Open Access
Add to BibSonomy
Abstract
For many years, light-matter interaction in the strong-field regime has benefited from continuous improvement of femtosecond lasers, in terms of peak power or repetition rate. One of the most current major challenges is the achievement of high-energy, near single-cycle pulses. Such performances are of primary interest in attosecond science for producing intense isolated bursts of extreme ultraviolet light through high-harmonic generation in gases or solids. We present here a detailed experimental and numerical study on a helium filled hollow-core fiber-based post-compression stage. Our measurements highlight the importance of the width and phase of the input spectrum on the spectral broadening, and on the resulting post-compressed pulse. Near Fourier-transform-limited pulses as short as 3.5 fs, carrying a 2.5 mJ energy centered at 750 nm at 1 kHz repetition rate, and leading to a compression factor greater than seven, are demonstrated. The numerical results are in good agreement with the experimental data. Here, spectral broadening is governed by the Kerr effect and the self-steepening on the trailing edge of the guided pulse.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
When a high-intensity (above 1014 W/cm2), ultrashort driving pulse interacts with a gas medium or a solid, a train of attosecond (1 as = 10−18 s) extreme ultraviolet (XUV) light pulses is generated through high harmonic generation (HHG) [1–4]. For many experiments [5], the production of intense isolated single attosecond pulses is crucial for studying light-matter interactions with unprecedented spatial and temporal resolutions. Among them, one can cite for example pump-probe experiments [6], nano-plasmonics [7], molecular vibrational wave packet mapping [8], atomic correlation studies [9], and investigations on attosecond electron dynamics in molecules [10]. The easiest way to achieve these pulses consists in confining the XUV emission within one-half of the optical cycle near the peak of the driving pulse. This temporal confinement can be obtained by using polarization-gating techniques [11,12]. The main disadvantage of these methods is their poor conversion efficiency. A more efficient way for producing single attosecond pulses is to use near single-cycle pump lasers. Such ultrashort pulses are obtained by post-compression of spectrally broadened high-energy, sub-10 fs pulses through self-phase modulation (SPM) in a gas-filled capillary [13,14] or a multi-pass gas cell [15]. Besides these nonlinear techniques, the possibility to generate energetic sub-cycle laser pulses by synthesizing together different laser pulses covering different spectral regions [16,17] has also been demonstrated. However, accessing pulse durations within the 3 to 5 fs range carrying an energy over one millijoule remains quite challenging. This is due to the experimental difficulty of producing a sufficiently large spectral bandwidth with controllable and compensable spectral phase variations. Thus, post-compression systems exhibiting pulse durations lower than 4 fs, i.e. approaching a single optical cycle at 800 nm central wavelength, with an output energy above 2 mJ, remain quite rare. For the best of our knowledge, there are less than five laser systems worldwide with such performances so far [18].
In this paper, we report on the generation of intense few-cycle pulses by efficient self-phase-modulation (SPM) induced spectral broadening of circularly polarized pulses in a gas-filled stretched flexible hollow-core fiber (HCF). We present a detailed study on the dependence of post-compressed pulse duration with the laser initial spectrum width. We show that an optimum initial bandwidth exists that allows producing near single-cycle pulses. Our study also highlights the extreme sensitivity of the final post-compressed pulse to the initial spectral phase. In parallel with the design of the experiment, we have completed a specific propagation code simulating the experimental conditions. The computation results agree well with the experimental data, as we shall see. Thus, in addition to helping us designing the post-compression system, these numerical calculations allow for a deeper understanding of the involved physical processes.
2. Experimental setup
2.1 ATTOlab-Orme facility laser
The HCF post-compression unit is implemented on the 1 kHz output of the ATTOlab-Orme facility laser. Amplitude Technologies has developed this laser in collaboration with CEA Saclay within their former joint laboratory Impulse. The laser system is a Ti:Sapphire based dual output system which can deliver routinely and simultaneously CEP stabilized 15 mJ energy, 23 fs duration pulses at 1 kHz repetition rate, and 1.8 mJ energy, 25 fs duration pulses at 10 kHz repetition rate. The long-term CEP stability of the 1 kHz laser is 350 mrad shot to shot, and the one of the 10 kHz laser is 250 mrad. Thanks to its specific design, the output pulse spectral width is tunable between 40 nm up to 110 nm leading to a pulse duration between 60 fs and 18 fs. [19–21].
Figures 1(a) to 1(d) show the input experimental spectra, and the reconstructed phases measured with a single shot SHG-FROG just before the post-compression system entrance, used in both the experiment and the simulations. The bandwidth, measured at 10% of the maximum intensity, is between 65- and 100-nm, and the spectra have a nearly super-Gaussian shape. Note that we use the 10% threshold for measuring the spectrum width all along the paper. Because of the strong intensity modulations on the broadened spectra, we found it more reliable than the commonly used full-width at half-maximum or 1/e2 criteria. In general, the phase is not flat in the main part of the spectrum of the driver pulse, due to residual second and third order dispersions from the chamber entrance window material and the quarter-wave plate used to produce the circular polarization. The pulse duration, measured at full-width at half-maximum is between 22- and 32-fs.
Fig. 1. Laser initial spectrum (solid line) and phase (dashed line) for (a) 65 nm, (b) 75 nm, (c) 85 nm, and (d) 100 nm widths, measured at 10% of the maximum intensity.
