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Single-shot ultrashort extreme-UV(EUV) pulse waveform measurement is demonstrated by utilizing strong field ionization of H2 gas for transmission gating. A cross-propagating intense near-IR gate pulse ionizes the EUV absorbing H2 molecules into EUV-non-absorbing (two protons) and creates a time sweep of transmission encoded spatially across the EUV pulse. The temporal envelope is then retrieved from the lopsided spatial profile of the transmitted pulse. This method not only measures EUV temporal envelope for each single shot, but also determines timing jitter and envelope fluctuation statistically, thus is particularly useful for characterizing low-repetition-rate fluctuating EUV/soft x-ray sources.
© 2015 Optical Society of America
1. Introduction
Recent development of coherent extreme-UV(EUV)/x-ray sources with ultrashort durations, such as laser driven EUV laser [1, 2], high-harmonic generation (HHG) [3–5], and EUV/x-ray free electron laser (XFEL) [6], has greatly extended the spectral range and time resolution of laser spectroscopy. By using these sources electron dynamics in atoms and molecules, surface chemical reactions, and extremely rapid structure changes can be probed in unprecedented time scale. An important issue in the applications of ultrashort EUV/x-ray pulses is the measurement of pulse waveform. For XFEL, the photon energy ranges from several tens of electronvolt to several keV with pulse duration from several tens of femtosecond [7–9] to sub-femtosecond [10]. In this spectral range the well developed waveform characterization methods based on nonlinear optics cannot be used due to lack of applicable nonlinear media [11–13]. Moreover, for XFEL the EUV/x-ray pulses are generated from self-amplified spontaneous emission. The intrinsic waveform fluctuation and timing jitter relative to an external reference laser pulse make single-shot measurement indispensable.
Several methods for single-shot measurement of EUV pulse envelope have been demonstrated. One is laser-driven terahertz streaking [7]. In this method, spectra of the photoelectron produced by an soft x-ray pulse and streaked by a synchronized terahertz pulse are recorded to retrieve the x-ray pulse shape. Pulses of about 50-fs duration were characterized with 5-fs accuracy. Tens of microjoule EUV/soft x-ray pulse energy is required to generate a sufficient number of photoelectrons. Further improvement was demonstrated by using near-IR streaking pulse to replace the terahertz pulse for higher temporal resolution [10]. X-ray pulses with average duration no longer than 4.4 fs were characterized. However, due to the energy-to-time mapping ambiguity of the photoelectron spectrum, data accumulation for statistical analysis was required. Another method is transient reflectivity modulation produced by EUV/soft x-ray absorption [8]. In this method, the EUV/soft x-ray pulse durations were retrieved from the reflectivity of an near-IR probe pulse reflected by an overdense plasma produced by obliquely incident EUV/soft x-ray pulses. With the assumption of a Gaussian shape for the EUV/soft x-ray pulses, durations of (184 ± 14 fs) at 41.5 nm and (21 ± 19 fs) at 5.5 nm were estimated from the measurements. This method also requires tens of microjoule EUV/soft x-ray pulse energy to fully ionize target membranes. Recently, EUV spectral phase interferometry for direct electric-field reconstruction (SPIDER) is demonstrated to reconstruct the envelope and phase of EUV pulses from FEL [9]. The required frequency-sheared EUV replicas are generated from energy-shifted electron bunch replicas. Several microjoule EUV energy are also necessary to get a single-shot measurement. Such a requirement of large EUV pulse energy can be restrictive for many experiments.
For high-harmonic generation produced from laser-driven rare gas atoms, the photon energy can reach 1 keV [14, 15] with pulse duration from sub-picosecond to sub-femtosecond [16]. Several cross-correlation and autocorrelation techniques have been developed to measure the HHG pulse duration, such as laser-assisted Auger decay processes [17], laser-assisted photoelectric effects [18–21], and ponderomotive streaking of the ionization potential [22]. Reconstruction of attosecond pulse waveforms were demonstrated by frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG CRAB) [23, 24], resolution of attosecond beating by interference of two-photon transitions (RABBITT) [25, 26], and two-photon-ionization autocorrelation of attosecond pulses [27–30]. In these techniques time-of-flight electron spectrometers are required to measure the energy of photoelectrons coming from rare gases ionized by an HHG pulse when it is overlapped with a reference laser pulse or its replica. The photoelectron spectrum as a function of the delay between the two pulses is used to reconstruct the HHG waveform. Without using time-of-flight electron spectrometers, all optical techniques based on gated absorption of the HHG pulse have also been demonstrated [31–33], where krypton ions produced by an intense laser pulse are used to control the absorption of the HHG pulse. The HHG temporal envelope can be reconstructed from the differential absorption with respect to the delay. In all these techniques, delay scanning and data accumulation are required, hence the measurement cannot be carried out on a shot-to-shot basis.
