**3. Experiments and applications**

If solids are used as a medium for the frequency upconversion to the XUV or x-ray regime, a different mechanism comes into play (Naumova et al. 2004); (Tsakiris et al. 2006); (Baeva et al. 2006)). At ultra-high intensities, the leading edge of a laser pulse can turn the solid surface into a high-density plasma where the electrons execute oscillations at the plasmavacuum interface driven by the ultra-intense field. The light pulse bounces back from the surface as if it were reflected by an oscillating mirror with relativistic speed (Bulanov et al. 1994) (Lichters et al. 1996); (Gordienko et al. 2004); (Tsakiris et al. 2006). Since the time it takes the mirror to sweep through a half period of the reflected field is contracted when the mirror and the incident wave counter-propagate, the reflected wave is blue-shifted. The highest occurring frequency is then given by the maximum Doppler upshift of Ωmax - 4γ<sup>2</sup> maxωL = 4(1 + a02)ωL, with γmax being the relativistic factor and ωL and a0 being the frequency and vector potential of the laser pulse. The emission of high-frequency photons is confined to small fractions of the laser period resulting in a periodic train of high-energy photon bursts. In a few-cycle laser field the emission of the high-energy photons is confined to the central wave cycle. Spectral filtering may therefore lead to single attosecond pulse generation (Ferenc Krausz 2009).

After its advent at the beginning of the century attosecond science soon was recognized to have the potential to add unprecedented temporal resolution to most of the spectroscopic techniques that have been developed at large scale facilities and laboratories around the world. Particularly (photo-) electron spectroscopy (see Fig. 4) was enriched by the attosecond toolbox when *attosecond streaking spectroscopy* emerged (cp. Fig 5) (Hentschel et al. 2001) (Itatani et al. 2002) (R Kienberger et al. 2002) (Markus Kitzler et al. 2002) (R. Kienberger et al. 2004). Attosecond XUV pulses are focused onto the sample atoms (usually in the gas phase but also surface emission experiments have been demonstrated) causing the release of electrons with a kinetic energy corresponding to the energy difference between the XUV photon energy and the electron affinity. This kinetic energy is detected by measuring the electron arrival time on a detector placed in a known distance of the interaction volume as in common electron time of flight spectrometry. For this type of spectroscopy (in contrast to techniques involving trains of attosecond pulses) it is a prerequisite that the XUV pulse duration is significantly shorter than a quarter of the laser period. For lasers with a central wavelength on the red side of the visible spectrum that amounts to round 500 attoseconds and as a direct consequence of the uncertainty principle this goes along with a minimal spectral width of 3 eV at a central photon energy around 100 eV. Together with the spectral resolution around 1% that is typically achieved in time of flight spectrometers this sets a lower limit to the spectral distance of features that shall be resolved and contrasts to the spectral resolution in the meV range that e.g. synchrotron sources achieve. Instead attosecond science exhibits its full strength in resolving ultrafast processes: For the sake of three orders of magnitude in spectral resolution it adds about 12 orders of magnitude in temporal resolution compared to the most contemporary XUV technologies known from synchrotrons and linear accelerators.

If the photoelectrons are set free in the presence of the electric field of a laser pulse their final kinetic energy can be altered (Hentschel et al. 2001) (Itatani et al. 2002). The net momentum change imparted on the electrons depends on the time delay between the attosecond XUV and the laser pulse (M. Schultze et al. 2011). A number of time of flight spectra is recorded with incrementally increased delay between the two pulses around the temporal coincidence.

#### Fig. 4. Attosecond Spectroscopy

Experiments designed to make use of the unprecedented temporal resolution that ultrashort laser pulses can offer usually follow the "pump-probe-scheme". A first laser pulse triggers the process under scrutiny and a second pulse probes the evolution after a defined time interval. From a sequence of a number of such measurements with variable temporal delay between the two pulses one can reconstruct the temporal evolution. The picture shows the inside of a vacuum chamber where such pump-probe experiments are performed based on the combination of visible laser pulses as pump- and attosecond XUV pulses as probe events. It is used to e.g. explore the electron dynamics in the atomic core. The gaseous sample streams out of the black nozzle into the interaction region and the released electrons are collected by a time-of-flight detector (cone from above) while the ionic fragments are detected by a mass spectrometer along the horizontal axis. The image was taken on the beam axis of the collinear propagating laser and xuv pulses .