2.2 Post-compression setup
Figure 2(a) shows the post-compression experimental set-up stage installed on FAB 1 line within ATTOlab-Orme at CEA Saclay. It is largely based on the designs shown in [22,23] and fits on a 4.5 m long optical table. The output laser beam is equipped with a first beam pointing stabilization system developed with the laser used for slow drift correction at the last laser amplifier output, before pulse compression. The laser beam is then steered in a vacuum chamber and its position is stabilized thanks to an ALIGNA system from TEM Messtechnik GmbH [24]. A leakage of one of the dielectric mirrors in front of the chamber is used to image the surface of StM1 mirror on the ALIGNA near field detector (StNF). A leakage of the last steering mirror, used for sending the focusing beam to the fiber, is also focused on the far field detector (StFF). Both motorized mirrors StM1 and StM2 adjust automatically beam position and angle in order to insure day to day fine alignment for optimal fiber coupling and thus stabilizes actively the beam pointing over several hours in addition to the first stabilization system.
Fig. 2. (a) Experimental set-up of the stretched HCF-based post-compression stage. StM1 and StM2, StNF and StFF are respectively the beam pointing stabilization motorized mirrors and the position detectors (ALIGNA). QW 1 and 2 are broadband quarter wave plates, DM and SM are dielectric and silver mirrors respectively. CM1 and CM2, DACM1 and DACM2 are respectively low spectral range around 800 nm and double angled broadband-chirped mirrors from Ultrafast Innovations, CC and CX respectively concave and convex spherical mirrors. The fiber entrance is in a vacuum chamber while the exit is in a gas-filled chamber. (b) Single-shot focal spot recorded positions at 100 Hz when the stabilization system is OFF (blue points cloud) and ON (white points cloud) (c) 340 µm diameter at 1/e2 focal spot recorded at HCF entrance.
As shown in Fig. 2(b), the focal spot instabilities recorded for an equivalent focal length of 5.9 m reduce from 25 µm RMS to 8 µm which corresponds to a 1.3 µrad stability when the stability control is set ON. One can also observe that the measured cloud moves on the camera in order to reach the good coupling position. One has to note that the distance between laser and compressor is roughly 3-m long as well as the distance between compressor output and post-compression entrance. The achieved pointing stability with such equivalent focal length is quite remarkable. After reflection on two chirped mirrors (CM1 and CM2), each introducing -250 fs2 group delay dispersion, the IR beam is steered to the focusing optics by two broadband dielectric mirrors (DM) surrounding a first quarter wave plate that turns the linear polarization to circular. They compensate for dispersion introduced by the 13 mm-thick fused silica chamber entrance window and by the quarter-wave plate used to convert the polarization from linear to circular. An aberration-free reflective focusing telescope composed of two spherical mirrors with a radius of curvature of - 2000 mm (CC1) and 800 mm (CX1) (5.9 m equivalent focal length) focuses the beam at the fiber entrance after passing a last close to normal incidence dielectric mirror. The incidence angles on CC1 and CX1 are different, respectively 2 ° and 3.8 ° specifically calculated in order to eliminate the astigmatism at the focal spot. This is the first step to ensure perfect coupling in the fiber. The second step consists in reaching the right focal spot size at the fiber entrance. It is determined by 2w0 = 0.64.d where w0 is the waist of the focal spot and d is the HCF inner diameter. According to the 30 mm diameter at 1/e2 of the incoming beam, the two spherical mirrors radii of curvature and the distance between them are fixed. An iris, closed to 25 mm, tunes perfectly the spot diameter to obtain the required 170 µm waist at focus, the latter being recorded continuously by a camera (Fig. 2(a)) using the last steering mirror leakage. A circularity close to 98% of the focal spot at 1/e2 is then achieved, as shown in Fig. 2(c), thanks to the astigmatism compensation calculation and set-up.
The stretched fiber, developed by Laser Laboratorium Göttingen [25] exhibits an internal diameter of 530 µm. Previous experiments proved that a large inner diameter associated with a long fiber length is an advantage for optimal coupling and spectral broadening [26]. However, in our case the available free space in the laboratory limits to 2.0 m the length of the HCF. This in turn limits the maximum coupling energy, due to the damage threshold of the mirrors surrounding the HCF, especially the last 45° output mirror. Thus, we had to limit the input energy to 6 mJ to limit the energy density at 50 mJ.cm−2 on the output mirror. A coupling efficiency in vacuum of 82% has been achieved, close to the 84% theoretical value. The active stabilization systems and good environmental conditions keeps this coupling efficiency stable over more than 8 hours.
The HCF entrance and exit are in two separate chambers. The entrance chamber is continuously pumped to maintain a pressure below 10−1 mbar in order to achieve an optimal coupling. The exit chamber is filled with helium, at peak pressures up to 3.0 bar. This configuration leads to a longitudinal pressure gradient that we have estimated with the Computational Fluid Dynamics (CFD) Siemens PLM software [27]. We found, as other laboratories [28,29], that the pressure scales as $\sqrt z $, where z is the position along the laser propagation axis. A pressure gradient in the HCF is useful for two reasons. First, keeping a pressure as low as possible at the entrance of the capillary prevents any defocusing effect due to the ionization of the gas that would deteriorate the laser spatial profile, and thus the coupling efficiency. Secondly, the pressure increases softly from the input to the output of the capillary, allowing for a smooth SPM-induced spectral broadening all along the interaction of the pulse with the gas. This ensures, together with circularly polarized light for limiting ionization-induced losses, for efficient energy coupling, over 2 mJ, in the gas-filled HCF while producing sub-5 fs pulses.
