# 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
#### 4.3.1 Attosecond Dispersion Control by Multilayer Mirrors above 100 eV  
Specially designed aperiodic (binary or ternary multilayers) EUV mirrors allow for a large degree of freedom in shaping the EUV pulse characteristics by the reflection of those mirrors [59]. So far, multilayer mirrors in attosecond physics applications have been used as bandpass reflectors to preserve the spectral phase of the attosecond pulse that is defined in the generation process and by the dispersion characteristics of all EUV optical elements passed by the pulse. In this work, we demonstrate how specially designed non-periodic multilayer EUV mirrors furnish attosecond technology with the ability to control the spectral phase in addition to the spectral intensity of attosecond pulses. This offers a great degree of freedom in influencing the EUV pulse characteristics, such as the pulse shape, duration, frequency sweep, and central wavelength. To prove the validity of the concept for precision chirp control of attosecond EUV pulses, three multilayer mirrors exhibiting distinctly different GDD but similar reflectivity characteristics were developed [58]. Optimized for an angle of incidence of 45\({}^{\circ}\), they exhibit high reflectivity within the range of 100-130 eV with a comparable FWHM energy bandwidth of \(\Delta E\) = 11-13 eV and peaking at different central energies within the range of 107-122 eV. The multilayer designs were calculated and optimized by a Fresnel equation thin film code coupled to a needle optimization algorithm [44]. The mirrors were designed such that the GDD is almost maximum and mostly linear within the final attosecond pulse spectrum. Small shifts of the mirror spectrum due to the thin metal filter or the shape of the high harmonic cut-off spectrum were estimated and considered in the designs. The calculated designs were optimized for additional suppressed reflectivity contributions in the near vicinity of the main Bragg peak and were tested for stability against small layer thickness deviations. The final multilayer coating designs are displayed in the lower panels d-f of Figure 3.  
Figure 3: Characteristics of EUV chirped multilayer coatings designed and manufactured for the experiments. A set of EUV multilayers with positive (**a**), near-zero (**b**), and negative (**c**) group delay dispersion (GDD). The diagrams compare the measured (solid black) with the designed (dotted green) reflectivity curves. The calculated group delays (derivative of the spectral phase with respect to angular frequency) are also displayed (dashed red curve). The transmission of a 150 nm thick palladium (Pd) foil is additionally qualitatively plotted in panel (**b**), depicted by the blue dash-dotted line. The lower panels (**d–f**) show the corresponding mirror designs of the appropriate mirrors above. Each color represents one material, as explained in the legend of (**e**). While the designs of the positively and the negatively chirped mirrors contain around 30 layers, Mo/B4C, the almost unchirped mirror is a 17-layer Mo/Si/B4C stack. The mirrors were deposited by means of dual ion beam deposition (D-IBD) on flat super-polished (roughness \(<\)0.1 nm) glass substrates. Interface losses and compound formation were included in the calculation and could be compensated for within the coating procedure by adapting the deposition time. Figure 3a-c show the calculated reflectivity and group delay of the three realized multilayer mirrors versus photon energy, compared with the reflectivity measured by EUV/soft X-ray reflectometry using synchrotron radiation [60]. The measured and calculated EUV reflectivities are in excellent agreement, revealing maximum peak reflectivities between 4 and 10%. Notable deviations in the peak shape appear only in Figure 3c near 120 eV, possibly due to minor uncertainties in the deposition layer thicknesses. In our proof-of-concept experiments, radiation at photon energies below 100 eV was suppressed by a 150 nm thick Pd filter (its transmittivity is shown in Figure 3b by the blue dash-dotted line).