# 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
The throughput of this high-pass filter combination could be enhanced by fine-tuning the filter thickness and the mirrors' high-reflectivity band. Since isolated attosecond pulses can be extracted by spectral filtering from the cut-off part of the generated high harmonic spectrum [1], the high-energy extent of the spectrum must coincide with the high-reflectivity range of the mirror. Reflectivity above this energy window thus does not affect the attosecond pulse generation. The three mirrors are designed to introduce substantially positive GDD, negligible GDD, and substantially negative GDD, with computed values of \(19.5\times 10^{3}\) as\({}^{2}\), \(-0.5\times 10^{3}\) as\({}^{2}\), and \(14\times 10^{3}\) as\({}^{2}\), respectively. We implemented attosecond streaking by liberating photoelectrons from the \(2p\) sub-shell of an ensemble of neon atoms with sub-300 as EUV pulses filtered by the combination of a Pd foil and one of the bandpass multilayer mirrors described previously. The energy distribution of the ejected electrons has been streaked by the controlled (linearly) polarized electric field of near-single-cycle NIR laser pulses [61; 32; 62]. The streaked spectra for electrons collected in a narrow cone aligned with the laser polarization were recorded as a function of the delay between the ionizing EUV pulse and the streaking electric field of the NIR. To access the temporal intensity profile of the synthesized attosecond pulses and their frequency sweep, we performed a frequency-resolved optical gating (FROG) analysis [63] of the acquired streaking spectrograms. This method gives not only access to a full characterization of the laser's vector potential, it allows as well to characterize the spectral intensity distribution and the group delay variation [64; 65] of the final attosecond EUV pulse reflected off the mirrors after passing the filter, allowing for a direct comparison of its GDD with the design values of the mirrors' GDD. The resultant streaking spectrograms recorded with the three mirrors of Figure 3a-c are depicted in Figure 4a-c, along with their corresponding FROG retrievals in Figure 4d-f, respectively. We can now turn our attention to a quantitative evaluation of the chirp which was carried by the attosecond (EUV) pulse in the three experiments performed with the three different realized mirrors. Figure 5 shows the retrieved intensity and group delay of the attosecond pulses after reflection off the EUV multilayer mirrors and filtration by the transmission metal filter, as evaluated from the photoelectron spectrograms in Figure 4.  
The solid black lines in Figure 5a-c show a direct measurement of the EUV pulse spectrum at the target after passing through the metal filter and the corresponding mirror. Comparison of the retrieved EUV spectra (green dotted lines) with the directly measured photon spectra shows a remarkable agreement between the respective bandwidths, spectral profiles, and central energy positions. This agreement between retrieved and measured spectra highlights the precision with which EUV mirrors are designed and manufactured. It also demonstrates the power of attosecond streaking measurements coupled with the FROG/CRAB (complete reconstruction of attosecond burst) retrieval procedure. Figure 4: Measured and retrieved attosecond electron streaking spectrograms in the upper and lower row, respectively. Panels (**a–f**) display spectrograms recorded with attosecond pulses reflected off the mirrors described in Figure 3a–c, respectively. The energy shift in the recorded spectra is proportional to the vector potential \(A_{L}(t)\) of the streaking laser field at the instant of photoemission; hence, the dependence of this energy shift on the delay between the attosecond EUV pulse and the NIR laser field reflects the temporal evolution of the NIR laser field’s vector potential, \(A_{L}(t)\). Narrowing and broadening in the streaked electron spectra at the zero crossings are displayed by enhanced and diminished electron count rates, respectively.