Manual horizontal and vertical translation stages allow for fine alignment of the input and output of the HCF. The position of the HCF entrance is fixed; thus, a translation stage on CX1 is used to move the focal spot position at the HCF entrance to ensure a perfect coupling of the beam. A second aberration free telescope placed 1.9 m after the fiber exit, composed by CX2 and CC2, with respectively 1000 mm and - 2000 mm radius of curvature, 3.0 ° and 1.7 ° angles of incidence, collimates the beam at 15 mm (1/e2) before exiting the output chambers through a 2 mm thick fused silica window. A second quarter wave plate turns the polarization of the spectrally broadened beam back to linear and horizontal. Optimal pulse compression is obtained after 12 reflections on two pairs of double-angled chirped mirrors (PC70 from Ultrafast Innovations), corresponding to a dispersion compensation of approximately −480 fs2, coupled to a motorized pair of fused silica wedges. A 1 mm thick KDP plate can be inserted in the beam for compensating the residual negative third-order dispersion. Because of its higher third order dispersion (TOD)/group delay dispersion (GDD) ratio, compared to fused silica, it allows reaching the shortest pulse duration [30]. A commercial FemtoEasy single-shot Second-Harmonic Frequency-Resolved Optical Gating (SHG-FROG) [31] measures the pulse spectral phase and duration.
3. Numerical model
The main equation of the model is the nonlinear envelope propagation equation, derived by Brabec and Krausz in the slowly evolving wave approximation (SEWA), valid for pulse durations as short as one optical cycle [32]. In the moving reference frame $\tau = t - {\beta _1}z$ and z, it is written, for a pulse propagating in the positive ξ direction:
In cylindrical geometry and in the general case, the field E depends on the three spatial coordinates r, ξ, and θ, and on the retarded time τ, i.e. E≡ E(r,ξ,θ,τ), and ${\beta _1} = {v^{ - 1}}$. v is an arbitrary reference frame velocity, generally taken as the group-velocity at the central pulse frequency ω0 in free-space propagation, and to the fundamental mode velocity in guided propagation. In the first term on the right-hand side of Eq. (1), $D = \mathop \sum \nolimits_{m = 2}^\infty \frac{{{\beta _m}}}{{m!}}{\left( {i\frac{\partial }{{\partial \tau }}} \right)^m}$ is the dispersion operator, linear in E. In the present study, we limit the development to $D \approx{-} \frac{{{\beta _2}}}{2}\frac{{{\partial ^2}}}{{\partial {\tau ^2}}}$, i.e. to the group-velocity dispersion (GVD). We checked that the higher-order terms are negligible here. The second term describes the diffraction, and the third term is the nonlinear polarization. The operator $T = 1 + \frac{i}{{{\omega _0}}}\frac{\partial }{{\partial t}}$ in front of PNL is responsible for the self-steepening of the pulse. ${\beta _0} = \frac{{{n_0}{\omega _0}}}{c}$ is the wavenumber, and n0 ≡ n($,$ω0) is the linear index of refraction at frequency ω0. Note that all quantities depend on ξ, the coordinate along the propagation axis, through the pressure gradient.
Note that we did not specify the polarization state of the field so far, Eq. (1) being valid for any polarization. For circular polarization, it is convenient to express the field in the rotating frame: ${\boldsymbol E} = {E_ + }{\hat{{\boldsymbol \sigma }}_ + } + {{\boldsymbol E}_ - }{\hat{{\boldsymbol \sigma }}_ - }$, where ${\hat{{\boldsymbol \sigma }}_ \pm } = \frac{{{{\hat{{\boldsymbol e}}}_{\boldsymbol x}} \pm i\widehat {{{\boldsymbol e}_{\boldsymbol y}}}}}{{\sqrt 2 }}$ stand for the unit vectors in the rotating frame. The + sign (resp. -) designates the left (resp. right) handed polarization. ${\hat{e}_x}$ and ${\hat{e}_y}$ are the unit vectors in the fixed frame. The advantage of the rotating frame is that we solve Eq. (1) for one or the other rotating field component, ${E_ + }$ or ${E_ - }$, thereby reducing considerably the computational effort. However, by doing so, we suppose implicitly that the polarization is conserved all along propagation. This assumption is well justified in the case of isotropic media, and is supported by polarization measurements at the output of the HCF.
The nonlinear polarization is due to the Kerr effect, and to the optical field ionization of the filling gas:
The ionization contribution to the nonlinear polarization is written:
The time evolution of the electron density is given by:
We solve Eq. (1), with auxiliary Eqs. (3), 4 and 5, using a standard symmetrized split-step Fourier method [41]. In the specific case of gas-filled HCF, the linear part of the equation is solved in the HCF eigenbasis [42], in the same way as in linear polarization. Indeed, circularly polarized (CP) eigenmodes may be built by linear combinations of the two linearly polarized (LP) orthogonal modes [43]. The integration of the nonlinear part is performed using a fifth-order Runge–Kutta method with Cash–Karp coefficients [44].
