrestrial Relations Observatory (STEREO) mission provided the first 3D images of the solar corona with its protuberances. Furthermore, since 2010, the Solar Dynamics Observatory (SDO), NASA's most advanced solar mission , has been continuously transmitting full-disk images of the solar corona every 10 seconds, simultaneously at 7 EUV wavelengths with 1 arcsec resolution. Observing the Sun with such unprecedented temporal and spatial resolution has led to groundbreaking discoveries related to the Sun's extremely complex magnetic field and has led to better understanding of extreme events such as solar flares and coronal mass ejections, which can seriously affect earth and space environments. These breakthroughs have been enabled by the development of new optical components dedicated to the EUV/ X-ray spectral range. The main challenges in fabricating EUV/X-ray optics come from the properties of materials in this spectral range. With the refractive index of any material being very close to 1, the refractive phenomena at any interface are weak and the reflectivity of any single material at non-grazing incidence angles is near zero. Moreover, all materials strongly absorb X-rays, so the transmission of any component is almost zero. Multi-layer interference mirrors are enabling optical components in most EUV/X-ray optical systems. Demonstrated experimentally for the first time in the 1970s by E. Spiller, these mirrors consist of periodic or aperiodic structures of alternating thin film layers of 2 or more materials with nanometer-scale thickness, deposited on an optical sub-strate. The constructive interference between the layers results in efficient reflectance at EUV/X-ray wavelengths even at near-normal incidence angles thus enabling the operation of a wide range of optical components including imaging and illumination systems, reflective filters, grating spectrometers and polarizers. However, the fabrication of high-performance multi-layer coatings poses serious technical challenges. Multi-layer coatings need to obey several stringent (and often conflicting) requirements, including: (i) contain materials with good optical contrast in the wavelength region of operation (ii) contain tens or hundreds of layers with nanometer-scale thickness, where each layer is deposited with picometer-scale precision (iii) form stable layer interfaces with minimal interdiffusion and with smoothness on the order of the atomic dimension, (iv) have low thin film stress, (v) have stable reflective performance for periods up to 10 years, or even longer. This special section aims to provide a survey of current topics and major development lines in the very active research area of X-ray and EUV multilayer coating development. It gathers studies of the properties of these nanoscale structures (microstructure, mechanical stress, lifetime stability) with a focus on new promising material combinations and on short-period multilay-ers, with individual layer thicknesses around (or less than) 1 nm. Technological developments, new characterization 516
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