Filamentation-assisted isolated attosecond pulse generation

Abstract

The advancement of attosecond science relies on achieving stable generation of isolated attosecond pulses (IAPs), which are essential for capturing ultrafast dynamics in atoms, molecules and solids. Our study in an extended gas medium demonstrates filamentation-assisted spatiotemporal reshaping of the infrared driving pulse, enabling transient phase-matching gating and the generation of bright, high-contrast IAPs. Our experimental and theoretical results reveal that a semi-infinite gas cell naturally forms a stable propagation region, where the driving pulse undergoes controlled self-compression and spatial cleaning. In an argon-filled gas cell, filamentation reduces the duration of Ytterbium-based 1030 nm pulses from 4.7 fs to 3.5 fs, while simultaneously producing high-contrast IAPs of 200 as, at 65 eV, with an excellent output beam profile. Similar filamentation-assisted transient gating is observed in neon and helium, yielding pulses of 69 as at 100 eV and 65 as at 135 eV. This filamentation-enabled transient phase-matching mechanism opens a simple and robust route to provide high-contrast attosecond sources, advancing both post-compression techniques and attosecond-based technologies.

The frontier of ultrafast science pushes the development of stable generation of isolated attosecond pulses. Here, the authors demonstrate a filamentation-assisted transient phase-matching mechanism, driven by post-compressed Yb-based few-cycle lasers. They produce stable, high-contrast, isolated attosecond pulses as short as 200, 69 and 65 as in argon, neon and helium.

Introduction

The generation of IAPs has revolutionized temporal resolution in light-matter interactions, enabling the observation of the fastest processes such as electron, exciton, and spin dynamics driven by few-cycle pulses^1–4. Recent studies have further demonstrated that ultrafast lightwaves can induce rapid phase transitions in materials^5–7. These studies highlight the profound impact of attosecond science, enabling exploration of new physics, uncovering novel mechanisms, and advancing the development of next-generation petahertz devices^8,9.

The development of intense, ultrafast laser pulses, carefully tailored in their spatial and temporal domains, has become a key technology for producing attosecond light pulses via high-order harmonic generation (HHG). This highly nonlinear process is triggered by an intense femtosecond laser pulse interacting with a gaseous or solid target—most typically a gas jet or gas cell. HHG can be understood through the semiclassical three-step model^10,11, which repeats every half-cycle of the driving pulse. First, when the pulse intensity is sufficiently high, an atom is tunnel-ionized. Next, the ejected electronic wavepacket is accelerated in the continuum. Finally, due to the oscillatory nature of the driving field, the wavepacket recombines with the parent ion, emitting high-frequency radiation. With multi-cycle driving pulses, an attosecond pulse train is generated in the time domain, producing multiple harmonic orders in the spectrum. This process occurs in many atoms across the whole target, so harmonic phase-matching needs to be taken into account^12–14. If the driving pulse is sufficiently short, a single emission event occurs, resulting in the generation of an IAP^15–17. Alternatively, other techniques relying on polarization gating^18–20, ionization gating²¹ or phase-matching gating^22,23 can also isolate an IAP from the attosecond pulse train, at the expense of wasting pulse energy.

Currently, the primary method for generating IAPs involves focusing few-cycle carrier-envelope phase (CEP) stabilized pulses—such as 5 fs pulses from a Ti:Sapphire laser ( ~ 2 cycles at 800 nm)^24,25 or 12 fs pulses from an optical parametric chirped-pulse amplifier (OPCPA) ( ~ 2 cycles at 1800 nm)^26–29, into a short gas cell (SGC). However, the use of a semi-infinite gas cell (SIGC) offers an alternative geometry for HHG^30–32 where nonlinear propagation effects of the driving pulse become pronounced. When the laser peak power (P_peak) approaches or exceeds the critical power, intense pulses focused within the SIGC can form a filament, resulting from the balance between Kerr self-focusing, diffraction and plasma defocusing, reshaping the driving electric field both spatially and temporally³³. Spatially, self-guidance confines the intense field into a narrow channel, extending propagation beyond the diffraction limit. Temporally, the pulse undergoes self-compression. Theoretical calculations suggest that filamentation over an extended propagation distance within the SIGC could enable IAP generation and enhance the high harmonic signal^34–36. This approach is particularly appealing for its simple setup, requiring only a strong pulse focused into a gas cell to produce IAPs. However, the particular parameters to properly activate the complex spatio-temporal reshaping of the IR pulse during a standard filamentation regime^37,38 explains why, to date, no successful IAP generation driven by filamentation has been reported in the literature.

In this work, we experimentally demonstrate robust IAP generation via filamentation driven by Yb-based laser pulses. By focusing a few-cycle driving pulse (<5 fs at 1030 nm)³⁹ into argon (Ar), neon (Ne) and helium (He)-filled SIGCs, we show that the resulting HHG supercontinuum exhibits high temporal IAP contrast. Through theoretical simulations, we attribute this result to the self-compression and self-guidance of the driving field induced during the filamentation process in SIGC, together with phase-matching gating^22,23 occurring near the pulse peak. Specifically, when 4.7 fs driving pulses are focused into an Ar-filled SIGC, nonlinear reshaping results in a 25% temporal pulse self-compression (from 4.7 fs to 3.5 fs), and in a cleaner spatial mode, leading to high spatial-spectral homogeneity. Compared to conventional SGCs, we demonstrate that IAPs generated in the SIGC exhibit higher temporal contrast, greater brightness, and clean spatial profiles, indicating that filamentation assists the efficient generation of IAPs. Our attosecond streaking measurements further confirm the stability of the filament generated in Ar, demonstrating the emission of bright 200-as IAPs at 65 eV. Additionally, we demonstrate that this filamentation-assisted IAP generation mechanism is consistently observed across multiple noble gases, including 69-as IAPs at 100 eV in Ne and 65-as IAPs at 135 eV in He. To the best of our knowledge, this is the first study to achieve IAPs directly driven by a post-compressed Yb laser. While Yb-based lasers are known for their robust, high-power femtosecond capabilities, they typically have longer pulse durations (>150 fs), requiring substantial post-compression (>40×) to reach few-cycle pulses. This often introduces satellite pulses and wavelength-dependent wavefront distortions that compromise the spatiotemporal pulse quality. Our filamentation-assisted method allows for straightforward spatio-temporal cleaning of these post-compressed pulses into the one-cycle regime. This unique and reliable approach is highly effective for generating high-contrast IAPs, establishing it as a promising technique for advancing attosecond technology.