In order to get as close as possible to the experimental conditions, we use measured spectra as input (see Sec. 2). We assume an incident Gaussian spatial beam profile of 170 µm waist, i.e. 0.64% of the HCF inner radius. The laser energy is 4.2 mJ, corresponding to 70% coupling efficiency of the 6.0 mJ input energy. Modal decomposition [45] is performed on the 10 first modes with cylindrical symmetry, i.e. on $C{P_{0m}}$ modes with $1 \le m \le 10$. In our conditions, the mode coupling is weak, and generally, at most 3 or 4 modes are necessary to insure convergence of the computations. The radial step size is 0.5 µm and time-step is 120 as (1 as = 10−18 s). This is small enough for numerical calculations to converge even in case of strong self-steepening.
4. Results and discussion
4.1 Experimental and numerical results
In this section, we present the experimental data obtained with the input spectra given in Fig. 1. Each set of data, i.e. the broadened spectra and post-compressed pulses, is collected for a given spectrum/pulse as a function of the gas filling pressure. Numerical calculations are performed using the experimental characteristics of the driver pulse. The results are directly compared to the experimental measurements.
Figure 3 depicts the evolution of the profile of the spectra measured at the output of the HCF with the helium peak pressure and the width of the input spectrum. The horizontal dashed line in Fig. 3(a) gives the 10% intensity threshold used to define the spectral width. The detection range of the spectrometer is limited to 950 nm. Beyond this wavelength, the grating diffraction efficiency and the camera sensitivity drop sharply. So we cut the experimental spectra at 950 nm wavelength in order to avoid the contribution of amplified noise by the software correcting the spectral response of the camera (the spectrometer is intensity calibrated), the CMOS sensor of the camera being peaked around 540 nm wavelength. In the operating range of the spectrometer, at given initial spectral width, the spectrum broadens with pressure as expected. As a general trend, the profile shows a main peak around the central wavelength, and a secondary peak on both sides. The red wing is slightly more intense and narrower than the blue one, making the spectrum asymmetric at high pressure. One can note that this asymmetry is independent of the initial spectral width, even though it is more pronounced for 85 nm and 100 nm driver widths. For the largest broadening, achieved with 3.0 bar gas pressure and 85 nm-100 nm initial pulse widths, it becomes difficult to conclude on the shape and width of the red wing because of the limitation of our spectrometer.
Fig. 3. Evolution of experimental spectra with helium peak pressure for (a) 65 nm, (b) 75 nm, (c) 85 nm, and (d) 100 nm initial spectral width. The dashed line in (a) gives the threshold for spectrum width measurements.
We now compare the experimental data with the results of the numerical model presented in Sec. 3. The model describes well the evolution of the spectral broadening measured as a function of pressure, i.e. a monotonic increase of the width of the output spectrum with pressure for a given input spectrum/pulse. The calculated values of the spectral width, as well as the Fourier transform-limited pulse durations, are in good agreement with the experimental data, as we shall see later on. However, the model is not as efficient in describing the evolution of the spectral shape with gas pressure, specially the red wing, as shown in Fig. 4, giving a direct comparison of experimental spectra (red plots), recorded at the output of the HCF, for He peak pressure in the 0.5-3.0 bar range and 85 nm initial bandwidth, with the calculated one (black curves). It should be noted that by “direct comparison” we imply that there is no adjustable parameter in the model. The calculated spectra exhibit typical features of self-phase modulation induced by the Kerr effect in the presence of strong self-steepening of the pulse, namely the generation of new frequencies on both sides of the spectrum, those on the blue one being created on the trailing edge of the pulse while frequencies on the red one are generated on the leading edge, with a strong dissymmetry between the blue and the red wings caused by the self-steepening of the pulse [18]. The amplitude and width of the wings increase with the pressure of helium at the detriments of the amplitude of the central peak. The dissymmetry between the blue and red wings also increases with pressure above 1.5 bar (Fig. 4(d), 4(e) and 4(f)). One can also observe that the red wing on the calculated spectrum is always wider and brighter than on the experimental one, especially when the pressure exceeds 1.0 bar. As already mentioned, one point is that the spectral range of the intensity calibrated spectrometer used in this experiment is limited to below 950 nm. This spectral limitation decreases the accuracy of the direct comparison between experimental and numerical spectra especially on the red wing at high pressure.
Fig. 4. Comparison of experimental (red line) and calculated (black line) spectra at the HCF exit for a 85 nm initial spectral width and helium peak pressures of (a) 0.5 bar, (b) 1.0 bar, (c) 1.5 bar, (d) 2.0 bar, (e) 2.5 bar, and (f) 3.0 bar.
The width of the output spectrum as a function of helium peak pressure, measured at 10% of the intensity on the experimental spectra of Fig. 3, is given in Fig. 5 for 65 nm (black), 75 nm (red), 85 nm (green) and 100 nm (blue) initial widths. The full circles depict the width of the spectra measured just at the output of the capillary, while the open circles correspond to spectra recorded after the chirped mirrors, at the FROG entrance (see the experimental setup in Fig. 2(a)). The solid curves show the numerical results. The spectra measured at the FROG entrance are modified by the reflection/transmission of the optics between the HCF output and the FROG device, especially by the double angled chirped mirrors pairs. The relative amplitude of the wings compared to the central part of the spectrum is increased and some small oscillations on the blue side of the spectra appear. The width is taken at 10% of the maximum of the spectral amplitude, limited to 950 nm on the red wing, due to the spectrometer spectral response.