In this paper we present a new method for measuring the temporal envelope of ultrashort EUV/soft x-ray pulse. By using a time-sweep of transmission gating encoded in the spatial profile of the transmitted pulse, the measurement is carried out without delay scanning. The effect of time delay with respect to the reference laser pulse is represented in the spatial image of the measured EUV pulse. The method is all optical. No photoelectron spectrometer is required. The pulse energy requirement is as low as nanojoule and no data accumulation or shape assumption is needed.
The transmission of an EUV pulse through an H2 gas jet can be turned on by an intense near infrared pulse. If the EUV pulse arrives before the gate pulse, it will be absorbed by H2 or subsequently by through photoionization for EUV photons with energy larger than the ionization potentials of H2 (15.4 eV) and (30.0 eV). If the EUV pulse arrives after the gate pulse, absorption of the EUV pulse is greatly reduced because the intense gate pulse ionizes EUV-absorbing H2 into EUV-non-absorbing (two protons) through strong field ionization. Utilizing this mechanism we cross the EUV pulse with a near infrared pulse at an angle θ. This non-collinear configuration results in a sweep of gate pulse arrival time across the EUV beam profile, leading to a spatially dependent attenuation of the EUV pulse. From the spatial attenuation curve the single-shot temporal envelope is retrieved.
2. EUV spatially encoded transmission gating
The experimental setup is shown in Fig. 1 (a). Two synchronized pulses from a 810-nm, 10-Hz Ti:sapphire laser system are used [34]. One for HHG driving and the other for spatially encoded transmission gating. A 13-mJ, 40-fs (FWHM) pulse is focused by a lens of 5-m focal length onto an Ar gas jet with 5-mm interaction length for high-harmonic generation. The peak intensity reaches 1.2×1015 W/cm2 at the focal spot, where the atom density is ≈ 1 × 1019 cm−3. High harmonics with wavelengths ranging from 24 nm to 45 nm are generated from Ar atoms. The energy of each harmonic is about 1 nJ. The EUV pulse passes through a collimator of 0.3-mm dia. and then an H2 gas jet of 600-μm interaction length. The collimator is used to ensure that the EUV beam size is smaller than the gate beam size on the H2 jet. Then the whole EUV beam can be gated. The H2 molecule density is ≈ 2 × 1019 cm−3. The beam diameter (FWHM) of the EUV pulse on the H2 gas jet is 290 μm. A 0.5-μm-thick Al filter is used to block the driving pulse, and the EUV pulse is imaged onto an EUV CCD camera with a spatial resolution of 5 μm. The original HHG spectrum is shown in Fig. 1 (b), which is measured by an EUV spectrometer behind the Al filter. Due to the the bandwidth limitation of the EUV optics, only the 23rd (35.7 nm), 25th (32.7 nm), and 27th-order (30.2 nm) harmonics are detectable after passing the imaging system. The relative energies of them are 0.54, 1, and 0.03, respectively, as shown in Fig. 1 (c). The temporal envelope we characterized is the superposition of these three harmonics with the 25th harmonic being the dominant one.
Fig. 1 (a) Experimental setup. (b) Original HHG spectrum measured after the Al filter (H2 jet off). (c) HHG spectrum after passing the EUV imaging system (H2 jet off).