Results

In our experiment we employed Yb-based CEP-stabilized pulses, with a central wavelength of 1030 nm, post-compressed to a pulse duration of 4.7 fs, and a maximum energy of 500 μJ, operating at a repetition rate of 4 kHz³⁷ (see Supplementary Note 1 for details). These pulses were focused to drive HHG into either a SGC or a SIGC using a concave mirror with a 35-cm focal length (see Fig. 1a and Supplementary Fig. 1). On the one hand, the SGC is composed of a stainless steel tube with an inner diameter of 2.2 mm, sealed at one end. The long tube of the SGC was aligned perpendicularly to the laser propagation direction and placed near the focus, where the laser itself self-drilled holes through the tube, as shown in Fig. 1b. On the other hand, the SIGC (Fig. 1c) was composed of a gas-filled chamber, with a 0.3-mm thick aluminium plate blocking the interface between the gas-filled and vacuum sections. The focus was positioned near the plate where a hole was self-drilled by the driver beam, allowing the generated high-order harmonics to exit. Ar, Ne and He gases were used to produce high-order harmonics. The resulting few-cycle IR pulses and high-order harmonics were refocused onto a Ne gas jet using an elliptical mirror for attosecond streaking experiments⁴⁰. Subsequently, an extreme-ultraviolet (EUV) spectrometer was employed to analyze the HHG spectrum.

Fig. 1. Experimental setup and CEP-dependent high harmonic spectra in SGC versus SIGC.

a Schematic representation of HHG in SGC b versus SIGC c, and pulse characterization using TIPTOE and attosecond streaking. d, e display the normalized CEP-dependent HH spectra, driven by post-compressed <5 fs pulses from an Yb laser, in SGC and SIGC, respectively. The solid line indicates the optimized CEP (CEP phase = 0.5 $\pi$) for maximum HHG yield. A relative change of 0.5 $\pi$ rad in CEP (dashed lines) results in pronounced variation in high harmonic yield. f shows a direct comparison of these CEP-dependent HH yields, with the insets displaying beam profiles at flux-optimized conditions. The average full-angle FWHM divergence is 2.13 mrad for SGC and 1.45 mrad for SIGC, indicating that SIGC produces a more collimated and symmetric beam. CM concave mirror; TOF time of flight; PMT photomultiplier tube, CF central filter with IR passing on the outer side and a 2-mm diameter thin metal filter, such as 200-nm Al, Zr, or Ag, suspended in the center by three thin wires, blocking IR while allowing HHG to pass through.

We first present our experimental results using Ar-filled SGC and SIGC configurations. To prevent overionization, which would reduce the HHG yield due to phase mismatch^13,14,41, we positioned a partially closed iris along the laser beam path before the entrance window. HHG was optimized by iteratively adjusting the iris aperture, the focal position, the gas pressure, and the wedge insertion until the brightest supercontinuum was obtained. The optimized parameters in SIGC—including the pulse energy after the partially closed iris, the input pulse duration, and the backing pressure—are listed in Table 1. The focal spot size and peak intensity are not included because nonlinear propagation readily alters them. Once the high-harmonic supercontinuum flux was optimized, we obtained the CEP-dependent high harmonic spectra (normalized to their respective global peaks) for both the SGC (Fig. 1d) and SIGC (Fig. 1e). These spectra exhibit a π radian periodicity due to the presence of two electric field peaks within one optical cycle²². Figure. 1f compares the maximum (solid lines) and minimum (dashed lines) CEP-dependent high-harmonic yield in both geometries—green for the SGC, red for the SIGC. In the SGC, the ratio between the maximum and minimum high-harmonic yield is around 2, with the high-harmonic spectra showing noticeable spectral modulations, indicating the presence of multiple attosecond pulses over time. By contrast, in the SIGC configuration the high-harmonic spectrum remains as a clean supercontinuum regardless of CEP variation, while varying in flux. Moreover, the ratio between the maximum and minimum high-harmonic yield in the SIGC exceeds a factor of 10, corresponding to an almost complete on/off switching of IAP generation. This supercontinuum and high ratio of CEP-dependent high-harmonic yield directly indicates the generation of high temporal contrast IAPs, as further corroborated through attosecond streaking measurements and theoretical simulations. Notably, the SIGC produces more than twice the HHG brightness of the SGC and delivers a more collimated, symmetric beam profile, as shown in the insets of Fig. 1f. A detailed comparison of the harmonic beam profiles obtained in the SIGC and the SGC is provided in Supplementary Note 3, highlighting the advantages of the SIGC. As a consequence of these results, we shall concentrate here on exploiting HHG in SIGC for bright IAP generation, leaving the details of the SGC results to SI.

Table. 1.

Optimized peak power for high harmonic supercontinuum vs. theoretical critical power for filamentation

Gas	Optimized Peak Power Ppeak			Theoretical Critical Power Pcr				Ppeak / Pcr
	Pulse energy (μJ)	Pulse duration (fs)	Ppeak (GW)	Center wavelength (nm)	Optimized pressure (torr)	n2 at 1 atm (×10-19 cm2/W)	Pcr (GW)
Ar	203	4.68	43.4	924	150	2.043	32.6	1.33
Ne	355	4.00	88.8	927	650	0.1434	108.3	0.82
He	420	3.30	127.3	928	1600 – 2000a	0.03848	162.5 – 130	0.78 – 0.98

^* 2000 torr is the maximum pressure our experimental chamber can provide. The HHG yield in He remains similar across the 1600 to 2000 torr range.

The optimal conditions to achieve the brightest EUV continuum in the SIGC included an Ar pressure of 150 torr and an iris aperture diameter of approximately 8 mm. These settings reduced the input pulse energy from 500 μJ to 203 μJ, resulting in an input P_peak of 43.4 GW. Figure 1c illustrates a nonlinear filament extending roughly 6 mm before being truncated by the thin metal plate. Interestingly, after optimizing high-harmonic supercontinuum, the P_peak of the input pulse coincidentally approached the critical power P_cr of self-trapping, which is given by⁴²

$$P_{cr}=1.8962{\lambda }^2/\left(4{\pi n}_0{n}_2\right),$$ 1

where n₀ is the linear refractive index at the central wavelength λ and n₂ is the nonlinear refractive index of the gas⁴³, which is directly proportional to the gas pressure. P_cr was calculated to be ~ 32.6 GW at 150 torr of Ar, as summarized in Table 1. In short, the optimal conditions for high-harmonic supercontinuum generation—corresponding to IAPs—align with those required for stable single filament formation.

