Aperiodic multilayer structures in soft X-ray optics

We review a series of studies that address the development and application of aperiodic multilayer structures (aperiodic multilayer mirrors) as soft X-ray (SXR) ($\lambda \approx 4$-$40$ nm) optical elements. We discuss the potential of such structures for reflecting SXR radiation in a broad wavelength range, primarily at normal radiation incidence, and as polarization elements (broadband polarizer mirrors and phase shifters). The results of multiparametric optimization are presented, and experimental data for aperiodic Mo/Si ($\lambda \ge 12.5$ nm) multilayer mirrors are outlined. The feasibility of advancing to the $\lambda \le 12.5$ nm domain by using other materials is examined, and the capabilities of aperiodic structures as elements of attosecond SXR optics are discussed. (instruments and methods of investigation)