Main

The generation of attosecond pulse trains through the synthesis of a comb of harmonics of an infrared many-cycle femtosecond laser pulse is well established1,2,3,4,5,6,7, and is essentially understood in the framework of the three-step model13,14. According to this model, an electron is ejected in the continuum after tunnelling through the atomic potential barrier formed by the instantaneous laser field. Subsequently, the electron accelerates away from the core until the field changes sign. Within a fraction of half the laser period, the electron may revisit the parent ion to recombine and emit a burst of continuum extreme-ultraviolet radiation. As the process is repeated twice per laser cycle, the emitted spectrum consists of a superposition of coherent continua, which in the time domain is equivalent to a train of sub-femtosecond pulses. Using high-power many-cycle laser pulses, intense attosecond pulse trains have been generated and already used for the study of nonlinear phenomena in the extreme-ultraviolet spectral region15,16,17,18,19,20,21,22. They thus afford the means for the temporal characterization of attosecond pulses on the basis of second-order autocorrelation techniques in the extreme-ultraviolet spectral region3,4,5,18,19, and open the road towards extreme-ultraviolet pump—extreme-ultraviolet probe experiments.

In the spirit of the three-step model, if the process is confined to a single revisit of the core by the driven electron, one single continuum is emitted in the form of an isolated pulse. In mathematical terms, the Fourier synthesis of a broad continuum corresponds in the time domain to a single temporal occurrence, whereas a discrete spectrum leads to a repetitive process. Thus, the emission of a single coherent continuum is an essential prerequisite for single attosecond pulse generation8,9,10. Indeed, the generation of isolated single attosecond pulses is based on the synthesis of a continuum extreme-ultraviolet radiation emitted, so far, by rare gases driven by few-cycle infrared laser fields. Emission ensues only during a small fraction of the highest amplitude optical cycle of the driving laser field, either by selecting the highest energy part of the spectrum9, or through the temporal modulation of the laser field ellipticity confining the linear polarization and thus the extreme-ultraviolet emission at the pulse centre23. In both techniques, the stabilization of the relative carrier-envelope phase (CEP) is highly pertinent24. Such isolated attosecond pulses are, so far, less intense and contain notably less photons than attosecond pulse trains.

The highly desirable generation of intense single attosecond pulses remains a formidable quest. Towards this goal, two different approaches are currently considered: either by developing high-power few-cycle laser systems or, starting with existing high-peak-power many-cycle laser pulses, by isolating half a laser period, during which intense extreme-ultraviolet radiation is emitted. The second approach can be implemented through the modulation of the ellipticity of the many-cycle pulse, a technique proposed by Corkum et al. 23, established as ‘polarization gating’. Owing to the strong dependence of the harmonic generation on the ellipticity (ɛ) of the driving laser field, an ellipticity-modulated laser pulse, acquiring linear polarization only at the pulse centre, provides an ultrashort time interval, during which the harmonic emission essentially takes place. In this way, a broadband single attosecond pulse can be formed. Using a different polarization-gating approach than that proposed by Corkum et al., and CEP-stabilized 5 fs laser pulses, Sola et al. 11 succeeded in controlling the electron wavepacket dynamics and thus generating tunable continuum extreme-ultraviolet radiation. Their approach uses a very compact and simple to operate arrangement but falls short in the efficient generation of intense continuum extreme-ultraviolet radiation by many-cycle high-power lasers25.

In our approach, which we refer to as ‘interferometric polarization gating’, the superposition of four many-cycle laser fields has been used to create and control the time interval during which efficient harmonic generation occurs. This interval is quantified by the temporal gate parameter τg, during which the ellipticity, ɛ, varies from zero to ɛth, where ɛth is the ellipticity at which the harmonic efficiency drops to half of its maximum value, that is, its value at ɛ=0. The gate is synthesized by the four fields using a double Michelson interferometer (Fig. 1) and is tailored by independently controlling their relative phase, amplitude and polarization (see the Methods section). In this way, the gate window has been successfully confined to widths that lead to the generation of a continuum extreme-ultraviolet radiation spectrum. Introducing appropriate delays between the four fields, two of them are brought to partial overlap interfering constructively at the exit of the first Michelson interferometer, whereas the other two synthesize a destructive interference minimum at the centre of the pulse exiting the second Michelson interferometer. The linear polarizations of the two outgoing pulses are set to be perpendicular to each other and the pulse durations and intensities are appropriately adjusted. On recombination of these pulses, the temporal ellipticity modulation of the final outgoing beam can be tailored at will, thus providing a fully controllable τg at optimum output power. Control parameters are (1) the ratio I1/I2 of the intensities entering the two interferometers and (2) the delay, δ, introduced by the first Michelson interferometer (variable in multiples of the laser period for constructive interference). The delay in the second Michelson interferometer is kept constant at 50.7 fs.