Fig. 5. (a) Spectral width as a function of helium peak pressure for 65 nm (black), 75 nm (red), 85 nm (green), and 100 nm (blue) initial bandwidths. The open circles correspond to experimental spectra measured just at the output of the capillary, and the full circles to spectra recorded after the chirped mirrors. The solid curves show the numerical results for optimized pulses. The dashed curve corresponds to calculations performed with a non-optimized initial spectral phase and a 65 nm initial bandwidth (see text for details). (b) Output versus input spectrum widths for a helium peak pressure of 3.0 bar.
The spectral broadening increases monotonically with pressure whatever the initial width of the spectrum. This trend is well reproduced by the numerical model. Difference between calculations and experimental data is the highest for 100 nm driver spectral width and pressures above 2.0 bar. The broadening is then similar to the 85 nm case. A careful inspection of the data shows that, at a given pressure below 2 bar, the spectral width increases linearly with initial width between 65 nm and 85 nm, and is almost constant above, as shown in Fig. 5(b) where we have reported the output versus input spectrum widths.
An arbitrary “saturation” effect beyond 85 nm bandwidth is observed on the experimental data in Fig. 5(b). This behavior is not reproduced by the simulations. It can be explained by the limited spectral response of the spectrometer on the red side, arbitrarily limiting the observed broadening on this side. Note that the effect is less clear when looking to the spectral widths after the chirped mirrors, since the latter have a limited spectral bandwidth. In addition, we observe that the comparison between calculated and experimental spectral widths is quite good, except for the 100 nm bandwidth. In this case, the measured widths are actually very close to the one observed with 85 nm initial width, and the calculations overestimate the spectral broadening whatever the gas pressure. This could be due to the difficulty of ensuring a flat phase over a broad spectral range, close to 100 nm, hence leading to pulse durations close to those achieved with a narrower bandwidth, despite the pulse duration optimization loop. Indeed, the pulse duration is optimized by measuring its duration before the input chamber with a single shot SHG-FROG. The measured residual spectral phase is flattened using a specific optimization loop between the FROG and the DAZZLER. Thus, a compromise must be found between the width of the input spectrum on the one hand and the quality of its phase on the other. The latter is controlled in our case by pre-compensating the effect of dispersion due to the fused-silica glass entrance window of the experimental chamber, and to the quarter-wave plate producing the circular polarization that are in the chamber. Therefore, the phase of the pulse which couples into the HCF is not known as precisely as expected and this limits the driver pulse duration shortening.
We have observed that the shape of the broadened spectrum is very sensitive to the initial pulse phase as well for some residual second order phase as third order phase. Thus this poor accuracy in determining residual spectral phase in the coupled pulse could be the main source of discrepancy between experimental and calculated spectra. The dashed line in Fig. 5 depicts the numerical results obtained with an initial spectral width of 65 nm in a case where the pre-compensation is not optimized. This curve illustrates how the width of the output broadened spectrum is impacted by residual second and third order dispersions, although the pulse duration is the same. The spectral broadening is then limited and the general shape of the spectrum is modified. At high pressure, the broadened spectrum can be 100 nm narrower than in the case where the spectral phase is better controlled. On the other hand, in the model we assume a perfectly Gaussian beam, focused exactly at the HCF entrance, while the experimental spatial profile is not necessarily Gaussian, and an uncertainty exists on the focus position along the propagation axis that could reduce the coupled energy and could alter the modal coupling, thus limiting the spectral broadening.
Figure 6 displays the evolution of the post-compressed pulse duration, measured at full-width at half-maximum of the intensity profile, with helium peak pressure, for spectral widths given in Fig. 5. The open circles are obtained by Fourier transform of the experimental spectra shown in Fig. 3 with open circles, while the solid triangles depict direct single shot SHG-FROG measurements (FEMTOEASY) performed in the best compression conditions. The durations given by the latter are very close to the Fourier transform limits whatever the conditions, the deviation always remaining in the error bars. The solid lines depict the numerical results performed with the optimal experimental conditions. As a general trend, pulse duration decreases continuously with pressure, in correlation with spectral width variations. The shortest duration is achieved for a 3.0 bar helium peak pressure, for all bandwidths.
Fig. 6. (a) Post-compressed pulse duration as a function of helium peak pressure, using 65 nm (black), 75 nm (red), 85 nm (green) and 100 nm (blue) initial spectral widths. The open circles are obtained by Fourier transform of the experimental spectra, while solid triangles correspond to SH-FROG measurements. The solid curves give the Fourier transform limited pulse durations predicted by the numerical model for optimized pulses. The dashed curve shows numerical results obtained with a non-optimized initial spectral phase and a 65 nm initial bandwidth (see text for details). (b) Post-compressed pulse duration as a function of input spectral width for a helium pressure of 3.0 bar.
The experimental value as a function of the initial spectral width is plotted in Fig. 6(b). A minimum Fourier transform-limited pulse duration of 3.0 fs is obtained with 85 nm initial width. Note that single shot SHG-FROG measurements corroborate the behavior observed on the spectral widths, reported in Fig. 5, i.e. a continuous variation between 65 nm and 85 nm initial widths, and a “saturation” beyond even though the measurements always give a slightly higher pulse duration. In addition to the possible imperfect residual dispersion compensation that can increase the pulse duration, compared to the Fourier transform-limited one, the calibration and the geometry of the spectrometer used in the FROG device limits the minimum pulse duration to about 3.5fs.