To better understand how filamentation enhances the contrast of IAPs, we analyzed the driving beam profile exiting the SIGC filled with Ar as an example. A wedge was inserted after the thin truncated plate to partially reflect the beam out of the vacuum chamber, enabling the measurement of beam profiles in both the near-field and far-field. Figure 2 presents a comparison of the beam profiles exiting the SIGC in vacuum (first row) and with 150 torr of Ar (second row). We assessed the far-field spatial-spectral homogeneity of the output beam after approximately 30 cm of free expansion (central panels of Figs. 2a and 2b) by sampling it with a 1-mm-diameter pinhole along the vertical axis, following the homogeneity criterium based on the spectral overlap as defined in⁴². The near field profiles, obtained via relay imaging, are depicted in the right insets. Although the near-field beam profile at the cell output under vacuum exhibits vertical asymmetry—likely arising from astigmatism of the concave mirror—the far-field beam remains highly homogeneous (98.3%) (Fig. 2a). The spot size (or beam divergence) remains nearly constant at ~6.1 mm across the entire spectrum, spanning 600 nm to 1200 nm.

Fig. 2. Self-guiding and self-cleaning effects in IR filamentation.

The first column presents a direct comparison of the far-field beam profiles from the SIGC, captured using a standard Si-based CMOS sensor: a under vacuum and b with 150 torr of Ar. The second column displays their normalized integrated power and spatial-spectral beam homogeneity. The third column illustrates the spatial-spectral distribution of the output beam along the vertical axis. Dotted lines in the second and third columns indicate the beam waist at 1/e² level. The fourth column depicts the mode profile of the IR beam at the exit of the gas cell, also captured via relay imaging using a standard Si-based CMOS sensor. c, d show corresponding beam profiles and spatial-spectral distributions from numerical simulations under vacuum and with 70 torr of Ar, respectively.

When 150 torr of Ar gas is introduced, nonlinear propagation within the filament reduces the spot size (beam divergence) by ~20%, resulting in a more symmetric beam profile in both the near and far fields (Fig. 2b). Spectrally, the filament induces blue-shift broadening, while the beam diameter remains relatively constant at ~5.5 mm after 30 cm of free expansion. On the contrary, for the red-shifted part above 1200 nm, the beam size increases by ~45%, reaching about 8.9 mm. Additionally, the center of the red-shifted part of the beam ( ~ 1200 nm) is vertically displaced by about 1 mm compared to the common center of other wavelengths. These two observations suggest that these longer wavelengths were not guided by the inner part of the filament. Further discussion is provided later. Nevertheless, as the red-shifted part constitutes a very small fraction of the total energy ( < 10%), the overall spatial-spectral homogeneity remains high (91.9%). The near-field beam, shown in the right inset of Fig. 2b, becomes smaller and more round compared to the one obtained when the cell is in vacuum due to the nonlinear cleaning mode process. Notably, at very high pressures, beam splitting into two was observed as a second filament began to form (see Supplementary Fig. 2), accompanied by a drop in HHG yield. This observation points out that optimizing the EUV supercontinuum involves iterative adjustments of the input iris aperture, the focal position within the SIGC, the gas pressure, and the insertion of a wedge pair to control spectral dispersion—essentially equivalent to optimizing single filamentation of the IR for IAP generation.

In order to corroborate the nonlinear nature of the spectral broadening and beam reshaping of our driving beam, we performed theoretical calculations comparing the vacuum and SIGC configurations. To do so, we solve the nonlinear driving beam propagation in the complete volume using as an input the measured experimental pulse before the cell. Our simulation method assumes cylindrical symmetry⁴⁴, and includes the complete dispersion of the gas, the Kerr effect, self-steepening and shock terms, and photoionization and plasma absorption. As depicted in Fig. 2c, d, the numerical simulations replicate the general trends observed experimentally when the SIGC is in vacuum or filled with 70 torr of Ar, respectively. When filled with Ar (Fig. 2d) a general ionization-induced blue-shift in the spectrum is observed, with a consistent spatial width across the whole spectrum. The beam size of the red-shifted portion ( > 1200 nm) is twice that of other wavelengths, aligning well with our experimental results. From a spatial perspective, we observe a distinctive nonlinear readjustment of the spatial profile in both the near and far fields induced by filamentation. Though the spatial cleaning process is minimal in this case, as a perfect spatial Gaussian profile is assumed at the cell entrance in both cases.

To investigate how filamentation reshapes the temporal profile of the driving pulse, we employed the TIPTOE method^45–47 (more details are provided in the Methods), which precisely characterizes the femtosecond pulse waveform. Figure 3a, b compare the IR waveforms at the SIGC exit with (blue) and without (red) 150-torr Ar, as obtained from TIPTOE. The negative values on the time axis indicate the leading time. In Fig. 3c, d we present the half-cycle-by-half-cycle temporal delay and the corresponding frequency shift between the two waveforms shown in Fig. 3a. Our analysis divides the time axis into five segments: I. Before −30 fs, both waveforms are nearly identical, as the electric field is too weak to induce nonlinear effects. II. Between −30 fs and −20 fs, we observe a red-shift in the waveform when the cell is filled with Ar. We attribute it to the Kerr effect, where the light wave undergoes a nonlinear phase delay caused by its own intensity. III. After −20 fs, in the central part of the pulse, the strong electric field ionizes Ar. Since the plasma refractive index is lower than 1, the light wave experiences a phase advance, resulting in a spectral blue shift. Specifically, different ionization rates between half-cycles lead to varying blue shifts within each half-cycle, effectively shortening the pulse duration (as shown in Fig. 3b). IV. After 10 fs, as the electric field weakens, the Kerr effect again dominates, causing another spectral red-shift. V. After 20 fs, similar to segment I), the laser intensity is insufficient to cause any changes in the waveform. As a result, the spectrum of the pulse when the SIGC is filled with Ar experiences pronounced blue-shift with some red-shift, leading to pulse self-compression from 4.7 fs to 3.5 fs, as shown in Fig. 3e (temporal domain) and Fig. 3f (spectral domain). Our theoretical calculations for the nonlinear driving field propagation (Fig. 3g, h) show strong agreement with our main experimental findings.