Figure 1: Dual Michelson interferometer device.
figure 1

BS: beam splitters. M: flat mirrors. TS1,2,3: piezoelectric translation stages. A: intensity attenuator. First and second MI: first and second Michelson interferometers.

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The contour plots of Fig. 2 show τg and the intensity ratio Ig/Iin, where Ig is the intensity of the driving laser field within τg and Iin is the total incoming intensity, respectively, as a function of δ and I1/I2. The phase difference between the two perpendicularly polarized fields is Δϕ=π/2 and the threshold ellipticity (ɛth) for the harmonic generation has been assumed to be 15% (ref. 11). The dashed black lines divide both plots into two regions, with τg>5 fs and τg<5 fs, respectively.

Figure 2: Polarization gating parameter definitions and gate specifications.
figure 2

a, Contour colour plot on a linear scale showing the dependence of the time gate width (τg) on the time delay, δ, between the two interfering pulses of the first Michelson interferometer, for different ratios, I1/I2, of the intensities entering the first and second interferometers. b, Contour colour plot on a linear scale showing the intensity ratio Ig/Iin (where Ig is the intensity of the driving laser field within τg and Iin is the total incoming intensity) as a function of δ for different intensity ratios, I1/I2. In both plots, the phase difference between the two perpendicularly polarized outgoing fields is Δϕ=π/2, the threshold ellipticity ɛth is set to 15% and the pulse duration of each of the beams is 50 fs. The black dashed line shows the locus of the 5 fs gate width. The red shaded area indicates the parameter range used in the experiment.

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The output beam is focused into an Ar gas jet, where coherent extreme-ultraviolet emission occurs. Using only one beam, a discrete spectrum with well-separated harmonics (15th to 25th) has been recorded. Using all four beams and choosing the parameters δ and I1/I2 so that τg and Ig/Iin are in the range defined by the red shaded area in Fig. 2a,b, a continuum harmonic spectrum spanning from 55 to 32 nm has been recorded (contour plot in Fig. 3a). A displacement of the mirror by λ/8 in one of the arms of the first Michelson interferometer leads to a discrete harmonic spectrum consisting of the well-separated 15th to 23rd harmonics (contour graph in Fig. 3b).

Figure 3: Generation of a continuum extreme-ultraviolet spectrum with a 5 fs gate width.
figure 3

a, Iso-intensity colour plot on a linear scale showing the continuum spectrum generated by an elliptically modulated pulse possessing almost linear polarization in a time gate of ∼5 fs width. b, Iso-intensity colour plot on a linear scale showing a discrete spectrum of harmonics generated by a linearly polarized pulse. c, Solid blue line: ellipticity of the polarization-modulated pulse used for the generation of the continuum extreme-ultraviolet radiation. Black dashed–dotted line: normalized intensity of the two pulses, which partially overlap to form a pulse with a destructive interference minimum in its central part (black dotted line). Red dashed line: intensity distribution of the pulse showing the constructive interference maximum. The threshold ellipticity ɛth=15% and the time gate width τg∼5 fs are shown.

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Figure 3c shows the calculated ellipticity of the polarization-modulated pulse and the relative intensities of the two perpendicularly polarized fields at the output of the device, for the case of the continuum extreme-ultraviolet generation (Fig. 3a). The width of the time gate is τg∼5 fs and the intensity ratios I1/I2 and Ig/Iin are 0.25 and 0.035, respectively. The red and blue solid lines in the spectra of Fig. 4a show the extreme-ultraviolet signal of the contour plots of Fig. 3a and b (the central cut), respectively. Each spectrum is an average of 300 shots.

