# Generation of Attosecond Light Pulses from Gas and Solid State Media

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## Abstract

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^{−18}s) time scale. During the last decades, continuous efforts in ultra-short pulse engineering led to the development of table-top sources which can produce asec pulses. These pulses have been synthesized by using broadband coherent radiation in the extreme ultraviolet (XUV) spectral region generated by the interaction of matter with intense fs pulses. Here, we will review asec pulses generated by the interaction of gas phase media and solid surfaces with intense fs IR laser fields. After a brief overview of the fundamental process underlying the XUV emission form these media, we will review the current technology, specifications and the ongoing developments of such asec sources.

## 1. Introduction

_{L}λ

^{2}< 10

^{18}W/cm

^{2}μm

^{2}) and relativistic domains (I

_{L}λ

^{2}> 10

^{18}W/cm

^{2}μm

^{2}), respectively. In both media, trains of asec pulses are generated, when they interact with multi-cycle driving fs (>5 fs) laser fields. Isolated asec pulses are generated when the medium interacts with carrier-envelope-phase (CEP) stable few-cycle driving laser fields [27] or few-cycle fields combined with Polarization Gating (PG) [62,63,64], Ionization Gating (IG) [49,65,66] or LightHouse (LH) [67,68,69] approaches. Also, the development of PG approaches which are applicable for multi-cycle high power driving laser fields [49,64,70,71,72] led to the generation of intense isolated XUV pulses with duration <2 fs [48]. Another kind of temporal gating based on incommensurate multi-color combinations has recently led to the generation of intense isolated pulses of asec duration [50,71,73].

_{XUV}, λ is the XUV photon energy and the carrier wavelength of the driving field, respectively) and the output from the medium XUV photon flux (which scales with λ

^{−5.5}[74]) depends on the carrier wavelength of the driving field [10,11], the type of the gas, the focusing geometry (which is associated with the intensity of the driving field) and the phase matching conditions used for the generation [42,75,76,77,78]. For “low” ionization potential (I

_{P}) noble gases (Xenon, Argon, Krypton) driven by high power infrared (IR) laser pulses, photon fluxes in the range of ~10

^{11}photons/pulse have been measured for XUV photon energies up to ~30 eV [44,46,47,48,49,50,53,71], while for “high” I

_{P}noble gases (Helium, Neon) the photon flux drops by more than 4 orders of magnitude [44] and the XUV photon energy is extended up to ~150 eV. According to the cut-off energy law and incorporating the ionization saturation effects, extension of the XUV photon energies up to the water window (280–530 eV) and to the keV range requires the use of driving fields with carrier wavelengths longer than IR. This has been recently shown using driving pulses in the mid-IR spectral range [79,80]. However, due to the λ

^{−5.5}scaling of the XUV yield the application of mid-IR determines a strong reduction of the XUV photon flux compared to the IR driving pulses. Increasing the XUV photon flux in gas phase media using larger scale IR laser systems (e.g., in the PWatt range) is in general a complicated issue as it requires extremely loose focusing geometries in order to avoid the ionization saturation effects of the gas medium which are taking place in the intensity range of I

_{L}~ 10

^{14}–10

^{15}W/cm

^{2}. Nowadays, using CEP stable few-cycle IR driving fields in gas phase media, “low” intensity (intensities which are not sufficient to induce non-linear processes) isolated asec pulses with duration <150 asec can be routinely generated in the 20–100 eV photon energy range [63,80,81], while mid-IR laser driven sources look very promising for efficient generation of isolated asec pulses in the water-window spectral region and duration in the range of atomic unit of time [79]. For studies in the asec time scale using non-linear XUV processes “high” intensity (intensities which are sufficient to induce non-linear processes, e.g., I

_{XUV}> 10

^{11}W/cm

^{2}) asec pulses are required. “High” intensity trains and isolated asec pulses of duration <700 asec are currently generated in the 15 eV–35 eV photon energy range [45,46,47,48,50] using high power multi-cycle IR driving fields, while recent progress on the enhancement of the XUV photon flux led to the observation of non-linear process in atoms using XUV radiation in the ~60 eV photon energy range [51,52]. Although there is a lot of ongoing development in this direction, gas-phase is considered as the main asec source which led to impressive progresses in the field of ultrafast extreme ultraviolet (XUV) spectroscopy and of asec science with a broad range of fascinating applications in all states of matter.

_{L}~ 10

^{20}W/cm

^{2}, pulses of duration ~200 asec in the ~60 eV photon energy range can be generated with conversion efficiency ~10

^{−1}(~10

^{15}photons/pulse), while the generation of ~5 asec pulses in the keV photon energy range can take place with conversion efficiency ~10

^{−4}(~10

^{11}photons/pulse). Although these predictions constitute the solid surfaces as one of the most promising XUV asec sources, challenges experimental obstacles associated mainly with the stringent requirements on properties of the focused IR driving field (like the laser pulse peak to background contrast both spatially and temporally) and target technology (like the availability of the surface quality and the mechanical stability for the entire number of laser shots) did not yet allowed the sufficient progress to materialize experimentally the full potential of this approach leading to the observation of the optimum predicted values. Up to now, XUV frequency combs (generated with measured conversion efficiency in the range of ~10

^{−6}–10

^{−4}[54,55] and coherent continuum XUV radiation have been measured in the photon energy range of ~12–40 eV using multi- and few-cycles driving IR laser fields [67,87,88]. The emission of photons in the keV energy range [89] has been measured using the Vulcan PWatt laser system at Rutherford Appleton Laboratories [90]. Although these spectra can support the formation of asec pulse structures, the asec temporal localization has been measured directly only in the XUV energy range of ~12–20 eV [54] where the CWE harmonic generation mechanism is dominating. Additional experimental evidence that CWE harmonics have asec structure has been demonstrated in Refs. [67,91]. Due to the experimental obstacles mentioned before, the solid surface harmonics as a robust asec source (that can be utilized for further experiments) is still in the development phase and applicability up to now is mainly dedicated to the studies of the ultrafast dynamics of laser-plasma interaction [82,83,84,85,86]. Nevertheless, recent experiments performed in the non-linear XUV regime [54,92] and recent progress in the laser pulse engineering and solid target technology [5,6,35,36,37,67] verifies the feasibility of using solid surface harmonics in ultrafast XUV spectroscopy and attosecond science.