Fig. 3. Filamentation-induced pulse self-compression.

Waveform measurements were conducted using TIPTOE. a The waveform of the few-cycle pulse propagating through a SIGC in vacuum (red lines) versus when filled with 150-torr Ar (blue lines), which is the optimized pressure for producing the brightest high-harmonic supercontinuum. To facilitate comparison, the curves are relatively normalized to the time point t = −50 fs. b Zoomed-in view of a, showing the half-cycle-by-half-cycle blue-shift of the waveform induced by ionization. Experimental data points, indicated by dots. The standard error of the mean is estimated to be ~0.24% in amplitude and ~18 as in time, smaller than the size of the dots (see stability analysis of TIPTOE measurements in Supplementary Note 2). c Half-cycle by half-cycle temporal delay extracted from a (dots: raw data; solid line: smooth curve weighted by the field amplitude). d Frequency shift derived from c. e, f show the corresponding normalized intensity profile and spectrum, respectively. The blue-shift results in pulse self-compression from 4.7 fs to 3.5 fs. g, h show the normalized intensity profile and spectrum obtained from numerical simulations.

It is worth noting that the red-shifted spectrum resulting from filamentation-based post-compression exhibits unique characteristics. Spatially, the beam divergence around 1200 nm is substantially greater than for wavelengths below 1200 nm (see Fig. 2b, d). Spectrally, a distinct phase shift behavior is observed around 1200 nm (see Fig. 3f, h). The Fourier analysis presented in Supplementary Fig. 3 also indicates that the red-shifted component primarily originates outside the main pulse—mainly from −20 fs, corresponding to segment II, and partially from +20 fs, corresponding to segment IV in Fig. 3d—where the local peak intensity induces self-phase modulation (SPM) but is insufficient to sustain filamentation. In contrast, the blue-shifted component arises from time segment III (the main pulse), where the peak intensity is sufficient to induce filamentation, enabling spatial guidance and temporal compression. A similar analysis in the SGC configuration is displayed in Supplementary Fig. 4. Notably, like the SIGC, the SGC exhibits a self-compression effect; however, it lacks a guiding effect, making the IR beam prone to splitting and resulting in a weaker, degraded HHG beam profile compared to the SIGC (see Fig. 1f, insets, and Supplementary Note 3).

In addition to Ar, we utilized Ne and He gases in the SIGC for HHG. After the same optimization procedure in Ne (He) SIGC, a partially closed iris reduced the input energy to 355 μJ (420 μJ), resulting in P_peak of approximately 88.8 GW (127.3 GW). The optimal Ne (He) pressure for achieving the brightest high-harmonic supercontinuum was found to be around 650 torr (1600 – 2000 torr, with nearly constant HHG yield in He). At these pressures and considering the corresponding nonlinear refractive index n₂^34,48, Eq. (1) estimates the critical power P_cr to be ~108.3 GW ( ~ 162.5–130 GW). A comparison between their P_peak and P_cr is summarized in Table 1. Remarkably, in all three independent SIGC experiments—Ar, Ne, and He—the optimal P_peak for generating the high-harmonic supercontinuum approached the theoretical P_cr required for stable single filament formation. As expected, similar to Ar, we observed self-guidance of the IR beam in space and self-compression of the IR pulse in time when using Ne and He (Supplementary Figs. 5 and 6), though the compression was less pronounced in Ne, as detailed in Supplementary Note 5. Furthermore, based on the measured EUV signals and accounting for the CCD quantum efficiency, grating efficiency, filter transmission, and EUV mirror reflectivity, we estimate that the conversion efficiencies are on the order of 10⁻⁶ for Ar and 10⁻⁷ for Ne and He. We emphasize that when using the 2.2-mm SGC, the brightest HHG from Ne was approximately 13 times weaker than that generated in the SIGC. Furthermore, we were unable to generate HHG from He in the SGC, even at very high gas pressures. These findings clearly demonstrate the critical role of filamentation-induced guiding of the IR beam in the SIGC for the successful generation of bright HHG.

After characterizing the nonlinear filamentation in the SIGC, we present in Fig. 4 the results of EUV attosecond streaking experiments conducted in Ar (first row), Ne (second row) and He (third row). The experimental setup is shown in Fig. 1a (details are provided in the Methods). By focusing both IR and EUV pulses into a Ne gas jet, and introducing a time delay between them, the momentum shift of the photoelectron across the entire photoelectron spectrum was recorded (first column in Fig. 4). The presence of only one distinct streaking trace confirms the generation of high-contrast IAPs. The IAPs generated in the SIGC filled with Ar (Ne and He) have central energies of 65 eV (100 eV and 135 eV), bandwidths of ~10 eV ( ~ 25 eV and ~35 eV), and can support transform-limited pulse durations of 163 as (58 as and 42.8 as). Using the retrieval algorithm PROOF⁴⁹ (details presented in Supplementary Fig. 7), the measured durations of the IAPs generated from Ar (Ne and He) are 203 as (69 as and 65 as). The presence of an IAP in all three experiments is further corroborated by the CEP-scan HHG spectra shown in Supplementary Fig. 8. The streaking experiments confirm that both the filamentation-based post-compressed IR and the IAPs are exceptionally stable. This result also marks the first demonstration of IAPs driven by a post-compressed Yb laser (see Supplementary Fig. 9).

Fig. 4. Attosecond streaking results.

Experimental spectrograms were obtained from self-compressed IR pulses and the resulting IAPs generated from filaments in a Ar, b Ne, and c He. The middle panel displays their EUV spectra along with the phase of the resulting IAPs, which exhibit a slightly positive chirp, while the pulse durations are shown in the right panel. Since the PROOF algorithm⁴⁹ assumes a quasi-continuum driver, regions approximating CW-like behavior were selected (dashed region) for valid retrieval. Based on ~10 trials for each case using a global genetic algorithm, we retrieved IAP durations of 203 ± 5.5 as for Ar, 69 ± 3.7 as for Ne, and 65 ± 4.3 as for He, compared with their transform limits of 163 as, 58 as, and 42.8 as.