Figure 4: Dependence of the extreme-ultraviolet spectrum on the CEP of the laser pulse.
figure 4

a, Blue solid line: normalized harmonic spectrum generated by a linearly polarized pulse. Red solid line: normalized continuum extreme-ultraviolet spectrum generated by the central part of the elliptically modulated pulse, that is defined by the time window τg∼5 fs. Each spectrum is an average of 300 shots. b, Evidence of the CEP variation, reflected in the different structure of the spectra and the frequency shift (Δω) between the harmonic peaks. Solid black line: normalized extreme-ultraviolet spectrum generated by a half cycle of the driving laser field. Red dashed and blue dotted lines: normalized extreme-ultraviolet spectra, each one generated by one cycle of the driving laser field with different CEPs. The inset shows the calculated temporal profile of the Fourier-transform-limited single attosecond pulse resulting from the 55 to 32 nm spectral range of the spectrum, transmitted by a Si filter.

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As the laser system used is not CEP stabilized, the latter result does not warrant emission of isolated pulses and thus has to be further scrutinized. The drifting of the CEP in the present experiment is reflected in the extreme-ultraviolet spectra of Fig. 4b. Each spectrum in this figure is the record of a single shot. The spectrum shown with the black solid line is a quasi-continuum, whereas the spectra shown with the red dashed and blue dotted lines are of a discrete nature. Furthermore, a clear frequency shift (Δω) of the harmonic peaks in the two different discrete spectra is observable. All of the above differences in the graphs of Fig. 4b are indicative of a different CEP in each spectrum. The influence of the CEP drift on the spectra of the three recordings is compatible with previous findings in experiments conducted with CEP-stabilized few-cycle pulses24. The spectrum shown with a black solid line can be attributed to have been generated by a half cycle of a ‘cosine’-type driving laser field, whereas the other two spectra generated by one cycle of a ‘non-cosine’ driving laser field with different CEPs. Using a Si filter transmitting between 55 and 32 nm, a single attosecond pulse can be isolated with a minimum duration of ∼340 as (inset in Fig. 4b).

It is worth noting that the full interferometric control of the parameters used here enables the creation of an ultrashort temporal gate with the highest possible energy content, which may reach several millijoules. Such gates either cannot be achieved or require strikingly longer delays when produced by previously mentioned methods11, forcing as a result the gate formation to occur at the far wings of the pulses, thus substantially reducing its energy content. Moreover, our approach is not based on refractive optical components and thus is sensitive neither to the initial laser pulse length nor to nonlinear effects occurring through propagation of high intensities. Application of polarization gating to many-cycle pulses is inevitably connected to a large percentage of energy waste. In general, for the same laser energy input and given gate width, the shorter the laser pulse the higher the energy content in the gate. The followed approach can be optimized with respect to the percentage of energy losses using shorter pulses with a duration of 10–20 fs for which CEP stabilization technology already exists. Notwithstanding this optimization there will be a reduction of the overall output power in the gate because so far the highest gate power content that can be achieved is with longer pulses only from few–10 TW laser systems. This constraint will be eased in the future when high-energy CEP pulses will be available. Nevertheless, the method is versatile and applicable to a large range of pulse durations and thus may serve different specific needs.

In summary, we have presented a novel approach for intense broadband extreme-ultraviolet continuum generation using high-peak-power many-cycle pulses. The generated bandwidth is as broad as to enable the synthesis of isolated extreme-ultraviolet pulses with pulse durations of a few hundred attoseconds. For a large number of existing high-peak-power laser installations, the present results open up exciting prospects for the generation of intense, tunable in duration and frequency, isolated attosecond extreme-ultraviolet pulses. In particular, the approach is applicable without any conceptual modification to the extreme-ultraviolet generation from laser surface plasma interactions at relativistic intensities12, aiming at the generation of isolated attosecond pulses with unprecedented extreme-ultraviolet intensities26. Although so far CEP has never been considered as an important parameter when many-cycle pulses are used, this work has revealed its importance to the generation of extreme-ultraviolet continua. This is because of the very narrow time gate formed by the transient linear polarization, which is effectively equivalent to using a few-cycle driving field. Exploitation of the approach in extreme-ultraviolet-pump–extreme-ultraviolet-probe applications will thus further require either stabilization of the CEP or tagging the recorded spectra with a simultaneously measured quantity (for example, the frequency spectrum) indicative of the shot-to-shot CEP. With these developments, unique extreme-ultraviolet radiation sources will become available, providing the highest ever temporal resolution at competitive intensities.

