# Attosecond Pulse Shaping by Multilayer Mirrors
## 4 Achieved Results and Examples of Multilayer Mirrors for Attosecond Pulses
### Above the Silicon L-Edge in the 100-150 eV Photon Range
#### 4.3.2 Cr/Sc Multilayer Mirror for Attosecond Pulses at 145 eV  
In this section, we present the first application of Cr/Sc multilayer mirrors to attosecond science. This material combination was optimized for attosecond pulses and is now applied to attosecond pulses for the first time. Most of the results were published in [66]. Previous sections demonstrated that multilayer mirrors provide a unique approach to spatial and spectral shaping, beam steering, and control of the spectral phase, with reasonably low reflective losses. It is shown below that optimizing this material system can not only be a key to (future) attosecond experiments in the water window [67] but is also a promising option for realizing new attosecond experiments around 130-160 eV--a spectral energy range wherein attosecond sources with sufficient photon flux are already available [28], but multilayer optics are limited. Figure 6 shows a simulated comparison of various established multilayer material systems reflecting attosecond pulses at a central energy of 145 eV, including an FWHM bandwidth of approximately 3 eV. The angle of incidence is 5\({}^{\circ}\) normal. The parameters were chosen as a trade-off between temporal and spectral resolution for attosecond experiments offering a high resolution. The simulations reveal an only weak suppression of (unwanted) low-energy out-of-band radiation in the range of \(\approx\)120 eV with lanthanum (La)-based multilayer mirrors (La/Mo, La/B\({}_{4}\)C). The typically used and necessary metal filter for blocking the near-infrared laser (typically a 200 nm thick Pd filter) cannot eliminate the out-of-band radiation due to its transmission properties. Therefore, (chirped) plateau harmonics are not sufficiently suppressed by such multilayer mirrors. This is a prerequisite for filtering single isolated attosecond pulses out of the cut-off region of the high harmonic spectrum. The suppression of low-energy (out-of-band) radiation is crucial for attosecond spectroscopy experiments for, e.g., direct observation of electron propagation [34] or delay measurements [68]. Mo/Si mirrors are well established and widely used in attosecond experiments at photon energies below the silicon L\({}_{3}\)-edge around \(\approx\)100 eV. This material system suffers from very low reflectivity above 100 eV. On the one hand, other molybdenum (Mo)-based multilayer systems like Mo/B\({}_{4}\)C, Mo/Y, Mo/Be, or Mo/Sr can provide a higher suppression of out-of-band radiation (in the case of Mo/B\({}_{4}\)C) together with a higher reflectivity (Mo/Y, Mo/Be, Mo/Sr) [69; 70; 71; 72]. However, on the other hand, they suffer from strong spectral modulations near the main reflectivity Bragg peak due to Kiessig fringes. As a result, this introduces additional group delay dispersion, which broadens the pulse in the time domain. Furthermore, beryllium (Be) is strongly toxic, and Mo/Sr is not stable since it shows long-term degradation. This limits experimental adoption  
Figure 6: The reflectivity performance of various material systems is compared around 145 eV. The simulated comparison is for a reflection of an FWHM bandwidth of 3 eV centered at a photon energy of 145 eV. A comparison in the time domain is shown in the small inset for the Cr/Sc and Pd/B\({}_{4}\)C system, including already the transmission through a 200 nm thick Pd filter. The Fourier-limit of the Cr/Sc mirror is shown in black. of these materials. A comparison of the reflection in the time domain is shown in the small inset of Figure 6. The multilayer mirrors are composed of Cr/Sc and the highly reflective system Pd/B\({}_{4}\)C [73]. The simulation takes the transmission through a 200 nm thick Pd filter (including its spectral phase) into account. The pulse reflection of the Cr/Sc mirror is close to its Fourier-limit and exhibits a Gaussian pulse shape, whereas the Pd/B\({}_{4}\)C system clearly shows unwanted temporal pulse broadening due to group delay dispersion. Temporal modulations resulting from the multilayer reflectivity fringes are also present.