Discussion

Our experimental results have demonstrated filamentation-assisted IAP generation using Yb-based few-cycle laser pulses undergoing self-compression and self-guidance in Ar, Ne and He. To gain a comprehensive understanding of the HHG process, it is essential to clarify the physical meaning of P_peak/P_cr and its impact on HHG: When the laser’s peak power exceeds the critical power, even without any focusing element, intensity-induced Kerr self-focusing overcomes diffraction, effectively self-focusing the beam and raising its intensity beyond what linear propagation allows. During propagation, self-focusing, where the wavefront bends inward, progressively narrows the beam until the rising intensity produces sufficient ionization, leading to plasma-induced defocusing, where the wavefront bends outward. This process eventually balances Kerr focusing, flattens the wavefront, and clamps the intensity (see Supplementary Note 4 for further discussion). This dynamic balance creates a self-guided filament, enabling long-distance propagation with a stable, high-intensity core, extending the laser–gas interaction distance. Note that the critical power is independent of beam size because both diffraction and self-focusing scale inversely with beam size. For instance, halving the beam size doubles both effects, preserving the balance. This is why beam size is not listed in Table 1.

With a focusing element, such as a lens or concave mirror, Kerr-induced focusing adds to the geometrical focus, requiring stronger plasma-induced defocusing to balance it. This demands higher ionization, achieved via a smaller beam waist and higher intensity, thus resulting in a higher clamped intensity⁵⁰. Notably, a clamped intensity can still be established even when the input power is below the self-focusing threshold (P_peak/P_cr < 1), as reported by Tosa et al.⁵¹ and Vismarra et al.³², provided that ionization-induced defocusing is sufficiently strong to counteract the geometrical focusing alone, as demonstrated theoretically by Shim et al.³⁶. However, under such conditions, self-spatial filtering (or self-cleaning) is suppressed, leaving beam imperfections uncorrected. Similarly, even when a conventional gas cell operates near the critical power (P_peak/P_cr ≈ 1), as reported by Rivas et al.⁵² and Major et al.⁵³, since the pulse mainly propagates in vacuum before entering the gas cell, little nonlinear reshaping occurs; consequently, self-cleaning and self-guidance remain very weak. In both cases, the lack of effective self-correction means that any imperfections in the driving IR beam can severely degrade HHG yield and beam quality. For instance, in our experiments, HHG generated in the SGC—where P_peak/P_cr ≈ 1 but self-spatial filtering is absent—consistently exhibited distorted EUV beam profiles that could not be corrected to a circular shape, regardless of optimization. By contrast, in the SIGC, once the HHG flux was optimized, the beam profile naturally evolved into a confined, symmetric shape (see Fig. 1f, insets, and Supplementary Note 3).

On the other hand, when P_peak/P_cr ≫ 1, the beam readily breaks into multiple filaments. Any minor intensity fluctuation across the beam profile can trigger local self-focusing wherever the local power exceeds P_cr, resulting in multiple filaments⁵⁴. For example, Steingrube et al.⁵⁵ operated at P_peak/P_cr ≈ 5, where multiple refocusing and filamentation occurred along the propagation axis. Their experiment showed two distinct HHG regions along the axis, indicating unstable filamentation dynamics. Such conditions are unfavorable for efficient HHG and likely contributed to their lower measured conversion efficiency ( ~ 10⁻⁷), compared to ours ( ~ 10⁻⁶). This is consistent with our own observation that when P_peak/P_cr > 2, a second filamentation channel emerges (Supplementary Fig. 2), accompanied by a drop in HHG yield.

In short, stable single filamentation occurs when P_peak/P_cr ≈ 1 in SIGC, enabling effective self-cleaning and efficient HHG. In this regime, the clamping intensity, maintained by the balance of Kerr self-focusing, diffraction, and plasma defocusing, together with the self-compression process, support ideal conditions for IAP generation. In contrast, when P_peak/P_cr << 1 (or in SGC), the absence of self-spatial filtering leaves beam imperfections uncorrected, substantially degrading both HHG yield and beam quality. When P_peak/P_cr >> 1, operating far above the critical power leads to unstable propagation and suppressed HHG performance.

To gain deeper insight into the phase-matching mechanism in filamentation-assisted IAP generation, we employ both analytic theory and advanced numerical modeling. Analytically, since the refractive index at EUV is ~1, meaning that the phase velocity is nearly equal to c, the speed of light, phase matching occurs when the refractive index change in the IR satisfies ∆n ≈ 0. All relevant dispersion contributions in the IR must therefore be included, comprising the transient changes induced by the Kerr effect (${\mathrm{\Delta }n}_{Kerr}$) and plasma (${\mathrm{\Delta }n}_{plasma}$), as well as the quasi-static shifts from the neutral gas (${\mathrm{\Delta }n}_{neu}$) and geometric effects (${\mathrm{\Delta }n}_{geo}$). Thus, the total refractive index change can be expressed as $\mathrm{\Delta }n={\mathrm{\Delta }n}_{Kerr}+{\mathrm{\Delta }n}_{plasma}+{\mathrm{\Delta }n}_{neu}+{\mathrm{\Delta }n}_{geo}$. As discussed in detail in Supplementary Note 5, on the leading edge of the laser pulse the phase velocity is slower than c due to the dominance of neutral atoms (∆n > 0), whereas on the trailing edge it becomes faster than c owing to gas ionization (∆n < 0). Consequently, phase matching is supported primarily near the pulse peak. Importantly, when few-cycle pulses are used, $\mathrm{\Delta }n$ varies strongly from half-cycle to half-cycle due to ionization-induced plasma dispersion (${\mathrm{\Delta }n}_{plasma}$). This produces an ultranarrow temporal window for phase matching, which results in high-contrast IAPs. Therefore, our filamentation-assisted phase matching—combining ionization gating²¹ with phase-matching gating^22,23—ensures the robust generation of high-contrast IAPs.

Complementary to this analytic framework, our numerical method combines the nonlinear driver propagation and the single-atom HHG calculations with the electromagnetic field propagator, which takes into account the integral solution of the Maxwell equations⁵⁶. At the single-atom microscopic level, we solve the time-dependent Schrödinger equation (TDSE) under the commonly used single-active electron approximation. It is important to note that approximations like the strong field approximation, while faster, fail to accurately reproduce HHG driven by few-cycle laser pulses like those used in our experiment⁵⁷. As commented above, we also account for the nonlinear propagation of the driving field using the method described in⁴⁴, as well as for harmonic propagation and phase-matching. Further details are provided in the Methods section. Note that this unique combination of nonlinear propagation and HHG has been successfully used in lower-pressure configurations were IAPs were obtained³².