Methods

The laser system used is a 10 Hz Ti:sapphire, delivering 50 fs pulses, with an energy of up to 150 mJ per pulse and a carrier wavelength of 800 nm. The laser beam is split into two parts by a beam splitter (see Fig. 1) and the resulting two pulses enter the double Michelson arrangement. One of the beams (first pulse) enters the first Michelson interferometer, introducing a multiple of the laser period time delay (δ) between the two arms, so that the output pulse possesses a constructive interference maximum at its centre. The other beam (second pulse) enters the second Michelson interferometer, where the delay is set to a fixed value of about 50 fs. Through fine-tuning of this delay, an output pulse marked by a destructive interference minimum at the centre is tailored. The 50 fs delay ensures the highest possible sharpness of the interference minimum allowed by the temporal envelope of the original pulse. The linear polarizations of the two outgoing beams are adjusted to be perpendicular to each other by a λ/2 zero-order waveplate. With this arrangement, the temporal ellipticity modulation of the outgoing superposition of the two pulses can be tailored at will, thus providing a fully controllable τg. The attenuator placed before the first Michelson interferometer, together with the variable delay of the first Michelson interferometer, serves to adjust the intensity distributions of the two outgoing pulses to result in an optimal combination of gate width and gate energy content avoiding any gate formation at the tails of the tailored pulse. This optimal combination can only be achieved through an independent manipulation of the two fields, here realized by the dual Michelson interferometer, and constitutes a significant advantage of the method. However, conditions close to the optimal ones can be achieved using the same delay but different amplitudes in each pair (one undergoing constructive and the other destructive interference) of pulses. The set-up can then be substantially simplified, increasing its throughput at the same time by a factor of 2. This possible modification will be presented elsewhere. On the basis of the calculated dependence of τg and Ig/Iin on δ and I1/I2 (Fig. 2a,b), the δ and I1/I2 parameter values have been chosen to result in a gate width τg∼5 fs and a ratio Ig/Iin∼0.035 (red shaded area in Fig. 2a,b).

The output tailored beam is focused into a piezoelectrically pulsed Ar gas jet, where the harmonic generation is taking place. The beam focus is placed before the Ar gas jet to select the short electron trajectory27,28. The harmonic radiation is monitored by an extreme-ultraviolet toroidal grating monochromator in a grazing-incident configuration, equipped with an imaging detector, coupled to a charge-coupled device (CCD) camera capable of recording single shot measurements.

It is worth noting that the longer the initial pulse duration is the more advantageous our method becomes. For pulse durations of ≤30 fs, our method has advantages only for high driving intensities at which induced nonlinear effects prohibit the use of refractive materials, owing to the accumulation of high B-integral values. For pulses with a duration of ≥50 fs, it becomes superior to other methods, if not the only alternative. As most of the high-peak-power (10–100 TW) laser systems deliver pulses with a duration of ≥40 fs, the use of our method in these systems provides a unique tool for intense isolated attosecond pulse generation. In this context, a current limiting factor is the lack of CEP-stabilized high-peak-power systems. Efforts towards such CEP stabilization are in progress in a number of large laser laboratories, but the timescale necessary for its implementation cannot be precisely foreseen. Awaiting this accomplishment, extreme-ultraviolet-pump–extreme-ultraviolet-probe experiments with isolated attosecond pulses will have to rely on tedious single-shot tagging approaches. It is fortunate that our results (see Fig. 4b) provide the required tag and thus serve this purpose too. Indeed, our method, besides its main task of intense isolated attosecond pulse generation, offers a versatile technique as a CEP diagnostic.