4.2 Best post-compression result
The different experimental studies presented here allowed us to determine the best conditions for producing the broadest spectrum, while keeping a high transmission of the HCF. We coupled a 6.0 mJ energy, 20 fs duration pulse (100 nm spectral bandwidth), at an estimated peak intensity of 4.0 × 1014 W/cm2, in the differentially pumped stretched HCF filled with 3.0 bar of helium. In this case, the duration of the post-compressed pulse, measured with a SHG single shot FROG, is as low as 3.3 ± 0.3 fs, with a calculated Fourier transform-limited pulse duration of 3.0 fs. Experimental single shot SHG-FROG trace is shown in Fig. 7(a) along with the reconstructed trace in Fig. 7(b).
Fig. 7. FROG measurement of the 2.5 mJ 1.5-cycle pulse. Panels (a) and (b) display respectively measured and retrieved FROG traces. Panel (c) displays initial (black line) and broadened (red line) spectra with the retrieved spectral phase (blue line). Panel (d) shows the retrieved temporal pulse shape (red line) and the calculated Fourier transform limited pulse (black dashed line).
The retrieved trace is in good agreement with the experimental one, with an error of 1.6 × 10- 2 on a 256 × 256 grid. The corresponding retrieved spectral phase and measured spectrum are shown in Fig. 7(c), leading to the temporal pulse profile given in Fig. 7(d). The best temporal compression is obtained by associating a 2 mm thick KDP plate to the motorized pair of fused silica wedges and to 12 reflections on the chirped mirrors. This corresponds approximately to a total group delay dispersion of −480 fs2. Only the central part of the HCF output is reflected by the optics of the compression stage. In this high-pressure regime, there is a ring surrounding the main beam that comes from the coupling conditions which degrade with pressure. The limited size of the chirped mirrors cuts this ring, containing about 20% of the HCF output. Taking into account the different transmission/reflectivity efficiencies, namely the gas-filled HCF coupling efficiency, the steering optics transmission and the chirped mirrors reflectivity, the overall transmission is limited to approximately 50% of the input energy in the post-compressed pulse. This leads to net output energy of 2.5 mJ. The large spectra obtained at a pressure of 3.0 bar and a 6.0 mJ incident energy are the most suitable for temporal compression down to durations below 5.0 fs, as suggested by the simulations.
As already mentioned, in such conditions we are approaching the experimental limits of our FROG device. Some signal at the edges below 500 nm and over 1000 nm can be lost in the doubling process. This spectral “clipping” could limit the measured pulse duration to values around 3.5 fs even if shorter duration could be obtained. If, for some conditions, we were able to generate even larger spectra, we were not able to achieve a pulse duration relevant measurement smaller than 3.3 fs. Other chirped mirrors, with an efficient spectral dispersion compensation over a larger spectral range, in the 450–1050 nm wavelength range, should be necessary to possibly reach pulse durations shorter than 3.0 fs.
4.3 High flux attosecond emission proof of concept
The 2.5 mJ 3.5 fs pulses obtained employing He in the HCF post-compression stage have been used for high-order harmonic generation (HHG) despite a degraded quality of the CEP stability after the post-compression stage. The shot-to-shot CEP residual noise was around 450 mrad because of some additional noise added by the post-compression stage. A better CEP stability could be achieved by placing the feedback loop after the post compression stage and the CEP noise could be reduced closer to its original 340 mrad value. Some work is still needed to achieve this correction after the HCF stage [22] by adapting our correction device specifically developed for the laser system.
In order to drive the high order harmonic generation, the beam was focused in a 1 cm long gas cell filled with Neon rare gas by a 2000 mm focal length silver coated spherical mirror. A silica plate at grazing incidence was used to remove the majority of the driving field and direct the extreme ultraviolet (XUV) radiation towards a variable line-space grating for spectrally resolving the XUV pulse. The spectrum was collected using an assembly of MCP stack and phosphorous screen imaged by an external CCD camera.
The spectra obtained for two different pulse compressions with active CEP stabilization of the driving laser pulse are shown in Fig. 8. The compression was tuned by optimizing the amount of glass in the beam path using the wedges described in section 4.2. When the pulse is under compressed (i.e. with additional positive GDD) the XUV spectrum in blue in Fig. 8 is measured. This spectrum displays clear harmonic features consistent with a multiple-cycles driver field compatible with a pulse duration close to 18 fs. Removing glass in the beam path compresses the driver pulse down to 4 fs and leads to the generation of the XUV spectrum in orange. This spectrum shows a large increase of the cut-off energy up to 100 eV and displays a continuous profile despite a slight 2ω modulation at lower energy. Spectral filtering of this XUV pulse using for example zirconium filters would remove the modulated spectral components and would hold the potential of generating isolated attosecond pulses.
We think that this experiment confirms the extreme short pulse duration achieved via post compression and that this few cycle source can be practically employed to generate isolated attosecond pulses.