## 2. Theoretical Description of the XUV Emission from Gases and Solids

#### 2.1. XUV Emission from Gases

#### 2.1.1. Single Atom Response

_{L}~ 10

^{14}–10

^{15}W/cm

^{2}) linearly polarized multi-cycle fs laser pulse into a gas-phase medium, an XUV frequency comb, which consist odd harmonics of the driving frequency, is emitted in the direction of the laser field (Figure 1a). Due to the non-linearity of the harmonic generation process the divergence of the XUV beam is smaller compared the IR driving field. In appropriate phase matching conditions (atomic and macroscopic response) the phase locking between the harmonics leads to the formation of an asec pulse train. A band pass XUV filter arrangement can be placed at the XUV beam path in order to remove the IR beam and to select the wanted harmonic bandwidth.

_{i}(t

_{i}is named ionization time which takes places during the half cycle of the driving field, i.e., t

_{i}< T

_{L}/2 and T

_{L}is the period of the driving cycle of the driving laser field) with a tunneling rate Γ(t

_{i}) which can be found by the PPT-ADK theory [93,94]. Each electron trajectory in the continuum is defined by the ionization time t

_{i}and is weighted by the corresponding tunneling rate Γ(t

_{i}) which depends on the field

**E**(t) = −∂

**A**(t)/∂t (

**A**(t) is the vector potential) at the moment of ionization t

_{i}. The motion of the electron in the continuum starts with zero initial velocity (

**v**(t

_{i}) = 0) at a distance ℓ(t

_{i}) = |I

_{P}|/|e

**E**(t

_{i})| (I

_{P}is the ionization potential of the atom) which is much smaller compared to the length of the electron trajectory in the continuum and thus can be ignored, i.e.,

**x**(t

_{i}) ≈ 0. We note that the dipole approximation is made for the

**E**(t) and

**A**(t) to be independent of the spatial coordinates [10,13]. In the second step the electron gains kinetic energy from the driving field. Neglecting the influence of the atomic potential, the momentum of the electron in the continuum is

**p**(t) =

**p**

_{i}− e

**A**(t) (where

**p**

_{i}= e

**A**(t

_{i}) is the drift momentum). The third step corresponds to the case where the electron recollides at t

_{r}with the parent ion. Ion and electron are then recombined towards XUV emission.

_{r}(with t

_{i}< t

_{r}< T

_{L}), the position of the electron with respect to the nuclei is

**x**(t

_{r}) ≈ 0 (where $\mathit{x}\left(t\right)=\frac{e}{m}\left[\left(t-{t}_{i}\right)\mathit{A}\left({t}_{i}\right)-{{\displaystyle \int}}_{{t}_{i}}^{t}\mathit{A}\left({t}^{\prime}\right)d{t}^{\prime}\right]$ is the trajectory of the electron in the continuum) and the kinetic energy is K

_{r}=

**p**

^{2}(t

_{r})/2m = e

^{2}[

**A**(t

_{r}) −

**A**(t

_{i})]

^{2}/2m. Maximizing K

_{r}with respect to t

_{i}can be obtained that for ωt

_{i}= 108° and ωt

_{r}= 342° the maximum recollision energy is ${K}_{\mathrm{r}}^{\left(\mathrm{max}\right)}$ = 3.17 U

_{p}(U

_{p}is the ponteromotive energy of the electron). The photon energy of the emitted XUV photons is the sum of the electron kinetic energy and the binding energy of the atom, i.e., ħω

_{XUV}= I

_{P}+ K

_{r}. As the recollission process takes place every half cycle of the driving field, the emitted spectrum is an XUV comb which consists of only odd harmonic peaks (blue filled area in the down panel of Figure 1c). The spectrum depicts a plateau region (where the XUV yield is approximately constant) which is extended up to a cut-off region (where there is a rapid reduction of the XUV yield) where the photon energy is ħω

_{XUV}= I

_{P}+ 3.17 U

_{p}.

_{i}), recombination time (t

_{r}), and momentum

**p**. Using a saddle-point analysis it can be shown that, for a given driving laser intensity I

_{L}, there are two interfering quantum [95,96,97,98,99] electron trajectories (the “Long” and the “Short” noted as L and S in the down panel of Figure 1b) with different flight times ${\tau}_{q}^{L}\left({I}_{L}\right)={t}_{r}^{L}-{t}_{i}^{L}$ (with ${\tau}_{q}^{L}\approx {T}_{L}$) and ${\tau}_{q}^{S}\left({I}_{L}\right)={t}_{r}^{S}-{t}_{i}^{S}$ (with ${\tau}_{q}^{S}\approx {T}_{L}/2$) dominating the emission of a given harmonic order q in the plateau region of the spectrum. The two paths degenerate to a single one (noted as C in the down panel of Figure 1b) for the harmonics laying in the cut-off region of the spectrum. The phase of each harmonic order q results from the phase accumulated by the electron trajectory in the continuum (which can be approximate by $\approx -{\tau}_{q}^{L,S}{U}_{p}=-{a}_{q}^{L,S}{I}_{L}$) and the phase (ω