Key parameters and the complete spatio-temporal intensity profiles of the driving field during nonlinear propagation through the output section of the 70-torr Ar-filled SIGC are presented in Fig. 5a. Owing to self-guiding during filamentation, the beam radius (blue curve) remains nearly constant in the final section of the SIGC. In contrast, the beam in the SGC diverges much more rapidly (similar analysis for SGC shown in Supplementary Fig. 10). We depict the peak intensity (green) and pulse duration (red) for the pulse on-axis. Overall, these results suggest favourable harmonic phase-matching conditions due to the excellent spatio-temporal characteristics of the driver (extremely short and almost perfectly collimated) in this region of the SIGC, comparable to those achieved in gas-filled waveguides^12,58,59 or to the horizontal phase-matching branch described in^41,60. These favourable conditions are evidenced in Fig. 5b, where HHG build-up is shown through the 3D-TDSE single-atom HHG temporal emission (top) and spectra (bottom) at every on-axis position across the propagation direction in this final region of the SIGC. Nonlinear propagation ensures clean HHG generation, especially near the focus position (z = 0). More specifically, filamentation-assisted self-compression of the driving pulse allows for the generation of clean IAPs already at the single-atom level. However, to take into account the complete HHG build-up, off-axis contributions and transverse phase-matching also need to be considered besides longitudinal phase-matching. The results of the complete macroscopic calculations are plotted in Fig. 5c, showing a qualitatively good agreement with the experimental measurements.

Fig. 5. Numerical simulations of nonlinear driving field propagation and IAP generation in a SIGC.

(a) Peak intensity (green) and size (blue) of the driving beam as it propagates along the trailing edge of the SIGC filled with 70-torr Ar. The temporal FWHM of the driving pulse that propagates on-axis is plotted in red, and the three bottom panels show the spatio-temporal intensity profile at three different positions along the SIGC. For the simulation we used a beam with 203 µJ input energy with the same temporal profile as measured in the experiment and with a Gaussian spatial shape (see Methods). With the SIGC evacuated, the beam has a waist of 40 µm at the focus (position z = 0 in the horizontal axis), which is located a few millimetres before the end of the SIGC. (b) 3D-TDSE single-atom HHG calculations along the SIGC propagation axis reflecting the attosecond temporal emission (top panel) and the corresponding harmonic spectra (bottom panel). (c) Attosecond pulse (top) and its EUV spectrum (bottom) obtained from the full macroscopic HHG simulations after propagation to a far-field detector. These macroscopic calculations predict the emission of a prominent isolated attosecond burst with a FWHM duration of ~320 as. A secondary burst appears with <10% intensity compared to the main one, resulting in spectral modulations.

Figure 5c presents the results of complete macroscopic propagation simulations, incorporating both longitudinal and transverse phase-matching. The temporal (top) and spectral (bottom) results confirm the generation of an IAP as short as 320 as, along with a secondary burst with less than 10% of peak intensity. This secondary burst introduces modulations into the correspondent HHG spectrum, which were not observed in the experimental results. We believe that the experimental optimization procedure consisting on an iterative adjustment of the the input iris aperture, the focal position in the SIGC, the gas pressure, and the insertion of a wedge pair to control spectral dispersion, which is computationally unfeasible to mimic, have helped to achieve the optimum transverse phase-matching conditions, similar to those reported in gas jet experiments^61,62. In addition, the simulation assumes a near-perfect Gaussian driving beam, whereas the experimentally post-compressed pulse (compressed by >40×) inevitably carries wavefront imperfections and wavelength-dependent aberrations⁶³, resulting in a more complex spatiotemporal focus that is difficult to fully incorporate into the model (see spatial–spectral distribution in Fig. 2). These differences also help explain why the simulation reproduces the trends of the nonlinear-propagation dynamics (see Fig. 3) while requiring a different nominal pressure, such as 70 torr, than used experimentally. Such non-ideal beam and wavefront characteristics may suppress the satellite burst experimentally, whereas the idealized simulated field tends to retain a noticeable satellite feature.

In summary, we have demonstrated that filamentation-assisted IAP generation in the SIGC enhances the temporal resolution of few-cycle IR pump and IAP probe experiments, by simultaneously shortening the few-cycle pulse and achieving high-contrast IAPs. We observed that a SIGC configuration more effectively facilitates IAP generation compared to SGC. Moreover, this versatile method is applicable across common inert gases used for HHG. Notably, IAPs generated in this work are driven by a turn-key Yb laser, which have become the mainstream high-power femtosecond sources. Therefore, the nearly maintenance-free IAP source demonstrated here promises to enhance accessibility and advances attosecond science and technologies. The filamentation-based self-compression scheme also shows great promise for shortening the pulse without the need for additional dispersion compensation, while preserving pulse quality. This approach could enable multistage setups, paving the way for sub-femtosecond, high-intensity IR pulses and advancing ultrafast science.

Methods

Attosecond streaking

An attosecond streak camera, shown in Fig. 1a, was used to analyze the filamentation-based post-compressed IR pulse and the resulting EUV pulses. After the SIGC, the EUV and residual IR passed through a customized filter: IR was transmitted through the outer section, while a 2-mm diameter thin metal filter, such as 200-nm Al, Zr, or Ag, suspended at the center by three thin wires blocked the IR, isolating the EUV in the center. The delay between the central EUV and annular IR was adjusted by moving the outer long mirror on a spatial delay stage. It consists of a long reflective mirror (30 mm by 120 mm) with a slot in the middle, into which a smaller long reflective mirror (2 mm by 20 mm) is inserted. This specialized beam splitter. is coated with Ag and operates at a grazing incidence angle of 6°, providing high reflectivity for the IR and EUV beams. Additionally, an iris was incorporated into the setup to control the IR intensity, optimizing the streaking addressing field. Both the EUV and IR beams were then reflected by a Ni-coated elliptical mirror (with a focal length of 20 cm) at a grazing angle of 6° and focused into a Ne gas jet, where the EUV beam generated photoelectrons. These photoelectrons were collected using a 60-cm-long magnetic bottle electron time-of-flight spectrometer, and the recorded spectrogram captured the time delay between the EUV and probe pulses. For precise delay control, a piezoelectric transducer, based on interference fringes from a CW 808 nm laser, was used to feedback control the delay between the EUV and IR pulses. The uncertainty in the relative delay is as low as approximately 50 as.