A 177-mJ, 50-fs (FWHM) pulse is used for EUV gating. A delay line is used to adjust the long-range delay between the HHG pulse and the gate pulse, as shown in Fig. 1. After that, the gate pulse is focused by an off-axis-parabolic mirror with 1-m focal length onto the H2 gas jet with 250-μm (FWHM) beam diameter and 5 × 1015-W/cm2 peak intensity. Under such short timescale and strong laser field, the dominant interaction of H2 molecule is photo-ionization. The effect of photo-dissociation can be neglected [35, 36]. Therefore, by applying the MO-ADK theory of molecular strong field ionization [37] directly, we calculate the H2, , and H+ densities as functions of time, with the assumption that the H2 molecules are randomly orientated. Fig. 2 shows the result that all H2 molecules are ionized into and then H+ ions at the front edge of the gate pulse. Calculation with 1/3 of the peak intensity yields similar result, showing that full ionization can be reached within the 300-μm diameter of the gate beam. With θ = 8.3° a temporal window of ≈ 150 fs is obtained for envelope measurement. Because only the H+ ions are non-absorbing for the EUV pulse, we fit the relative H+ density as a function of time to the Boltzmann sigmoid function
which dictates the transient transmittance of the EUV pulse according to Eq. (4). The fitting parameters a and ti are 1.7185(±0.0065) fs and −31.98(±0.0074) fs, respectively. The 10%-to-90% rise time of nion(t) is 7.6 fs and its effect on the temporal resolution can be suppressed by deconvolution.Fig. 2 Relative densities of H2, , and H+ as functions of time calculated by the MO-ADK theory. Blue dashed line: H2 molecule. Green dot-dashed line: molecule. Red dotted line: 2H+ ions. Black solid line: fitted ion density nion(t). Gray area: gate pulse intensity profile.
The harmonic driving pulse will also arrive the H2 gas jet. However, due to the 1.05 m distance between the first and the second jets, the intensity of the harmonic driving pulse drops to about 1012 W/cm2. Such intensity is less than 1/1000 of the gate pulse and will not affect the ionization process.
3. EUV temporal envelope retrieval and stability characterization
The EUV beam profiles at the position of the H2 gas jet are shown in Fig. 3. Fig. 3A is the profile without gas jet. When the gas jet is present, the EUV pulse is absorbed by the H2 molecules and its intensity drops uniformly (Fig. 3B). If we adjust the long-range delay line that the gate pulse is completely ahead of the EUV pulse (long-range delay τL = −73.4 fs, Fig. 3C), the absorption is suppressed and the beam profile is the same as Fig. 3A. If the gate pulse is completely behind the EUV pulse (long-range delay τL = 93.4 fs, Fig. 3E), the absorption of the EUV is unchanged and the beam profile is the same as Fig. 3B. If the gate pulse arrives at the gas jet simultaneously with the EUV pulse (long-range delay τL = 0 fs, Fig. 3D), a nonuniform absorption across the horizontal direction of the beam profile is observed as anticipated. By integrating these images vertically
where Iα (x,y) is the profile image, and α represents the images A, B, C, D, or E, we get the vertically integrated intensity distributions as functions of horizontal position x. The results are shown in Fig. 4(a). Since the H2 gas is fully ionized within the 300-μm gate pulse diameter, we analyze the transmittances Tα (τ) ≡ Iα (x)/IA(x) of images C, D, and E in the range of ±150μm, where α = C, D, E, andFig. 3 The EUV single-shot profile images at the position of the H2 gas jet. Image A: EUV pulse only. Image B: with H2 gas. Image C: with H2 gas and gate pulse (long-range delay τL = −73.4 fs). Image D: with H2 gas and gate pulse (long-range delay τL = 0 fs). Image E: with H2 gas and gate pulse (long-range delay τL = 93.4 fs). All images are normalized to the peak value of image A.
Fig. 4 (a) the intensity distributions of the transmitted EUV pulse. IA: EUV pulse only. IB: with H2 gas. IC: with H2 gas and gate pulse (delay τ = −73.4 fs). ID: with H2 gas and gate pulse (delay τ = 0 fs). IE: with H2 gas and gate pulse (delay τ = 93.4 fs). (b) Measured transmittances TC = IC/IA, TD = ID/IA, TE = IE/IA, retrieved transmittance Tr, and retrieved EUV temporal envelope (gray area).
The results are shown in Fig. 4(b). Curve TC is nearly flat, showing that the H2 molecules are fully ionized. The transmittance value for curve TC is not equal to 1 because there exists other attenuation channel such as inverse-bremsstrahlung absorption and Thomson scattering. However, they will not affect the computation for envelope retrieval. The effect of spatially encoded transmission gating is clearly shown in TD.