_{q}t

_{r}) introduced by the recombination time measured with respect to the reference time of the laser period (upper panel of Figure 1c), i.e., ${\phi}_{q}^{L,S}\approx {\omega}_{q}{t}_{r}^{L,S}+{\tau}_{q}^{L,S}{U}_{p}$. The green solid line in the down panel Figure 1c shows the harmonic spectral phase distribution calculated using the semi-classical 3-step model. It is evident that the harmonics generated in rare gases have an inherent linear chirp (which is positive for the S- and negative for the L-trajectory harmonics) due to the lack of synchronization during their generation process. Quantitatively, for a superposition of the harmonics this can be expressed as a quadratic dependence of the relative spectral phase on the harmonic frequency, i.e., for the qth harmonic the corresponding spectral phase is given by ${\phi}_{q}^{L,S}\left({\omega}_{q}\right)\propto \frac{{\left(q-{q}_{0}\right)}^{2}{\omega}_{L}}{4}\Delta {t}_{r}^{L,S}$, where $\Delta {t}_{r}^{L,S}$ is the temporal drift (harmonic chirp) between harmonics and q

_{0}is the first harmonic used in the superposition towards the formation asec pulse structure (detailed discussion on this matter can be found in Ref. [100].

#### 2.1.2. Generation of Asec Pulse Trains

#### 2.1.3. Generation of Isolated Asec Pulses

#### 2.1.4. Macroscopic Effects in HHG

- Linear effects: during propagation even linear dispersion causes a temporal stretch of the broad bandwidth laser pulse. Due to diffraction/focusing (and HHG is usually achieved in a focusing arrangement) the intensity distribution changes both along propagation, and in the transverse plane, affecting both the amplitude and the phase of the generated radiation.
- The high intensity laser beam evokes the Kerr-type non-linear refractive index of the generating medium, leading to self-focusing of the beam, and a blue-(red) shift on the rising (falling) slope due to self-phase modulation.
- Due to the ionization of the medium by the driving field, the presence of free electrons modifies both the linear and non-linear properties of the medium. This can even result in defocusing of the beam.

- Neutral dispersion—for XUV spectral domain negative, for IR components it is positive.
- Plasma dispersion—it is always negative, and scales as λ
^{2}, so IR is effected more. Since ionization fraction varies in space and time, this contribution is also varying. - Gouy phase shift—affects the focused IR beam, there is a negative contribution as we go from before focus to after focus.
- Dipole/atomic phase—proportional to the intensity of the IR field, and depends on whether the generation occurs via the short or long trajectory. As the driving field intensity is space and time dependent, this component also varies spatiotemporally.

- (a)
- Long (few tens of cm scale), low pressure (few mbar) target: Scaling up high order harmonic generation by increasing driving laser powers in the low density target regime has been investigated thoroughly in [99,112]. Phase matching conditions by balancing the effects of Gouy phase shift, neutral and plasma dispersion provides scaling principles. It has been found, that for this low ionization regime increasing laser powers requires the up-scaling of the geometric parameters (focal length, target length) and downscaling the target pressure. In this phase matching regime today’s state of the art laser pulses will require focusing of several tens (to a hundred) meters and gas target lengths of tens of centimeters (to meters).
- (b)
- Short (mm scale), high pressure (tens to thousands of mbar) target: Generating intense XUV radiation by intense laser pulses can also be achieved in a different phase matching regime, using high density short gas targets (jets) [113]. In this case the required focal lengths are somewhat shorter (few to ten meters), leading to higher intensity in the target. This means that the target will be ionized stronger than in the previous case, but due to the shorter medium length the distortion of the laser pulse can be reduced. The high number of interacting atoms, required to achieve a high XUV flux, in this case is confined in a small volume.
- (c)
- Quasi phase matching: Various quasi phase matching techniques have been applied for gas HHG to reduce the phase mismatch naturally accompanying the nonlinear process see [114,115] and references therein. In these arrangements either the target or the propagating laser beam is periodically modulated (by means of successive gas targets, propagation of the beam in a modulated waveguide or superposing a secondary modulating laser beam counter- or perpendicularly propagating with the generating laser pulse).

#### 2.2. XUV Emission from Solid Surfaces

_{L}value, which in terms of the focused laser intensity I

_{L}and laser wavelength λ

_{L}is given by ${a}_{L}^{2}={I}_{L}\text{}{\lambda}_{L}^{2}/[1.38\times {10}^{18}\text{}\mathrm{W}/{\mathrm{cm}}^{2}\text{}{\mathsf{\mu}\mathrm{m}}^{2}]$. The ROM mechanism prevails when a

_{L}is larger than unity, while for ${a}_{L}\lesssim 1$ the CWE mechanism is considerably more efficient. In the transitional range, the two processes can coexist and which one of the two dominates depends sensitively on the gradient of the plasma density profile [117,118]. Due to its superior properties and predominance at high intensities, the basis for the generation of single asec light pulses [87,119] will most probably be the ROM mechanism. More recently, theoretical work has revealed that, under certain conditions, another mechanism can dominate and produce harmonic radiation with superior efficiency [120,121,122,123,124,125]. In this mechanism dense electron nanobunches are formed at the plasma vacuum boundary giving rise to XUV radiation by coherent synchrotron emission (CSE). Simulations have shown that the dynamical evolution of the plasma filaments during the relativistic laser-plasma interactions allow the formation of such dense electron nanobunches on ultra-fast timescales. These charges accelerated by the strong fields of a relativistically intense laser pulse result in the generation of CSE extending to the x-ray regime. In what follows, the main features of the two most well-known mechanisms are described.