TIPTOE

The TIPTOE setup^45–47 is similar to the attosecond streaking setup, shown in Fig. 1a, with two modifications: (1) the central IR filter (a 2 mm diameter metal foil, such as Al, Zr, Ag) was removed, and (2) ~ 30 torr of Ar were introduced into the streaking chamber to fully absorb the generated EUV radiation. A spatial beam splitter was used to divide the IR beam into central and annular parts. The delay between the central and annular beams was adjusted by moving the outer long mirror. After passing through the beam splitter, the two beams were focused by an elliptical mirror. The intense annular beam ionized the ~30 torr of Ar at the focus, while the central beam perturbed the ionization yield. To prevent overionization, a partially closed iris was placed along the annular beam path. The ionization fluorescence was collected by a photomultiplier, and a boxcar integrator was used to improve the signal by averaging 100 ionization events. The modulation of the ionization yield, measured as a function of the time delay between the two pulses, provided a direct representation of the electric field of the pulse. All TIPTOE data presented here were obtained after spectral filtering in the range of 500 nm to 1300 nm. Note that when the chamber is filled with ~30 torr of Ar, the distance from the exit of the filamentation to the TIPTOE focus is approximately 120 cm. The corresponding GDD is only 0.8 fs², which hardly stretches the 3.5 fs IR pulse.

Numerical methods

Our numerical simulations combine the nonlinear propagation of the linearly polarized driving field with full-quantum HHG at the single-atom level, and subsequent macroscopic propagation of the harmonics to a far-field detector, thus including the effects of phase-matching. The input beam to the code is obtained from experimental data by multiplying the retrieved complex temporal profile $\mathcal{E}\left(t\right)$ (envelope and phase) of the 4.68-fs IR pulse from the TIPTOE measurement (see Fig. 3e) by an ideal Gaussian spatial profile at focus, i.e., ${\mathcal{E}}_{\mathrm{ini}}\left(r,t\right)={\mathcal{E}}_0\mathcal{E}\left(t\right)\exp \left(-r^2/w_{\mathrm{ini}}^2\right)$, where $w_{\mathrm{ini}}$ is the initial beam waist, $t$ is the time in the laboratory reference frame, and $r$ denotes the radial coordinate in cylindrical symmetry. The input pulse amplitude ${\mathcal{E}}_0$ is chosen to match the experimental pump energy.

This beam is then expanded, collimated and focused with ideal achromatic mirrors by solving the non-paraxial unidirectional pulse propagation equation in vacuum^64–66. Focusing elements are numerically modeled in the frequency domain as quadratic spatial phases. The initial beam size $w_{\mathrm{ini}}$ and free-space propagation distances are calculated such that, after the final focusing stage with the concave mirror ($f^{\prime }=35\mathrm{cm}$), the driving beam reaches a waist at focus of 40 μm in vacuum, which is consistent with the experimental measurements (Fig. 2a).

The complex spatio-temporal amplitude of the linearly polarized driving beam after the final concave mirror is used as input to the simulations of nonlinear propagation inside the SIGC or SGC. In SIGC simulations, the full space between the mirror and the cell output ( > 35 cm) is filled with Ar at constant pressure. On the contrary, in SGC simulations, the gas occupies a 2.2-mm-long region around the geometrical focus, while the rest of the space from the concave mirror is kept in vacuum. In both configurations, the nonlinear propagation of the driving beam is computed by solving the standard nonlinear envelope equation for the complex pulse envelope assuming cylindrical symmetry⁶⁷. Complete simulations include diffraction and space-time defocusing, chromatic dispersion, the Kerr effect, self-steepening and shock terms, nonlinear absorption, and photoionization and plasma dynamics. The equation governing the evolution of the complex pulse envelope along the propagation direction $z$ reads^44,68:

$$\frac{\partial }{\partial z}\mathcal{E}\left(r,\mathrm{\Omega },z\right)=\frac{i}{2k_0}{\left(1+\frac{\mathrm{\Omega }}{{\omega }_0}\right)}^{-1}{\nabla }_{\perp }^2\mathcal{E}\left(r,\mathrm{\Omega },z\right)+i\left(k\left(\omega \right)-k_0-\frac{\mathrm{\Omega }}{v_{\mathrm{g}}}\right)\mathcal{E}\left(r,\mathrm{\Omega },z\right)\mathcal{+}\mathcal{F}\left\{\widehat{N}\left[\mathcal{E}\left(r,T,z\right)\right]\right\}$$ 2

where $\mathrm{\Omega }=\omega -{\omega }_0$ represents the detuning from the pulse central frequency ${\omega }_0$, $k\left(\omega \right)=n\left(\omega \right)\omega /c$ is the pulse propagation constant with $n\left(\omega \right)$ being the refractive index of the medium and $c$ the speed of light in vacuum, $k_0=k\left({\omega }_0\right)$, ${\nabla }_{\perp }^2$ denotes the transverse Laplace operator, and $\mathcal{F}$ stands for direct Fourier transform. The above equation is written in a local time $T=t-z/v_{\mathrm{g}}$ measured in a reference frame traveling with the pulse at the group velocity $v_{\mathrm{g}}$, and the nonlinear operator gathers all the nonlinear source terms related to the Kerr effect, ionization and nonlinear absorption and is given by:

$$\widehat{N}\left[\mathcal{E}\left(r,T,z\right)\right]={\widehat{N}}^{\mathrm{Kerr}}\left[\mathcal{E}\left(r,T,z\right)\right]+{\widehat{N}}^{\mathrm{ioniz}}\left[\mathcal{E}\left(r,T,z\right)\right]+{\widehat{N}}^{\mathrm{abs}}\left[\mathcal{E}\left(r,T,z\right)\right]$$ 3

$${\widehat{N}}^{\mathrm{Kerr}}\left[\mathcal{E}\left(r,T,z\right)\right]=\frac{i{\omega }_0{n}_2}{c}\left(1+\frac{i}{{\omega }_0}\frac{\partial }{\partial T}\right)\mathcal{E}\left(r,T,z\right){∣\mathcal{E}\left(r,T,z\right)∣}^2$$ 4

