# Attosecond Pulse Shaping by Multilayer Mirrors
## 4 Achieved Results and Examples of Multilayer Mirrors for Attosecond Pulses
### A Normal Incidence Broadband 30-60 eV Mirror  
Many attosecond experiments are performed in the spectral range between 30 and 60 eV, which is easy to access with high harmonic sources [50; 51; 52]. The shortest attosecond pulses in this spectral range could be generated by polarization gating. [PERSON] et al. realized 130 as long pulses around 40 eV [51]. This and other experiments may benefit from broadband normal incidence EUV optics suitable for attosecond beam guidance and focusing. An aperiodic broadband mirror (B\({}_{4}\)C/Mo/Si) reflecting between 35 and 50 eV with a reflectivity up to 20% was designed and published by [PERSON] et al. [53]. In the following section, we present a periodic Si/Sc mirror centered at nearly the same central energy of \(\approx\)40 eV with comparable bandwidth to [PERSON] mirror but with periodic layers; it is thus an almost flat phase for a close to dispersion free reflection. This allows for spectrally filtering the high harmonics cut-off from krypton, offering isolated attosecond pulses below 200 as. Its design is chosen such that the high single interface reflectivity of Si and Sc is extended by an appropriate quarter-wave design to a bandwidth of more than 20 eV. Until now, Si/Sc multilayers have mainly been used at energies between 25 and 35 eV [54], just below the Sc M\({}_{2,3}\)-edge. Above this energy, both Si and Sc are highly absorbing, and the number of contributing periods in Si/Sc multilayers is very limited. The normal incidence reflectivity saturates between 35 and 45 eV for only \(\approx\)5 periods. The relatively high reflectivity between 5 and 7% is mostly independent of the mirror design due to a high single interface reflectivity of about 2%. This property has been utilized for the design of the following ultra-broadband mirror. Its design is chosen such that the already high Si, Sc reflectivity is extended to the high-energy side for a larger overall bandwidth. A 10-period Si/Sc coating with a period thickness of 14 nm (for a central energy of \(\approx\)50 eV) was chosen (Figure 1b). The mirror's designed and measured reflectivity are plotted together with the calculated phase in Figure 1a. A comparison with simulations reveals a maximum thickness error of below 0.8%, which is directly convertible to the shift in central energy. The measured EUV reflectivity confirms a successful implementation, a bandwidth of more than 20 eV, and a reflectivity between 5 and 15%. Simulations show that this mirror is capable of supporting the reflection of Fourier-limited 165 as long pulses that correspond to only 1.7 EUV field oscillations at 42 eV central energy (Figure 1c). This mirror thus allows for the phase-correct reflection of sub-2 cycle EUV pulses and is therefore at the possible duration limit at this energy. Figure 2a) and is in good agreement with the simulations. Figure 2 concludes the spectral (panel a) and the temporal (panel c) characteristics of this bandpass. Simulations reveal that the mirror alone supports the reflection of nearly Fourier-limited pulses of 64 as (Fourier-limit of the mirror: 63 as) calculated from the simulated spectrum (black line in Figure 2c) and the phase (red dash-dotted line). The effective bandpass bandwidth is experimentally limited by the transmission of the Zr filter, which is required for suppression of the infrared laser light and for tuning the spectral phase. Different filter thicknesses (150, 300, and 450 nm) allow for some tunability of the GDD for the sake of reducing the effective bandwidth (the peak of the multiplied spectrum, plotted by the blue dashed line, is shifted toward higher energies). It turned out that the combination of the mirror with a 300 nm Zr filter (yellow line, Figure 2a) compresses the incoming pulse to almost its Fourier-limit.