#### 2.2.1. The Coherent Wake Emission (CWE) Mechanism

_{p}satisfies the condition: ω

_{p}= qω

_{L}, with q an integer number. At these points, the plasma waves undergo linear mode conversion into EM-waves at harmonics of the fundamental laser frequency via inverse resonance absorption [128].

_{max,e}then the highest harmonic produced is ${q}_{cut-off}=\sqrt{{n}_{max,e}/{n}_{c}}$ with n

_{c}the plasma critical density for the given laser frequency. This property has been exploited in the autocorrelation experiment described in Ref. [54].

_{q}∝ q

^{3}(see Ref. [54]).

#### 2.2.2. The Relativistic Oscillating Mirror (ROM) Mechanism

_{L}≥ 1.0 is the so called relativistic oscillating mirror model. It was first proposed by Bulanov et al. [129] and later formulated and developed in detail by Lichters et al. [60]. The basic idea of the model is rather simple and is schematically shown in Figure 3. According to this model, the up conversion of the laser pulse light is due to the Doppler shifted reflection off a moving at relativistic speed surface.

^{−q}with q ≈ 5/2 [130]. It was also shown that the harmonic spectrum extends up to a maximum cut-off frequency ${\omega}_{co}\approx 4{\gamma}_{max}^{2}{\omega}_{L}$ where ω

_{L}is the incident laser frequency and γ

_{max}denotes the relativistic γ-factor corresponding to the maximum velocity at which the mirror moves towards the incoming light. The factor $4{\gamma}_{max}^{2}$ relates to the basic underlying mechanism which is Doppler shifted backscattering of light on a relativistic mirror. It should be pointed out here that these very important predictions of the ROM model have been confirmed not only in 1D-PIC simulations [82,130] but also in experiments [89,133]. Subsequent reports derived a more accurate exponent for the power-law (q ≈ 8/3 instead of q ≈ 5/2) and for the actual cut-off frequency ${\omega}_{co}\approx {\gamma}_{max}^{3}$ beyond the power-law roll-off [21,132]. Of late comprehensive semi-analytical models that take into account realistic experimental scenarios while working over a wider parameter space [134,135] have been proposed revealing correlation of different HOH regimes.

#### 2.2.3. Particle-in-Cell (PIC) Simulations

_{XUV}of the harmonic radiation as a function of the vector potential a

_{L}associated with the laser pulse (see Figure 4).

#### 2.2.4. Asec Lighthouse Effect

## 3. Asec Beam Lines

^{12}W/cm

^{2}[52]. Parabolic mirrors have been used for focusing solid surface harmonics of ~20 eV photon energy in a focal spot diameter of ≈ 16 μm reaching in this way intensities in the range of ~10

^{12}W/cm

^{2}[92]. Normal incidence spherical mirrors with reflectivity 10%–20% have been used for focusing an XUV beam of ~20 eV photon energy in the sub-4 μm level reaching intensities >10

^{13}W/cm

^{2}[150] while multilayer mirrors have been used for focusing an XUV beam of ~90 eV photon energy [29]. This XUV focusing geometry has been extensively used for the temporal characterization of asec pulses via IR/XUV cross-correlation [29,97,146], 2nd-order autocorrelation approaches (using spit spherical mirror in unit 5 or spit silicon plates in unit 3) [45,47,48,50,54,97], and for imaging the ion distribution produced by linear and non-linear processes at the focus of the XUV beam [98,150]. In order to characterize the XUV beam after the interaction with the system under investigation, XUV diagnostics as those described in unit 4 can also be placed at the output of the 5th unit.

#### 3.1. Asec Beam Lines for Gas Phase Media

^{14}W/cm

^{2}have been achieved at the focus of the XUV beam [150]. The energy of the XUV radiation in the interaction region was obtained from the measured pulse energy using an XUV calibrated photodiode (PD

_{EUV}) taking into account the reflectivity of the gold spherical mirror. The PD

_{EUV}has been placed after the aperture (A) and the filter (F). The harmonic spectrum measured by recording energy resolved photoelectron spectra resulting from the single-photon photoionization of Ar by the harmonic comb, is shown in Figure 8b. The electron spectra were recorded using a μ-metal shielded time-of-flight (TOF) ion/electron spectrometer, attached to a second XUV beam-line branch (upper branch in unit 5 of Figure 8a). The TOF can be set to record either the photoelectron energy distribution or ion-mass spectrum. The measured photoelectron distribution does not differ significantly from the XUV spectral distribution as in the photon energy range between 15 eV and 30 eV the single-photon-ionization cross section of Argon is almost constant. Ions are measured using an Ion Microscope (IM) [98,155] (down branch in unit 5 of Figure 8a) that images the focal area onto a Micro-channel Plate (MCP) detector equipped with a phosphor (Ph) screen anode. The resolution of the IM is ≈ 1 μm. In order to have the same experimental conditions in both the TOF and the IM set-ups, the TOF branch was constructed in an identical way to the IM. Thus, the two symmetric branches in Figure 8a are used for different diagnostics, i.e., for measuring energy resolved photoelectron spectra resulting from the interaction of the XUV with gas targets (upper branch) or the spatially resolved ion distribution resulting from the interaction of the XUV with gas targets (lower branch). Figure 8c shows the spatial ion distributions at the XUV focus induced by single- and two-XUV-photon ionization of Ar and He, respectively. We note that as the single-XUV-photon ionization process is proportional to the intensity of the radiation, the Ar

^{+}distribution corresponds to the intensity distribution of the XUV at the focus.