$${\widehat{N}}^{\mathrm{ioniz}}\left[\mathcal{E}\left(r,T,z\right)\right]=-\frac{\sigma }{2}\left(1+i{\omega }_0{\tau }_{\mathrm{c}}\right){\left(1+\frac{i}{{\omega }_0}\frac{\partial }{\partial T}\right)}^{-1}\rho \left(r,T,z\right)\mathcal{E}\left(r,T,z\right)$$ 5

$${\widehat{N}}^{\mathrm{abs}}\left[\mathcal{E}\left(r,T,z\right)\right]=-\frac{W\left({∣\mathcal{E}∣}^2\right)U_{\mathrm{i}}\left({\rho }_{\mathrm{at}}-\rho \left(r,T,z\right)\right)}{2{∣\mathcal{E}\left(r,T,z\right)∣}^2}\mathcal{E}\left(r,T,z\right)$$ 6

where $\sigma$ is the cross section for inverse Bremsstrahlung, ${\tau }_{\mathrm{c}}$ is the electron collision time, $U_{\mathrm{i}}$ is the ionization potential of the atoms of the medium, ${\rho }_{\mathrm{at}}$ is the number density of neutral atoms, and $W\left({∣\mathcal{E}∣}^2\right)$ denotes the photo-ionization rate which is computed using the Perelomov-Popov-Terent’ev (PPT) model⁶⁹. The free electron density $\rho \left(r,T,z\right)$ is obtained by solving the evolution equation ${\partial }_T\rho \left(r,T,z\right)=W\left({∣\mathcal{E}∣}^2\right)\left[{\rho }_{\mathrm{at}}-\rho \left(r,T,z\right)\right]$. Computationally, the nonlinear propagation equation for the driving pulse is solved using a standard split-step scheme, with the nonlinear source term integrated with a fourth-order Runge-Kutta (RK4) algorithm, and the linear term solved with a Crank-Nicolson finite difference method.

The output pulse from the nonlinear propagation simulation at each point in the gas cell is used to build the real electric field as $E\left(r,t,z\right)=\mathfrak{R}\left\{\mathcal{E}\left(r,t,z\right)\exp \left(-i{\omega }_{0}t+i{\varphi }_{\mathrm{CEP}}\right)\right\}$⁶⁶, with ${\varphi }_{\mathrm{CEP}}$ being the pulse CEP. This field is finally used as input to the HHG simulations, where the generation volume (final region of the cells where the field intensity is high enough to efficiently drive HHG) is discretized into elementary radiators. Single-atom HHG at each radiator is computed through the full integration of the three-dimensional time-dependent Schrödinger Eq. (3D-TDSE) under the single active electron approximation. The latter is numerically solved with a Crank-Nicolson algorithm. Finally, the emissions ${\mathbf{E}}_j$ from each charge in the generation volume are propagated to a far-field detector at the position ${\mathbf{r}}_{\mathrm{d}}$ through the electromagnetic field propagator, and all elementary fields are coherently added in the detector to obtain the total signal ${\mathbf{E}}_{\mathrm{tot}}\left({\mathbf{r}}_{\mathrm{d}},t\right)$ as follows⁵⁶:

$${\mathbf{E}}_{\mathrm{tot}}\left({\mathbf{r}}_{\mathrm{d}},t\right)=\mathbf{E}\left({\mathbf{r}}_{\mathrm{d}},t\right)+{\sum }_{j=1}^N{\mathbf{E}}_j\left({\mathbf{r}}_{\mathrm{d}},t\right)$$ 7

$${\mathbf{E}}_j\left({\mathbf{r}}_{\mathrm{d}},t\right)=\frac{q_{\mathrm{e}}}{c^2∣{\mathbf{r}}_{\mathrm{d}}-{\mathbf{r}}_j∣}{\mathbf{e}}_{\mathrm{d}}\times \left({\mathbf{e}}_{\mathrm{d}}\times {\mathbf{a}}_j\left(t-∣{\mathbf{r}}_{\mathrm{d}}-{\mathbf{r}}_j∣/c\right)\right)$$ 8

where ${\mathbf{r}}_j$ denotes the position of the j-th radiator inside the generation volume, ${\mathbf{e}}_{\mathrm{d}}={\mathbf{r}}_{\mathrm{d}}/∣{\mathbf{r}}_{\mathrm{d}}∣$ is a unitary vector pointing to the detector, $q_{\mathrm{e}}$ is the electron charge, and ${\mathbf{a}}_j\left(t\right)$ is the electron dipole acceleration obtained from the mean value of the acceleration operator after solving the single-atom 3D-TDSE⁶⁶. In the propagation of the harmonics towards the detector we also include linear absorption in the gas cell through Beer’s law. Using the electromagnetic field propagator for the harmonics accounts for the exact integral solution of Maxwell’s equation in vacuum. Thus, we assume that harmonics are weakly perturbed as they propagate through the gas cells, which is a reasonable approximation in partially ionized gases at low pressures^13,56, as is the case in this study. In addition, our model assumes that the propagation of the driving field and the harmonics are decoupled, such that the influence of HHG back in the nonlinear propagation of the driver is neglected.

Full macroscopic simulations of HHG are parallelized and were ran in supercomputing resources. The spatial positions of the radiators within the gas cells are chosen randomly to avoid artificial diffraction effects. The total number of radiators $\left(N\right)$ as well as all numerical grid resolutions were adapted to ensure the convergence of the simulations. Finally, different values of driver CEP were also tested in full macroscopic HHG simulations to optimize the final IAP at the detector.

Author contributions

Y.-E.C., M.-S.T., and M.-C.C. designed and constructed the experimental setup. Y.-E.C. and M.S.T. collected the data. Y.-E.C., A.-Y.L., and M.-C.C. analyzed the TIPTOE and streaking data. M.F.-G., E.C.-J., J.S., J.S.R., and C.H.-G. performed simulations of nonlinear propagation and HHG. All authors contributed to writing the manuscript, which was first drafted by Y.-E.C. M.F.-G., J.S.R., C.H.-G. and M.-C.C. All authors discussed and interpreted the experimental data.

Peer review

Peer review information

Nature Communications thanks Omair Ghafur, Olga Kosareva and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data that supports the findings are presented in the article and Supplementary Information.

Code availability

The code and datasets generated and/or analyzed during this study are available from the corresponding authors upon request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-70903-4.