The transmittance curves in Fig. 4(b) are the cross-correlations of the EUV temporal envelope IEUV(t) and the transient transmittance Ttrans(t) which is a function of the relative H+ density nion(t)
where Tmax is the maximum transmittance (the average value of curve TC with nion = 1). Theoretically the parameter β is determined by the absolute ion density, absorption cross-section, and the total interaction length. In practice, it can be easily obtained from the measured data by β = −ln(Tmin/Tmax), where Tmin is the minimum transmittance, namely the average value of curve TE with nion = 0. Therefore curve TD is related to IEUV(t) by where the factor cosθ comes from the projection of the EUV propagation wavefront to the ionization front of the gate pulse. The detailed configuration is shown in Fig. 5. We apply the iterative Richardson-Lucy algorithm [38,39] to deconvolve TD. After each iteration, we use the retrieved envelope to generate a retrieved transmittance curve Tr and compare E(τ) ≡ Tr(τ) − TD(τ) with the fluctuation of TE. When it becomes smaller we close the iteration to prevent from numerical noise amplification. The retrieved EUV temporal envelope and transmittance after 20 iterations for a typical shot are shown in Fig. 4(b). The duration of the EUV envelope is 43(±2) fs (FWHM) with a driving pulse duration of 40 fs. The value in the parentheses represent the overall uncertainty, which is determined by the ionization front distorsion, the spatial resolution of the imaging system as well as the accuracy of deconvolution limited by signal-to-noise ratio.For comparison, we lengthen the driving pulse duration to 80 fs (FWHM) and double its energy to maintain the same intensity span. The measured transmittance curves and retrieved EUV envelope for a typical shot are shown in Fig 6. The duration is 78(±4) fs (FWHM) and the envelope is significantly distorted to be fast rising and slow falling. This is a clear demonstration of the EUV envelope distortion relative to the pump pulse due to the combined effects of the intensity-dependent dipole phase and medium ionization discussed in Ref. [40], which has not been resolved in previous experiments.
Fig. 6 Measured transmittances as functions of gate pulse delay. The EUV driving pulse duration is 80 fs. Green dashed line: gate pulse long-range delay = −226.8 fs. Red dot-dashed line: gate pulse long-range delay = 0 fs. Blue double-dot-dashed line: gate pulse long-range delay = 226.8 fs. Gray area: retrieved EUV pulse.
4. Stabilities of the EUV pulses
To show the capability of our single-shot measurement technique, we measured shot-to-shot envelope fluctuation by retrieving individual envelopes for 10 consecutive shots with 40-fs driving pulse. The results are plotted in Fig. 7. To analyze the timing fluctuation, we define the “weighted pulse center”
where tj represents the time grid determined by the pixel separation of the EUV CCD camera and the position-to-time conversion (Eq. 3). Then the timing fluctuation of the EUV pulses is evaluated from the fluctuation of tC. For the EUV pulses shown in Fig. 7, the fluctuation of tC is 7.1 fs. Since the pointing fluctuation of the HHG beam affects the measurement of timing fluctuation, we measure the pointing fluctuation in advance by turning off the H2 gas jet and monitoring the weighted profile center where I(x) is the vertically integrated EUV beam profile, as defined by Eq. 2. The measured fluctuation of xC is 12 μm, corresponding to a false timing fluctuation of 5.6 fs. Therefore, the real timing fluctuation is [(7.1fs)2 − (5.6fs)2]1/2 = 4.4 fs.In addition to the small timing jitter, the envelope of each shot also carries some fluctuation. To extract envelope fluctuation we align all the weighted pulse centers together and calculate the average of these aligned envelopes. Then we evaluate the rms deviation of each envelope relative to the average envelope. The average value of this rms deviation, referred as “rms envelope fluctuation”, is 7%. Since the spatial profile fluctuation of the HHG beam affects the measurement of envelope fluctuation, we measure the spatial profile fluctuation in advance by turning off the H2 gas jet and monitoring the vertically integrated EUV profile I(x). The rms fluctuation of the EUV beam profile is 3%. Therefore, the real envelope fluctuation is [(7%)2 − (3%)2]1/2 ≈ 6%. In comparison, the EUV pulse energy fluctuation is 8%.