5. Conclusion
Post-compressed pulses of 3.5 fs duration and 2.5 mJ have been demonstrated on the FAB 1 laser facility at ATTOlab-Orme. This is the first step towards high-energy single attosecond pulse generation, paving the way for attophysics experiments. To the best of our knowledge, there is at most four other Ti:Sapphire laser systems worldwide, based on the HCF compression technique, delivering near-single pulses with more than 2 mJ energy per pulse at 1 kHz repetition rate. The propagation code, simulating the nonlinear coupling of the laser in the HCF, provides valuable insights even though it does not reproduce in detail all the spectral modulations. In particular, it describes well the evolution of the spectral broadening with the gas pressure and initial bandwidth, and predicts that spectral broadening is solely due to the Kerr effect, the self-phase modulation induced by field-ionization of the gas being negligible, as the peak focused laser intensity at the capillary entrance never exceeds 4.0 × 1014 W/cm2. At such an intensity, the ionization of helium is very weak, especially with circularly polarized light [46], and with sub-picosecond pulses [47]. Both experimental and numerical results reveal the extreme sensitivity of the spectral broadening and post-compressed pulse duration to the initial bandwidth and phase of the driver pulse. Such a behavior has not been pointed out previously. First demonstration experiments already showed the possibility to use those extreme short pulses for efficient HHG. Thus, these near single-cycle duration pulses will soon be used in the generation and characterization of high-intensity isolated attosecond pulses and/or pump-probe experiments in attoscience at the ATTOlab-Orme facility, thanks to the CEP stabilization of the FAB 1 laser already demonstrated on the driver pulses.
Funding
Agence Nationale de la Recherche (21-CE29-0005-08-AttoChemistry, 20-CE30-0007-02-DECAP); Université Paris-Saclay (Graduate School of Physics, PHOM); Laserlab-Europe (EU-H2020-871124, JRA PRISES); Conseil Régional, Île-de-France (SESAME2012-ATTOLITE, 11-EQX0005-ATTOlab); H2020 Marie Skłodowska-Curie Actions (ITN-641789-MEDEA).
Acknowledgment
The authors want to acknowledge T. Nagy and P. Simon for fruitful discussions and information about the stretched hollow core fiber. The authors want to acknowledge H. Marroux, L. Maeder and P. Salières for their help and collaboration for the HHG proof of concept experiment.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8(3), 178–186 (2014). [CrossRef]
2. A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond Physics,” J. Phys. B 39(1), R1–R37 (2006). [CrossRef]
3. H. Vincenti and F. Quéré, “Attosecond Lighthouse: How to Use spatiotemporally coupled Light Fields to Generate Isolated Attosecond Pulses,” Phys. Rev. Lett. 108(11), 113904 (2012). [CrossRef]
4. C. Thaury and F. Quéré, “High order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms,” J. Phys. B 43(21), 213001 (2010). [CrossRef]
5. M. Nisoli and G. Sansone, “New frontiers in attosecond science,” Prog. Quantum Electron. 33(1), 17–59 (2009). [CrossRef]
6. M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H. G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunneling in atoms,” Nature 446(7136), 627–632 (2007). [CrossRef]
7. M. I. Stockman, M. F. Kling, U. Kleineberg, and F. Krausz, “Attosecond nanoplasmonic-field microscope,” Nat. Photonics 1(9), 539–544 (2007). [CrossRef]
8. C.-D. Lin, X.-M. Tong, and T. Morishita, “Direct experimental visualization of atomic and electron dynamics with attosecond pulses,” J. Phys. B 39(13), S419–S426 (2006). [CrossRef]
9. S. Laulan and H. Bachau, “Correlation effects in two-photon single and double ionization of helium,” Phys. Rev. A 68(1), 013409 (2003). [CrossRef]
10. M. Nisoli, P. Decleva, F. Calegari, A. Palacios, and F. Martín, “Attosecond Electron Dynamics in Molecules,” Chem. Rev. 117(16), 10760–10825 (2017). [CrossRef]
11. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagire, S. De Silvestri, and M. Nisoli, “Isolated Single-Cycle Attosecond Pulses,” Science 314(5798), 443–446 (2006). [CrossRef]
12. H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett. 100(10), 103906 (2008). [CrossRef]
13. S. Bohmann, A. Suda, T. Kanai, S. Yamaguchi, and K. Midorikawa, “Generation of 5.0fs, 5.0mj pulses at 1kHz using hollow-fiber pulse compression,” Opt. Lett. 35(11), 1887–1889 (2010). [CrossRef]
14. C. Fourcade Dutin, A. Dubrouil, S. Petit, E. Mével, E. Constant, and D. Descamps, “Post-compression of high-energy femtosecond pulses using gas ionization,” Opt. Lett. 35(2), 253–255 (2010). [CrossRef]
15. L. Daniault and Z. Cheng., J. Kaur, J.F. Hergott, F. Réau, O. Tcherbakoff, N. Daher, X. Delen, M. Hanna, and R. Lopez-Martens, “Single stage few cycle nonlinear compression of milliJoule energy Ti:Sa femtosecond pulses in a multipass cell,” Opt. Lett. 46(20), 5264–5267 (2021). [CrossRef]
16. A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. D. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011). [CrossRef]
17. S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. T. Bhardwaj, J. R. Birge, L. -J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011). [CrossRef]
18. T. Nagy, P. Simon, and L. Veisz, “High-energy few-cycle pulses: post-compression techniques,” Adv. Phys.: X 6(1), 1845795 (2021). [CrossRef]
19. A. Golinelli, X. Chen, E. Gontier, B. Bussière, O. Tcherbakoff, M. Natile, P. D’Oliveira, P.M. Paul, and J.-F. Hergott, “Original Ti: Sa 10 kHz front-end design delivering 17 fs, 170 mrad CEP stabilized pulses up to 5 W,” Opt. Lett. 42(12), 2326–2329 (2017). [CrossRef]
20. C. Feng, J.-F. Hergott, P.-M. Paul, X. Chen, O. Tcherbakoff, M. Comte, O. Gobert, M. Reduzzi, F. Calegari, C. Manzoni, M. Nisoli, and G. Sansone, “Complete analog control of the carrier-envelope-phase of a high-power laser amplifier,” Opt. Express 21(21), 25248 (2013). [CrossRef]
21. A. Golinelli, X. Chen, E. Gontier, B. Bussière, P.M. Paul, O. Tcherbakoff, P. D’Oliveira, and J.-F. Hergott, “CEP-stabilized, sub-18 fs, 10 kHz and TWclass 1 kHz dual output Ti:Sa laser with wavelength tunability option,” Opt. Express 27(10), 13624 (2019). [CrossRef]
22. M. Ouillé, A. Vernier, F. Böhle, M. Bocoum, A. Jullien, M. Lozano, J.-P. Rousseau, Z. Cheng, D. Gustas, A. Blumenstein, P. Simon, S. Haessler, J. Faure, T. Nagy, and R. Lopez-Martens, “Relativistic-intensity near-single-cycle light waveforms at kHz repetition rate,” Light: Sci. Appl. 9(1), 47 (2020). [CrossRef]
23. T. Nagy, M. Kretshmar, M.J.J. Vrakking, and A. Rouzée, “Generation of above-terawatt 1.5-cycle visible pulses at 1 kHz by post-compression in a hollow fiber,” Opt. Lett. 45(12), 3313–3316 (2020). [CrossRef]
24. https://tem-messtechnik.de.
