We present a method that allows for a convenient switching between high harmonic generation (HHG) and accurate calibration of the vacuum ultraviolet (VUV) spectrometer used to analyze the harmonic spectrum. The accurate calibration of HHG spectra is becoming increasingly important for the determination of electronic structures. The wavelength of the laser harmonics themselves depend on the details of the harmonic geometry and phase matching, making them unsuitable for calibration purposes. In our calibration mode, the target resides directly at the focus of the laser, thereby enhancing plasma emission and suppressing harmonic generation. In HHG mode, the source medium resides in front or after the focus, showing enhanced HHG and no plasma emission lines. We analyze the plasma emission and use it for a direct calibration of our HHG spectra.
© 2009 Optical Society of America
We describe a convenient method to calibrate a vacuum ultraviolet (VUV) spectrometer used to analyze high harmonic spectra. In high harmonic generation (HHG) spectroscopy [1, 2], the spectral calibration is essential to convert the HHG spectral content to information about the transient electronic structures of the source medium. The other two applications of HHG, which are the creation of attosecond pulses for time resolved spectroscopy [3, 4, 5, 6, 7] and lensless imaging of nanostructures [8, 9], are less demanding on an accurate spectral calibration.
High harmonic generation spectroscopy relies on the interaction of a strong laser field with an atomic or molecular target. The strong laser field tunnel ionizes the target atoms or molecules forming a free electron wave packet that is accelerated first away and then toward the parent ion as the field changes sign. The free electron wave packet returns to the parent ion and recombines resulting in the emission of a VUV photon. The kinetic energy Ekin(t) of the recombining free electron wave packet at the position of the atom changes in time during recombination. It is related to the emitted photon energy hν by hν=Ekin(t)+IP=h2=(2meλdB(t)2)+IP, where IP is the ionization potential and λdB(t) is the de Broglie wavelength. During recombination, the chirped electron with wavelength λdB(t) “scans” the atomic electron wave function giving rise to interferences which appear as modulations in the harmonic spectrum. The modulations in the HHG spectrum reflect structural features of the electronic wave function of a molecule [10, 11, 12, 13] or atom [14, 15, 16].
The better the high harmonic spectrometer is calibrated in wavelength and intensity, the more accurate the information about the wave function under study will be. The statement is amplified by recent reports on the appearance of a Cooper minimum in the HHG spectra of argon having small energy shifts with respect to the photoionization Cooper minimum [14, 15, 16]. An important issue which can be addressed in this context is the effect of the strong laser field on the spectral position of the Cooper minimum. Typical field strengths during recombination lie in the range of 0.1 atomic units and below and we expect shifts on this order in the recombination energy. To accurately determine the shift, a factor of 10 better resolution (.01 a.u. or 0.3 eV) is therefore desirable. We concentrate on improving the VUV spectrometer calibration in the following. Comparable shifts could be expected for any laser-induced structure in the continuum.
Two different methods are commonly implemented for wavelength calibration. First, metal filters with different transmission windows can be used . For example, a thin Al filter has a transmission range from 20 eV (the plasmon resonance energy) to 70 eV (the L edge of Al). The low energy edge is rather smooth and, in addition, is strongly affected by oxide layers so that it cannot be used for calibration purposes. In contrast the high energy edge is sharp and usable for calibration. However, when calibrating a spectrum of discrete harmonics the metal filter edge can only be determined to within the energy difference of two odd harmonics, an accuracy of 3 eV if 800nm is the central wavelength. An additional problem in the use of filters is that no sharp transmission edges exist below 70 eV. A different method uses the harmonics themselves for calibration. The problem here is to identify the order of the harmonics visible in the spectrometer. Since the fundamental is usually blocked by metal filters and the free spectral range of the spectrometer does not reach into the UV, visible, and IR range, one cannot count harmonics from the fundamental up to the VUV range. The order of the harmonics can be deduced from the distance between the harmonic peaks in the detector plane if the grating dispersion is known. Sometimes this is problematic because of the use of variable line space gratings (VLSG), which have different dispersions at different grating positions [18, 19]. A more fundamental problem in using harmonics for calibration purposes lies in the extreme sensitivity of the harmonic wavelength to the fundamental pulse parameters and to phase matching. The fundamental laser chirp, duration and the HHG phase matching influence the harmonic wavelength; shifts in wavelength of half an odd harmonic are not unusual [20, 21].
We describe a simple calibration method using plasma emission lines that can be implemented easily in an HHG setup. The calibration depends on the alignment of the harmonics on the grating via the simple grating diffraction formula and is complicated by the spatial dependence of the line spacing in a VLSG. Therefore a quick everyday method for calibration is needed. We show that lines emitted by a laser generated plasma of rare gases and molecular nitrogen can be conveniently used to calibrate harmonic spectrometers. The plasma generation and HHG use the same beam geometry. Laser plasma emission is radiated incoherently over a large solid angle, whereas harmonics are efficiently phase matched along the laser propagation axis. Bright plasma emission is efficiently produced at laser intensities which generate significant plasmas. This regime is unfavorable to HHG because of ionization saturation and phase matching effects due to the free electrons generated [22, 23]. It is possible to access both efficient HHG and plasma emission as we show below. In a typical HHG focusing geometry, the laser is focused with a long focal length (larger than 400 mm) to extend the Gouy phase jump over a large region thereby achieving optimal phase matching [24, 25]. The best phase matching is accomplished slightly behind the focus and the intensity directly at the focus is not high enough for an efficient plasma production. We overcome this problem by implementing a short focal distance, which increases the focal intensity for efficient plasma generation. The phase matching for HHG behind the focus is reduced compared to a long focusing element. However, for the application of HHG spectroscopy, the harmonic flux is not crucial and we can accumulate spectra with good signal to noise in a reasonable time. By changing the gas target position with respect to the laser focus, one can switch between a calibration mode, where the plasma lines are intense and the harmonics are relatively weak, and an HHG mode, where the plasma lines are weak and the harmonics are strong. To change between the modes, no re-alignment of the laser needs to be done; the target gas jet is simply moved with respect to the fundamental laser beam.
