Table-top sources of coherent extreme ultraviolet (XUV) radiation are nowadays used in many laboratories, delivering pulses with attosecond duration. These sources are based on high-order harmonic generation (HHG), a process that requires intensities of around ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, thus setting stringent requirements on the driving laser. Ultrashort laser pulses with rather high pulse energy are typically employed, implicitly limiting the repetition rate to a few kilohertz. Many techniques, such as coincidence spectroscopy [1,2], photoelectron spectroscopy on surfaces [3], and time-resolved microscopy [4,5] would, however, benefit greatly from higher repetition rates. A promising route toward multimegahertz attosecond sources relies on HHG inside a passive enhancement cavity [6,7]. In such a scheme, subsequent laser pulses are coherently superimposed, leading to a total power enhancement of two to three orders of magnitude [8]. Although successfully demonstrated for attosecond pulse trains [6,7,9–11], the generation of isolated attosecond pulses (IAPs) inside a cavity remains an unsolved challenge, limited mainly by dispersion management [12,13] and outcoupling problems [14]. Traditional IAP gating concepts [15,16] usually imply severe manipulations of the laser field and cannot easily be brought in line with passive enhancement cavities. Especially dispersion control increases in complexity if shorter pulses and IAP gating schemes are considered. Recent attempts are however pointing towards intracavity gating and improved outcoupling [11,17].

We recently proposed a new gating concept for IAPs [18], noncollinear optical gating (NOG), which has the potential to facilitate intracavity gating and efficient outcoupling at once. Similar to the attosecond lighthouse [19], NOG employs angular streaking [20] and combines this concept with noncollinear HHG, proposed [21,22] as an outcoupling method for intracavity HHG. The noncollinear generation of several angularly separated synchronized IAPs includes the functionality of an all-optical broadband XUV beam splitter, offering new possibilities for IAP–pump–IAP–probe experiments [23,24] where the low photon flux of today’s IAP sources is a severe limitation. Moreover, NOG can simplify the separation of the generated IAPs from the driving field, thus reducing XUV photon flux losses.

In this Letter, we provide, to the best of our knowledge, first experimental evidence that angular streaking of attosecond pulse trains can be realized in a noncollinear geometry (Fig. 1). We demonstrate a time-to-angle mapping of attosecond pulse trains, which leads to the emission of angularly separated spectral XUV continua, indicating the generation of several IAPs. We further investigate how the time-to-angle mapping process depends on the time delay between the driving laser pulses and on their carrier envelope phase (CEP), allowing us to control the number and emission direction of the generated XUV pulses.

 

Fig. 1. (a) Schematic of the experimental setup. W, motorized pair of wedges; ${\mathrm{H}}_2\mathrm{O}$, water cell; CM, chirped mirrors; BS, beam splitter; TS, translation stages; HM, holey mirror; FM, focusing mirror ($f=400\mathrm{mm}$); Gas, argon; MCP, multichannel plate; PS, phosphor screen; OA, optical axis. (b) Illustration of the IR laser pulses in the far-field before focusing ($\mathrm{\Delta }t>0$) and (c) at the position of the gas cell in gating conditions, and (d) of the angularly separated spectral XUV continua (simulation) showing the time-to-angle mapping.

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Noncollinearly superimposing two identical laser pulses at the position of the geometrical focus results in a transverse intensity grating with a periodicity of $a\approx \lambda /2\gamma$ and a transverse envelope corresponding to the focal spot size (with beam radius $w_0$) of either pulse. Here $\lambda$ is the carrier wavelength of the pulses and $2\gamma$ denotes a small noncollinear angle. For a sufficiently small $\gamma$, such that $a\approx w_0$ (all spatial beam dimensions are specified at $1/e^2$ of the intensity profile), the intensity grating collapses into a single maximum with weak satellites. In the far field (before focusing), this corresponds to a separation of the two beams by $\delta \approx \pi D/2$ (independent of focal length), where $D$ is the diameter of either beam. For two identical pulses being focused noncollinearly with complete temporal overlap into a nonlinear medium, the attosecond pulses generated are emitted along the bisector angle of the two fundamental beams, i.e., the optical axis, the emission direction being defined by the wavefront orientation of the driving field. If a temporal delay ($\mathrm{\Delta }t$) is introduced, the resulting temporal amplitude variation leads to an ultrafast wavefront rotation. If the rotation is fast enough, the XUV pulses originating from consecutive half-cycles are angularly separated from each other. This results in angularly streaked XUV emission, mapping time into spatial position in the far field. The wavefront orientation angle can be expressed as a function of the amplitude ratio $\xi (t,\mathrm{\Delta }t)={\epsilon }_2/{\epsilon }_1$ between the two driving field envelopes ${\epsilon }_{\mathrm{1,2}}$ [18]:

Figure 1 illustrates the experimental setup together with the principle of the gating technique. We use a Ti:sapphire-based chirped pulse amplification laser system, delivering CEP-stabilized pulses with a repetition rate of 1 kHz and energy of up to 5 mJ. Few-cycle pulses, centered around 720 nm, are obtained by post-compression using a hollow capillary in combination with a chirped mirror setup and a water cell [25] (see Supplement 1 for details). A pair of motorized fused silica wedges is used for dispersion fine control, temporal characterization [26], and scanning the CEP of the pulses. A change of 28.9 μm of the thickness of the fused silica corresponds to a CEP slip of $\pi$, i.e., we scan the CEP by multiple $\pi$ without significantly influencing the pulse duration. After post-compression, pulses with duration of $\tau =3.2\mathrm{fs}$ (FWHM, Fourier limit of 2.9 fs) and $\sim 0.5\mathrm{mJ}$ energy enter an interferometer setup (after passing through an aperture, less than 0.2 mJ per interferometer arm are available for HHG) consisting of a dispersion-balanced beam splitter and two translation stages to spatially ($\delta$) and temporally ($\mathrm{\Delta }t$) separate the pulses [Fig. 1(a)]. The laser pulses enter vacuum through a thin (0.5 mm) antireflective-coated fused silica window and are focused noncollinearly with a $f=400\mathrm{mm}$ spherical mirror into a pulsed Ar gas cell (length $L_{\mathrm{med}}=3\mathrm{mm}$). Figure 1(c) illustrates the wavefront rotation obtained at the focus in gating conditions. The XUV pulses are recorded in the far field with a flat-field XUV spectrometer [Fig. 1(d)].

Best gating can be achieved for $\mathrm{\Delta }t\approx \tau$ [18], provided the phase delay between the two driving fields is 0 (modulo $2\pi$) at the point of intersection. For the short pulse duration in our experiments, this condition is fulfilled best for $\mathrm{\Delta }t\approx \pm T$, where $T$ denotes the field cycle period. In this condition, the pulses overlap partially and the wavefront orientation of the total driving field changes rapidly in time. The attosecond pulse train is thus streaked across the angle sector [$-\gamma$, $\gamma$] (with $\gamma =7.3\mathrm{mrad}$), leading to a wide angular spread of the emitted XUV radiation [Fig. 2(a)]. Spatially, several emission maxima with almost continuous spectral composition are visible, indicating the emission of several IAPs. The angular streaking is illustrated in Fig. 2(b), which displays a simulation of the fundamental field distribution on the optical axis. The temporal field distribution $|\mathfrak{R}[E(t)]|$ is mapped onto the emission angle (giving $|\mathfrak{R}[E(\beta )]|$) via the mapping function $\beta (t)$. $E(\beta )$ is defined via Eq. (1) using the inverse function $t(\beta )={\beta }^{-1}(t)$ such that $E(t)=E[t(\beta )]$.

 

Fig. 2. (a) Measured angularly resolved far-field XUV spectrum in gating conditions ($\mathrm{\Delta }t\approx T$). The side panels show the spectrally integrated spatial profile (right) and lineouts (emission angle indicated with arrows in the main panel) of the XUV emission spectra (bottom). (b) Illustration of the time-to-angle mapping of the IR field in gating conditions ($\mathrm{\Delta }t=T$) for a CEP of both pulses equal to 0. The bottom panel shows $|\mathfrak{R}[E(t)]|$, the left panel shows the corresponding $|\mathfrak{R}[E(\beta )]|$, and the middle one shows the time-to-angle mapping function $\beta (t)$.

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Figure 3(a) displays the XUV spatial far-field profile, integrated over photon energy, as a function of the temporal delay. At delays much larger than the pulse duration, the two laser pulses do not interact, leading to angularly well-separated XUV emission at $\beta =\pm \gamma$ [see Figs. 3(b) and 3(d)]. In this condition, the XUV beams are co-propagating with the fundamental IR fields. The intensity modulations with delay can be explained by a spatial movement of the fundamental intensity grating in the focus [18]. Even for $|\mathrm{\Delta }t|\gg \tau$, such modulations are visible, most likely due to the influence of weak temporal satellite pulses. The far-field XUV intensity distribution shows further a distinct asymmetry relative to the optical axis, which is inverted when the delay changes sign. For negative (positive) delays, the fundamental pulse generating the XUV beam in the lower part of the figure ($\beta \le 0$) comes first (second) [see also Fig. 1(b)]. Because of ionization of the nonlinear medium, XUV generation is less efficient for the second IR pulse. For delays around $\pm T$, i.e., in gating conditions, several spatially separated IAPs are emitted across the angle sector [$-\gamma$, $\gamma$] (see Fig. 2). The fundamental beams are still propagating at $-\gamma$ and $\gamma$, therefore, the XUV emission around $\beta =0$ can be spatially separated from the fundamental field. Finally, at complete temporal overlap, the spatial emission profile is confined to a small angle sector around the optical axis [see Figs. 3(c) and 3(e)]. In this case, the amplitude ratio of the two fundamental fields does not change in time ($\beta =0$).