We also characterized the shot-to-shot fluctuation with 80-fs driving pulse. The retrieved envelopes for 10 consecutive shots are shown in Fig. 8. The envelopes are analyzed with the same procedure described above. The results show that the absolute timing jitter is about 6.4 fs, and the rms envelope fluctuation is 12%. In comparison, the pulse energy fluctuation is 12%.
5. Discussion and conclusion
In many experiments the HHG pulse duration is shorter than the duration of its driving pulse. However, in our experiment the Ar gas is fully ionized over the duration of the driving pulse. The plasma results in large dispersion for EUV propagation. Diffraction and ionization induced defocusing for the driving pulse also cause variation of the atomic dipole phase which is highly intensity dependent. These two factors scramble the phase matching of the HHG process and make the EUV pulse duration not much shorter than that of the driving pulse, as explained in Ref. [40]. Our measurements and results are in agreement with the HHG pulse durations reported in Ref. [18] with similar driving pulse durations and intensities (1–2 × 1015 W/cm2). In addition, owing to the better temporal resolution of this technique, the asymmetry of EUV envelope produced by 80-fs pump pulse is clearly resolved which confirms the theoretical calculation of the HHG envelope distortion with long pump pulse in Ref. [40].
In our measurement the lower limit of EUV pulse energy is determined by the detector sensitivity. If a more sensitive detector (e.g. a micro-channel plate) is used, the required EUV pulse energy can be further reduced. The lower limit of the gate pulse energy is determined by its beam size, since its intensity must be high enough for strong field ionization. In addition, the gate beam size must be larger than the EUV beam, otherwise its intensity distribution across the EUV beam is nonuniform, making the ionization front in the H2 gas more advanced at the center. In our measurement, the delay of the ionization front at the edge of the EUV beam is ∼ 5 fs relative to that at the center of the EUV beam. Simulation shows this effect contributes half of the pulse shape error in our measurement. Increasing gate beam size helps reducing such error.
The gate beam size and the crossing angle together determine the time window of measurement and the temporal resolution. For fixed magnification of the EUV imaging system and pixel density of the EUV camera, larger gate beam size and larger crossing angle yield wider time window, whereas smaller crossing angle yields higher temporal resolution. Increasing the magnification of the EUV imaging system or the pixel density of the EUV camera yields higher temporal resolution. Temporal resolution is also limited by the gate pulse duration. In our measurement, the 50-fs gate pulse results in a 7.6-fs rise time of the H2 ionization, which limits the temporal resolution to 1–2-fs after deconvolution. If intense, few-cycle IR pulses are used as gate pulses, full ionization within 1 fs can be achieved to obtain sub-femtosecond resolution. Since the EUV temporal envelope is retrieved from the gated spatial profile of the EUV beam, it is essential that the EUV beam has a stable spatial profile. This requirement holds for all single-shot ultrafast temporal waveform characterization techniques.
In our measurement the range of EUV photon energy is limited to 15–80 eV, which is determined by the photoionization cross section of the H2 molecule [41]. Since the cross section decreases as the photon energy increases, transmission gating is not efficient enough when photon energy is higher than 80 eV (photoionization cross section < 10−19 cm2). However, if helium gas is used as the interaction medium, the range can be extended to 25–140 eV [42].
In summary, we demonstrated a new technique for single-shot, all-optical measurement of ultrashort EUV temporal envelope. The technique is based on time sweep of transmission spatially encoded in the transmitted EUV pulse that results from the bleaching of EUV absorbing gas due to optical field ionization produced by a crossing gate laser pulse. Time-of-flight electron energy spectrometry is not required, nor is delay scanning and data accumulation. As the absorption of the EUV pulse is dictated only by the photoionization process, the technique can be applied to various EUV sources with a wide spectral range, especially for EUV/X-ray free-electron laser. Moreover, since the EUV pulse is not involved in any nonlinear process, sensitivity is only limited by the detector. In prospect, by replacing the EUV camera with an imaging EUV spectrometer, single-shot measurement of the EUV pulse spectrum as a function of gating delays can be performed. Such a measurement is equivalent to the cross-correlation frequency-resolved optical gating [43]. Hence this technique can be extended to retrieve the complete field waveform (including the phase) with modest increase in experimental complexity.
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