^{14}W/cm

^{2}[48], while their durations can be obtained by means of 2-IVAC measurements in case the CEP of the driving field is stabilized or measured and tagging approaches are applied [48,156]. These pulses were used for the observation of two-XUV-photon double ionization in Xenon gas (which has been placed in T-GJ) [48], for time-resolved XUV spectroscopy studies [157] and XUV-XUV pump-probe measurements of ~1 fs scale dynamics in atoms [48] and molecules [158]. The temporal characterization of asec pulses generated in gas-phase media will be described in Section 4.

#### 3.2. Asec Beam Lines for Solid Surface Media

^{11}W/cm

^{2}. A 1.5 m long magnetic bottle (MB) electron spectrometer was attached to the third chamber with its axis perpendicular to the beam propagation axis (Figure 9a). The MB was used in order to record energy-resolved PE spectra produced through single- and two-photon ionization (ATI) of Argon (Figure 9b,c). The concept of the above experimental arrangement was used for the temporal characterization of the asec pulse trains generated by the CWE process in the photon energy range of ~12–20 eV [54].

## 4. Characterization of XUV Sources

#### 4.1. Temporal Characterization of Asec Pulses Generated in Gases

#### 4.1.1. The 2-IVAC Method in Gas-Phase Harmonics

^{11}W/cm

^{2}), a dispersionless autocorrelator (XUV wave front spitting device like split mirror) and a spectrally flat and temporally instantaneous non-linear detector. The non-linear detector is an atomic/molecular system which is ionized by a non-resonant 2-XUV-photon excitation process [45,47,169,170] or a 2-XUV-photon excitation process where the width of the resonances are much smaller than the bandwidth of the XUV radiation [48,156]). The ionization products (electrons or ions) can be detected by a TOF spectrometer. In case of fulfilling these requirements the measurement of the asec pulse duration can be directly obtained by the width of the peak of the 2-IVAC trace (${\tau}_{AC}$) after dividing with $\sqrt{2}$, i.e., ${\tau}_{XUV}={\tau}_{AC}/\sqrt{2}$. We note that the peak to background ratio of a 2-IVAC trace cannot be higher than ≈2:1 [169] and in case of pulse trains the resulted duration reflects the average duration of the individual asec pulses in the train. Figure 10 shows a 2-IVAC measurement of an asec pulse train and an isolated ~1 fs XUV pulse as has been obtained using the arrangement Figure 10a. A high power ≈ 35 fs IR laser beam was focused into the Xenon gas jet where the harmonics were generated. The laser focus was placed before the Xenon gas jet at a position which is favorable for temporal confinement in the asec scale. The harmonic beam was passed through 150 nm thick Indium filter to select the 9th–15th harmonic. This beam was then focused by a split spherical gold mirror of 5 cm in focal length into a Helium pulsed gas jet. The relative field amplitudes of the harmonics in the interaction region were measured to be 1, 0.4, 0.3, and 0.25 for the 9th, 11th, 13th, and 15th harmonics, respectively. The Helium ions produced by a 2-XUV-photon ionization process (Figure 10b) were recorded by a μ-metal-shielded time-of-flight (TOF) spectrometer. The 2-IVAC trace synthesized by the 9th–15th harmonics is shown in Figure 10c. The trace was obtained by recording the He

^{+}signal as a function of the delay between the XUV replicas. The duration of the asec pulses in the train was found to be (660 ± 50) asec. Asec pulse trains have been also temporally characterized by means of mode-resolved autocorrelation techniques using 2-XUV-photon-above-threshold ionization (ATI) schemes [159]. This technique is promising for extending the 2-IVAC method to high XUV photon energies and performing FROG-type [171] measurements in the XUV domain.

^{2+}ions produced by a 2-XUV-photon direct double ionization process (TPDDI) (Figure 10d) were recorded by a time-of-flight (TOF) spectrometer. In this process, the single-XUV-photon absorption is by passing the XUV continuum through an ensemble of autoionizing states (AIS). The 2-IVAC trace synthesized by the broadband continuum XUV radiation is shown in Figure 10e. The trace was obtained by recording the Xe

^{2+}signal as a function of the delay between the XUV replicas in an interval around zero delay values. At longer delay times the 2-IVAC trace provides information about the wave packet evolution induced by the atomic coherences associated with the coherent excitation of the AIS. The duration of the XUV pulse was found to be ≈${1.5}_{-0.7}^{+0.2}$ fs, which is an overestimation of the pulse duration. The measured “broad” pulse is a consequence of the appearance of not resolved side peaks present due to the unstable CEP of the high power multi-cycle laser system and the measurement of averages for many laser shots at each delay. We note that the influence of the AIS in the measured pulse duration is negligible as the width of the states is much smaller compared to the bandwidth of the XUV pulse or equivalently the measured beating periods are much larger than the pulse duration. Detail information on this matter can be found in Ref. [48].