 

Fig. 3. (a) Measured spectrally integrated (25–50 eV) and at each time delay normalized XUV far-field profile versus time delay $\mathrm{\Delta }t$. The panel at the top displays the normalization factor. Panels (b) and (c) show measured angularly resolved far-field XUV spectra for $|\mathrm{\Delta }t|\gg \tau$ and $\mathrm{\Delta }t=0$, respectively. Panels (d) and (e) show illustrations of the corresponding time-to-angle mapping of the IR field for a CEP of both pulses equal to 0, analogous to Fig. 2(b).

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The angular streaking process is strongly dependent on the CEP of the driving fields. Figure 4 shows the spatially resolved XUV signal integrated over photon energy as a function of CEP. A clear downward shift (toward negative $\beta$) of the XUV emission maxima is visible as the CEP decreases. For the experimental scan shown here, the beam splitter in the interferometer was replaced with a D-shaped mirror and the noncollinear angle was reduced, resulting in less divergent emission. In these conditions, fewer attosecond pulses were observed, most likely due to an even better compressed laser pulse. The angular shift of the XUV emission pattern with CEP arises due to the time-to-angle mapping process. A shift of the time of emission induced by changing the CEP of both driving fields results in a corresponding shift of the emission direction. If an aperture is placed on the optical axis and if the CEP is adjusted accordingly, one IAP can be selected. Alternatively, two attosecond pulses can be selected off-axis for attosecond pump–probe experiments [27] if the CEP is changed by $\pi /2$.

 

Fig. 4. Spectrally integrated (20–50 eV) spatial XUV far-field profile as a function of CEP (with arbitrary offset) for $\mathrm{\Delta }t\approx -T$. In the right panel, two lineouts with a CEP offset of $\pi /2$ are shown. The lineout location is marked in the main panel.

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Since the CEP strongly affects the gating process, the XUV emission direction becomes a sensitive probe for shot-to-shot CEP fluctuations on-target. In our measurements, the XUV signal was integrated over a few shots. The fluctuations visible in Fig. 4 correspond to a stability of $\approx 500\mathrm{mrad}$ (see Supplement 1 for details). The shot-to-shot CEP fluctuations result in a loss of contrast in the recorded spatiospectral patterns [see also Figs. 2(a) and 3(a)]. As predicted by simulations, a residual higher order chirp [see the pulse profile shown in the inset in Fig. 1(a)] can also reduce the contrast or even prevent IAP gating. Because of both effects, individual IAPs appear angularly less separated than predicted theoretically. Numerical simulations show a clear angular separation and thus IAP gating for pulse lengths exceeding 5 fs. A general pulse length limit of approximately four cycles can be derived analytically [18].

In conclusion, we have experimentally demonstrated noncollinear angular streaking of attosecond pulse trains. We have studied the streaking process as a function of temporal pulse separation and CEP, allowing us to control the direction and number of emitted IAPs. NOG does not require major manipulations of the driving laser pulses and allows a direct angular separation of XUV and laser fields. These aspects make NOG a promising candidate for intracavity IAP generation. Note that NOG can even be extended to the tight-focus regime as usually employed for intracavity HHG if $\gamma$, $L_{\text{med}}$, and gas pressure $p$ are adjusted accordingly. For a typical intracavity configuration (see, e.g., Ref. [10]) and considering phase-matched generation, the required parameters would reach values in the range of $2\gamma \approx 50\mathrm{mrad}$, $L_{\text{med}}\approx 250\mathrm{\mu m}$, and $p$ approaching 1 bar [28]. In a cavity, the noncollinear geometry can be achieved by either synchronizing two independent enhancement cavities [29] or designing an enhancement cavity with two circulating pulses [21]. With elaborate dispersion management, such approaches promise IAPs at unprecedented repetition rates and power levels, as well as broadband XUV frequency combs.