26. T. Nagy, V. Pervak, and P. Simon, “Optimal pulse compression in long hollow fibers,” Opt. Lett. 36(22), 4422–4424 (2011). [CrossRef]
27. https://www.plm.automation.siemens.com.
28. A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Generation of sub-10-fs, 5-mJ-optical pulses using a hollow fiber with a pressure gradient,” Appl. Phys. Lett. 86(11), 111116 (2005). [CrossRef]
29. J.S. Robinson, C.A. Haworth, H. Teng, R.A. Smith, J.P. Marango, and J.W.G. Tisch, “The generation of intense, transform-limited laser pulses with tunable duration form 6 to 30 fs in a differentially pumped hollow fibre,” Appl. Phys. B 85(4), 525–529 (2006). [CrossRef]
30. M. Miranda, J. Penedones, C. Guo, A. Harth, M. Louisy, L. Neoricic, A. L’Huillier, and C.L. Arnold, “Fast iterative retrieval algorithm for ultrashort pulse characterization using dispersion scans,” J. Opt. Am. Soc. B 34(1), 190–197 (2017). [CrossRef]
32. T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997). [CrossRef]
33. R.W. Boyd, Nonlinear Optics, 2nd ed. (Elsevier, 2002).
34. H. M. Milchberg, Y. –H. Chen, Y. –H. Cheng, N. Jhajj, J. P. Palastro, E. W. Rosenthal, S. Varma, J. K. Wahlstrand, and S. Zahedpour, “The extreme nonlinear optics of gases and femtosecond optical filamentation,” Physics of Plasma 21(10), 100901 (2014). [CrossRef]
35. P.B. Corkum, N.H. Burnett, and F. Brunel, “Above-Threshold Ionization in the Long-Wavelength Limit,” Phys. Rev. Lett. 62(11), 1259–1262 (1989). [CrossRef]
36. D. Bauer, “Plasma formation through field ionization in intense laser–matter interaction,” Laser Part. Beams 21(4), 489–495 (2003). [CrossRef]
37. A.M. Perelomov, V.S. Popov, and M.V. Terent’ev, “Ionization of an atom in an alternating electric field,” Soviet Physics JETP 23(5), 924–934 (1966).
38. A.M. Perelomov, V.S. Popov, and M.V. Terent’ev, “Ionization of an atom in an alternating electric field: II,” Soviet Physics JETP 24(1), 207–217 (1967).
39. A.M. Perelomov and V.S. Popov, “Ionization of an atom in an alternating electric field: III,” Soviet Physics JETP 25(2), 336–343 (1967).
40. X. Chen, A. Jullien, A. Malvache, L. Canova, A. Borot, A. Trisorio, C. G. Durfee, and R. Lopez-Martens, “Generation of 4.3 fs, 1 mJ laser pulses via compression of circularly polarized pulses in a gas-filled hollow-core fiber,” Opt. Lett. 34(10), 1588–1590 (2009). [CrossRef]
41. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).
42. E.A.J. Marcatili and R.A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” The Bell Syst. Tech. J. 43, 1783–1809 (1964). [CrossRef]
43. Z. Ma and S. Ramachandran, “Propagation stability in optical fibers,” Nanophotonics 10(1), 209–224 (2020). [CrossRef]
44. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University, 1992).
45. F. Tani, J.C. Travers, and P. St. J. Rusell, “Multimode ultrafast nonlinear optics in optical waveguides: numerical modeling and experiments in kagomé photonic-crystal fibers,” J. Opt. Soc. Am. B 31(2), 311–320 (2014). [CrossRef]
46. T. Auguste, P. Monot, L.A. Lompré, G. Mainfray, and C. Manus, “Multiply charged ions produced in noble gases by a 1 ps laser pulse at λ=1053nm,” J. Phys. B 25(20), 4181–4194 (1992). [CrossRef]
47. D. N. Fittinghoff, P. R. Bolton, B. Chang, and K. C. Kulander, “Polarization dependence of tunneling ionization of helium and neon by 120-fs pulses at 614 nm,” Phys. Rev. A: At., Mol., Opt. Phys. 49(3), 2174–2177 (1994). [CrossRef]