#### 4.1.2. The RABBITT Method in Gas-Phase Harmonics

_{q}signal is proportional to cos(2ω

_{IR}τ + φ

_{q}

_{−1}-φ

_{q}

_{+1}+ Δφ

_{at}) (where q = 12, 14, 16 is the order of the sideband ω

_{IR}is the frequency of the IR field, τ is the delay between the IR and the XUV and Δφ

_{at}are the atomic phases of each of the two photon transitions responsible for the sideband peaks [146]) the phase difference between the consecutive harmonics can be obtained by the measured phase shift between the sideband oscillations. Figure 11c shows the RABBITT traces (dependence of the sideband (S12, S14, S16) signal as a function of τ for three different positions of the laser focus with respect to the Xe gas jet normalized to the “total” signal (lower line in each panel). The oscillation period of the “total” signal which corresponds to the period of the driving field, i.e., ω

_{IR}, is due to IR intensity changes caused by interference effects of the two IR beams (shown as “RABBITT beam” and “annular IR beams used for XUV generation” in Figure 11a) in the harmonic generation region. This oscillation disappears in case of using a non-interacting with the XUV generation medium IR auxiliary pulse (red dashed line in Figure 7). Figure 11d shows the phases of the consecutive harmonics obtained by the RABBITT traces (the phase of the 9th harmonic was extrapolated from a quadratic fit to the measured phases of the 11th to 17th harmonics as is shown in solid line of Figure 11d). It is evident that as the focus of the IR beam is moving from the position “Focus before jet” to the position “Focus after jet” as the chirp is changing from positive to negative values. The corresponding reconstructed asec pulse trains are shown in Figure 11e.

#### 4.1.3. Temporal Characterization of Asec Pulses Using FROG-CRAB

#### 4.2. Characterization of Asec Pulses Generated in Solid-Surfaces

#### 4.2.1. Temporal Characterization of Asec Pulses Using the 2-IVAC Method

^{18}W/cm

^{2}, yielding a normalized amplitude a

_{L}≈ 1.5 for λ = 800 nm. At this intensity region, both mechanisms (CWE and ROM) may play a role in the harmonic generation. However, the appearance of a distinct cut-off in the harmonic spectrum and the scaling of this with the target density (with a higher density target (BK7) the cut-off moved to higher order harmonics) suggest that the CWE mechanism provides a dominant contribution in the harmonic generation process of this experiment. The harmonic beam was passed through 150 nm thick Indium filter to select the 8th–14th harmonic. This beam was then focused by a split spherical gold mirror of 15 cm in focal length into a Helium pulsed gas jet. The Helium ions produced by a 2-XUV-photon ionization process were recorded by a time-of-flight (TOF) spectrometer.

_{XUV}≈ 44 fs. The fact that this value is very close to the laser pulse duration indicates that CWE scales nearly linearly with laser intensity, which agrees with the findings in Ref. [22].

_{L}, is clearly discernible. This is in contrast to the time structure of atomic harmonics, which is characterized by a pulse spacing of T

_{L}/2 due to the absence of even harmonics in the emission spectrum. Fitting a train of Gaussian pulses to the measured AC trace gives an estimate for the duration of the individual pulses of τ

_{XUV}≈ (0.9 ± 0.4) fs FWHM.

#### 4.2.2. Spectrally Resolved Spatial Phase and Amplitude Retrieval of Solid-Surface Harmonics

_{2}~ 5 × 10

^{19}W/cm

^{2}) a softer plasma mirror (higher L/λ) is more dented compared to a stiffer one (smaller L/λ) during the high harmonic generation resulting in an increase in the measured beam divergence [118], whereas at a comparatively lower laser intensity (I

_{1}~ 1 × 10

^{18}W/cm

^{2}) the light pressure is not sufficient to affect the mirror curvature during the harmonic generation leading to the shaded area in Figure 14e. This information can in turn be used to infer the light induced curvature of the plasma mirror validating models of relativistic optics [84].

## 5. Conclusions and Ongoing Development on Gas-Phase and Solid-Surface Asec Sources

_{2}[186] that have been used are not applicable at higher photon energies because the target will be single photon ionized. Candidate processes for this extension are two-photon multiple ionization [156] and two-photon ATI [92]. Such types of developments are currently designed and will be soon implemented in asec laboratories. ELI-ALPS will provide advanced features for such developments, i.e., high XUV pulse energies at kHz repetition rates.

^{−1}, leading to an asec duration that scales as λ

^{−1/2}and thus to shorter pulse durations; (ii) Since the ponteromotive potential scales as λ

^{2}and so does the kinetic energy of the recolliding electron at the moment of the recombination and thus the cut-off energy of the harmonic spectrum [9,10] very high photon energy asec pulses can be generated. However, the harmonic generation (HHG) efficiency scales as λ

^{−5.5}. This bottleneck defines new challenges for mid-IR laser sources with increased peak power and at the same time consolidation of phase matching approaches that increase the HHG efficiency. One step further, considering relativistic interactions, the crucial parameter is the normalized vector potential $a={\left(2{e}^{2}{\lambda}_{0}^{2}I/\pi {m}_{e}^{2}{c}^{5}\right)}^{1/2}$ = 0.855 × 10

^{−9}I

^{1/2}[W/cm

^{2}] λ [µm]. The relativistic regime is reached when α ≥ 1. Consequently, long wavelengths are entering the relativistic regime at lower intensity. Interactions with mid IR lasers become relativistic at 10

^{16}–10

^{17}W/cm

^{2}.