Experiments designed to make use of the unprecedented temporal resolution that ultrashort laser pulses can offer usually follow the "pump-probe-scheme". A first laser pulse triggers the process under scrutiny and a second pulse probes the evolution after a defined time interval. From a sequence of a number of such measurements with variable temporal delay between the two pulses one can reconstruct the temporal evolution. The picture shows the inside of a vacuum chamber where such pump-probe experiments are performed based on the combination of visible laser pulses as pump- and attosecond XUV pulses as probe events. It is used to e.g. explore the electron dynamics in the atomic core. The gaseous sample streams out of the black nozzle into the interaction region and the released electrons are collected by a time-of-flight detector (cone from above) while the ionic fragments are detected by a mass spectrometer along the horizontal axis. The image was taken on the

Fig. 4. Attosecond Spectroscopy

beam axis of the collinear propagating laser and xuv pulses .

#### Fig. 5. Attosecond Streaking

If an attosecond XUV pulse releases photoelectrons from an atom while at the same time a strong visible laser pulse shines on the sample a streaking spectrogram can be recorded. When leaving the atom, the photoelectrons have a characteristic kinetic energy that corresponds to the difference between the electron affinity and the XUV photon energy. In the presence of an ultrastrong laser pulse this kinetic energy is modified by the electric field (as an electron is accelerated towards the positively charged plate in a capacitor). Since the electric field oscillates the change in kinetic energy depends on the difference in arrival time of the two pulses involved. The figure shows a measurement where the photoelectrons kinetic energy spectrum (along the vertical axis) is recorded for about 100 different delay settings between the two pulses (along the horizontal axis, the delay is given in femtoseconds). The result is an "oscilloscope" recording of the electric field of the laser pulse. Here Neon gas was ionized by an attosecond XUV pulse with photon energy about 120 eV (corresponding to 10 nm wavelength) and a duration of 200 attoseconds. The photon energy is sufficient to release electrons form either the *2p* or the *2s* shell of Neon thus the measurement allows to investigate potential timing differences in in the electron emission (M Schultze et al. 2010) .

With a step size roughly matching the XUV pulse duration the resulting spectrogram can look as in Fig. 5 and it is immediately evident that this so called "streaking spectroscopy" reveals the temporal evolution of the laser electric field (more precisely its vector potential) (E Goulielmakis et al. 2004) (Fiess et al. 2010). Beyond that, this sort of spectrograms resembles the signal of frequency resolved optical gating devices (FROG) known from laser science (Trebino & Kane 1993); (Mairesse & Quéré 2005); (Justin Gagnon & Vladislav S. Yakovlev 2009). Since their origin is a cross-correlation of two unknown pulses recorded with a known response function (here the photoionization) adaptive algorithms can extract all relevant parameters of **both** pulses involved (Michael Hofstetter et al. 2011). Such algorithms identify the temporal structure of the attosecond pulses and their temporal and spectral phase and thus fully characterize these light bursts that are the shortest signals that can be synthesized in the laboratory. It is an interesting feature of this streaking concept that the reconstruction actually explores the temporal structure of the released photoelectron wavepacket rather than of the light pulse and thus gives access to characteristics of the photo emission process that so far remained inaccessible to experimental physics. For photon energies that are sufficiently high to address two or more individual atomic orbitals and thus liberate electrons from different energetic states (as shown in Fig. 5) the streaking technique facilitates the investigation of subtle timing differences between them. The growing ability to shape the XUV emission according to the requirements of a particular experiment extends the technique to a wider spectral range. With specially tailored attosecond XUV pulses it was possible to discover that the emission of electrons from the neon 2s shell precedes the liberation of electrons originally bound in the 2p shell by about 20 attoseconds, the shortest time interval ever sampled directly (M Schultze et al. 2010).