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) A schematic representation of High-order harmonic generation (HOHG) in gas-phase media; (

**b**) (upper panel) An oversimplified picture of the recollision process. t

_{i}, t

_{r}, MI, XUV, ATI are the ionization time, recollision time, multiple ionization, generation of XUV radiation and ATI photoelectrons, respectively. The red arrow shows the polarization direction of the driving field and the black line the electron trajectory; (down panel) High-order-harmonic generation process in the spirit of three-step model. L (black line), S (green line) show the “Long” and “Short” electron trajectories contribute to the plateau harmonic emission, respectively. t

_{e}

^{L}and t

_{e}

^{S}are the corresponding emission times. C (red line) shows the electron trajectory contribute to the cut-off harmonic emission; (

**c**) (upper panel) Emission times as a function of the harmonic order (calculated using the semi-classical 3-step model for I

_{L}= 2 × 10

^{14}W/cm

^{2}and I

_{P}= 15 eV, and λ = 800 nm). t

_{e}

^{L}(I

_{L}) and t

_{e}

^{S}(I

_{L}) depict the emission times (which depend on I

_{L}) corresponding the “Long” and “Short” trajectory harmonics. In the spirit of semi-classical 3-step model the emission times is the real part of the recombination time t

_{r}. (down panel) Calculated harmonic spectrum (blue filled area) with ω

_{q}= (2q + 1)ω

_{L}(where ω

_{L}is the frequency of the IR field). The “Long” and “Short” trajectory harmonics, which contribute in plateau region, degenerate to a single trajectory in the cut-off region of the spectrum. The green solid line is the spectral phase distribution of the S and L trajectory harmonics. The black solid line illustrates the XUV continuum spectrum emitted in case of a single electron recollision. The line-shaded area illustrates the bandwidth of the XUV radiation which passes through a band pass XUV filter.

**Figure 4.**Variation of the XUV pulse efficiency η

_{XUV}with the normalized vector potential a

_{L}for three different spectral ranges determined by the indicated thin filter used. Part of the figure from Ref. [87].

**Figure 5.**Asec lighthouse effect for few-cycle laser-driven plasma mirrors. (

**a**) When an intense few-cycle laser pulse interacts nonlinearly with a plasma mirror, the sub-cycle modulation of the temporal laser wavefronts is associated with the generation of a train of asec light pulses, which all propagate in a collimated beam along the direction normal to the laser wavefronts at focus; (

**b**) When the laser wavefronts are made to rotate in time at focus (WFR), each asec pulse of the train is emitted in a slightly different direction. From Ref. [67].

**Figure 6.**Asec ligthouses from plasma mirrors. (

**a**) Schematic of the experimental set-up; (

**b**) Measured XUV beam profile in the absence of WFR for a fixed arbitrary CEP value (left panel) and the corresponding XUV spectrum at the center of the XUV beam profile (right panel); (

**c**) Measured XUV beam profile in the presence of WFR for a fixed arbitrary CEP value (left panel) and the corresponding XUV spectrum at the center of the spatial XUV beam profile (right panel). From Ref. [67].

**Figure 8.**(

**a**) Beam line for the generation of intense asec pulses in gas phase media. L: Lens; P-GJ: Pulsed gas jet used; Si: Silicon plate; A: Aperture; F: Filter; PD

_{EUV}: Calibrated XUV photodiode; T-GJ: Target gas jet; TOF: Time of flight ion/electron spectrometer; IM: Ion Microscope; SM: Spherical mirror; MCP: Microchannel plate detector; Ph: Phosphor screen; CCD: CCD camera. The y-axis is parallel to the TOF axis and the x-axis is parallel to the plane of the detector (MCP + Ph); (

**b**) The spectrum of the harmonics used in the TOF and IM branch; (

**c**) Spatial ion distributions at the XUV focus induced by single- and two-XUV-photon ionization of Ar and He; (

**d**) Continuum XUV spectrum generated when the PG optical arrangement [64] is introduced in unit 1. Figures (

**a**–

**c**) from Ref. [150] and Figure (

**d**) from Ref. [48].

**Figure 9.**(

**a**) Schematic diagram of the experimental setup. PM1, 2, 3: parabolic mirrors; ST: solid target; IL1, 2: imaging systems; F: filters; S: XUV flat field spectrometer; S-Si, Si: silicon plates; GJ: Ar gas jet; Sc: the scintillator used for the imaging of the XUV focus (the image in the inset); MB: 1.5 m long magnetic bottle; MCP: microchannel plates; M: mirrors; P: turbo pumps; (

**b**) Single-photon photoelectron spectrum of Ar (black line). The ionizing radiation consists of harmonic 11th–16th. The measured PE (crossed circles) and calculated overall spectral transmission (red rhombs) of the setup is shown in the inset; (

**c**) Two-XUV-photon ATI photoelectron spectrum of Ar. The black line filled in green shows a single-shot trace, the gray dotted line is an average of nine shots and the red line is obtained from the nine shots average (gray dotted line) after a 150 points moving average is performed. The orange and green shaded areas depict the SPI and ATI signals, respectively. Figure from Ref. [92].

**Figure 10.**(

**a**) Experimental set-up showing the 2nd order volume autocorrelation (2-IVAC) arrangement. It is a 3D illustration of a part of the beam line shown in Figure 8; (

**b**) 2-XUV-photon ionization scheme of Helium using the 9th–15th harmonics passing through Indium filter; (

**c**) 2-IVAC trace of an asec pulse train synthesized by the 9th–15th harmonics. The duration of the asec pulses in the train is found to be (660 ± 50) asec. The trace was obtained by recording the He

^{+}signal as a function of the delay between the XUV replicas. Gray dots are the raw data and the yellow correspond to a 10-point running average. The purple line is a 12-peak sum of Gaussians fit to the raw data; (

**d**) 2-XUV-photon direct double ionization (TPDDI) scheme of Xenon using the broadband coherent continuum XUV radiation (orange filled area) generated in Xenon gas jet by means of PG arrangement. The XUV spectrum is also shown in Figure 8d. In this process the single XUV photon absorption is passing through an ensemble of autoionizing states (AIS); (

**e**) 2-IVAC trace of a ≈ ${1.5}_{-0.7}^{+0.2}$ fs XUV pulse. The trace was obtained by recording the Xe

^{2+}signal as a function of the delay between the XUV replicas. The blue squares are the raw data and the red line is a Gaussian fit to the raw data. The pulse broadening is a consequence of the appearance of side pulses due to the unstable carrier-envelope-phase (CEP) of the high power multi-cycle laser system. Figure (

**c**) from Ref. [97] and Figures (

**d**,

**e**) from Refs. [48,156].

**Figure 11.**(

**a**) Experimental set-up showing the Resolution of Attosecond Beating by Interference of Two photon Transitions (RABBITT) arrangement. It is a 3D illustration of a part of the beam line shown in Figure 8; (

**b**) XUV + IR ionization scheme; (

**c**) RABBITT traces at three different positions of the laser focus with respect to the Xenon gas jet (focus before jet, focus on jet and focus after jet). The gray dots are the measured data, the yellow circles correspond to a running average of 15 points and 40 points for the total signal. The solid purple lines are sinusoidal fits to the raw data over 13 oscillations on the sideband traces and over 6 oscillations on the total signal; (

**d**) Phases of the consecutive harmonics obtained by the RABBITT traces; (

**e**) Reconstructed asec pulse trains. Figures (

**a**,

**c**–

**e**) from Ref. [97].

**Figure 12.**(

**a**) Experimental Frequency Resolved Optical Gaiting for Complete Reconstruction of Attosecond Bursts (FROG-CRAB) traces for an isolated asec pulse generated by the polarization gating technique in Argon using an Al filter with a thickness of 100 nm (

**a**) and 300 nm (

**b**), respectively; (

**c**,

**d**) Reconstructed amplitudes (black solid lines) and phases (red dashed lines) for the experimental traces shown in (

**a**,

**b**), respectively. From Ref. [63].

**Figure 13.**2-IVAC measurement of high-order-harmonics emitted from solid-surface. The data are obtained from He

^{+}and H

_{2}O

^{+}signal in the TOF mass spectra by varying the delay between the two parts of the split mirror. The red circles represent the He

^{+}signal produced by 2-XUV-photon ionization and the blue circles the H

_{2}O

^{+}signal produced by single photon ionization. (

**a**) A coarse scan over the laser pulse duration. A Guassian fit to He

^{+}raw data yields a duration of ≈ 44 fs; (

**b**) a fine scan near zero delay. The raw data are shown as grey circles connected by grey lines. The green line is a fit to the raw data (grey circles) of a sequence of Gaussian pulses to the second-order XUV AC signal yielding τ

_{XUV}≈ (0.9 ± 0.4) fs. In both panels, the H

_{2}O

^{+}signal serves as reference for monitoring the XUV intensity and provides a clear indication of the absence of modulation as a result of single-photon ionization. From Ref. [54].

**Figure 14.**(

**a**–

**d**) Angle-resolved high harmonic spectra from plasma mirror diagnosed under different interaction conditions. The main pulse is contrast cleaned with a double plasma mirror temporal contrast cleaning set up and the plasma density gradient (L/λ) is tuned with a delay controlled pre-pulse; (

**e**) The beam divergence Δθ(ω) shows different behavior with L/λ at different intensity regimes (I

_{1}~ 1 × 10

^{18}W/cm

^{2}and I

_{2}~ 5 × 10

^{19}W/cm

^{2}). The figures (

**a**–

**e**) from Ref. [118].

**Figure 15.**Retrieved amplitude |h

_{12}| (solid curve) and phase profile φ

_{12}(dashed curve) of the 12th harmonic in the focal plane (

**a**) for ROM case (peak intensity on target is I

_{L}~ 7 × 10

^{18}W/cm

^{2}, main beam waist w

_{0}= 6.2 µm and appropriately long plasma density gradient [118]) and (

**b**) for CWE case (peak intensity on target is I

_{L}~ 3 × 10

^{17}W/cm

^{2}, main beam waist w

_{0}= 14.4 µm and appropriately short plasma density gradient [118]). x is the focal plane coordinate. Figure from Ref. [86].

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chatziathanasiou, S.; Kahaly, S.; Skantzakis, E.; Sansone, G.; Lopez-Martens, R.; Haessler, S.; Varju, K.; Tsakiris, G.D.; Charalambidis, D.; Tzallas, P.
Generation of Attosecond Light Pulses from Gas and Solid State Media. *Photonics* **2017**, *4*, 26.
https://doi.org/10.3390/photonics4020026

**AMA Style**

Chatziathanasiou S, Kahaly S, Skantzakis E, Sansone G, Lopez-Martens R, Haessler S, Varju K, Tsakiris GD, Charalambidis D, Tzallas P.
Generation of Attosecond Light Pulses from Gas and Solid State Media. *Photonics*. 2017; 4(2):26.
https://doi.org/10.3390/photonics4020026

**Chicago/Turabian Style**

Chatziathanasiou, Stefanos, Subhendu Kahaly, Emmanouil Skantzakis, Giuseppe Sansone, Rodrigo Lopez-Martens, Stefan Haessler, Katalin Varju, George D. Tsakiris, Dimitris Charalambidis, and Paraskevas Tzallas.
2017. "Generation of Attosecond Light Pulses from Gas and Solid State Media" *Photonics* 4, no. 2: 26.
https://doi.org/10.3390/photonics4020026