Figure 1 shows a sketch of a typical HHG setup, that we also use for calibration. We focus the laser pulse (duration 30 fs, center wavelength 800 nm, repetition rate 1 kHz) into a continuous gas jet using a 200 mm lens. The jet streams out of a small orifice (about 100 µm diameter) that is backed up by 1–2 bar gas pressure. The gas jet is optimized for rotational cooling of molecules via supersonic gas expansion, leading to enhanced non-adiabatic alignment . The laser beam crosses the gas jet at a distance of 0.4 mm from the nozzle. The jet parameters are calculated from the nozzle geometry  resulting in a nearly-Lorenzian profile with 0.5 mm full width half maximum and a column density in the range of 1015 cm-2. Harmonic emission is expected to depend quadratically on the gas density. We checked this for our pressure range. Plasma emission has a complex density dependence, since many-body processes like electron inelastic scattering at ionic cores are involved. Documented density dependence of plasma emission can be found in Ref. .
The gas jet is mounted on an x-y-z stage with z pointing in the propagation direction of the laser beam. Since we are using plasma emission lines for calibration, we assure high gas purity of 99.999% for Ne, Kr and Xe and 99.998% for Ar and N2. The 40.8 eV line in helium would also be convenient as a calibration standard with our conditions. This calibration method has the advantage of well known plasma emission lines. Even if the atom or molecule of interest in HHG spectroscopy is different from the calibration gas, it can either be used after the calibration or simply mixed with the calibration gas.
The maximal laser intensity at the focus lies in the range of 1-2×1015 W/cm2, which enables the creation of a plasma and high harmonic generation. In order to switch between effective plasma line generation and HHG, we move the gas jet along the z-direction. The VUV light from the harmonics or plasma lines between 20 and 70 eV photon energy is transmitted through a 100 nm Al filter into the spectrometer, consisting of a VLSG with 450 lines/mm on a toroidal substrate. Just before the grating the harmonics pass an aperture of 5 mm diameter. The VUV light hits the grating under a grazing angle of 19.4°. The object plane of the grating coincides with the focal point of the fundamental laser beam; thus the plasma or HHG region acts as an entrance slit of the spectrometer. The VLSG disperses the VUV light on a back-thinned CCD detector which is cooled to 230 K. In our experiments we typically integrate the spectrum on the detector for 500 laser pulses (0.5 s) and afterwards average over 20 spectra.
For comparison we give a few plasma parameters. Our plasma densities are around 1017 to 1018 cm-3, assuming a gas jet density of 1017 cm-3 at the interaction region and a 7 times ionized target. At an intensity of 1015 W/cm2, the electron temperature from the ponderomotive potential is about 60 eV.
3. Results and discussion
Figure 2 shows the VUV spectra for Xe and N2 as a function of the gas jet position in the z direction. The focus of the fundamental beam corresponds to z=0. The wavelength calibration has been performed with the method described in this article. In Fig. 2A and B, a regular pattern of VUV lines is observed before and after the focus, corresponding to the strong field laser harmonics. The long wavelength harmonics span a wide range in the z direction, while the shorter wavelength harmonics are visible only in a small range around z=0. This is explained by the fact that the harmonic cutoff (highest harmonic generated) scales with the ponderomotive potential and therefore the intensity of the laser field. The laser intensity has its maximum at z=0 and drops as the jet is moved away from z=0. In a small range around the focus an irregular pattern of emission lines due to plasma emission dominates. We expect that the plasma emission is most intense where the fundamental laser reaches the highest intensity because that will lead to the strongest multi-photon and tunnel ionization of the target gas. Thus, we use the maximum of the plasma emission to determine the laser focus position. The harmonic signal is reduced in the region of high laser intensity around z=0. This can be explained by the creation of a highly ionized gas target in which most valence electrons, which are responsible for HHG, are removed. We tested this mechanism by recording the Ne HHG spectrum for different z positions. The reduced amplitude of the harmonics at the focus is less dramatic than for Xe because of the much higher IP. It is also well documented that phase matching of the harmonics is poor for a gas jet at the focus [24, 25]. The model predicts optimal phase matching in front and after the focus, depending on the emission phase of the harmonics. Figure 2C shows how the harmonic emission shifts in wavelength as a function of the gas jet position. This is once more an indication that the harmonics themselves are not usable for a very accurate calibration of the spectrometer. From +0.4 mm to -1.2 mm in the z position we get a shift of 0.5 eV in photon energy corresponding to nearly 1/6 of the distance between two odd harmonics.
Since we use a rather short focusing lens, it is easy to move the gas jet over the entire rayleigh range without the need for realignment. Typical high harmonic setups use much longer focal lengths to improve phase matching and thereby the photon number in the high harmonics [24, 25]. However, for the HHG spectroscopy application, highly efficient HHG is not necessary and phase matching is even considered to distort the single molecule response in the spectrum .
Figure 3 shows different VUV spectra from various gases. The Ar spectrum is taken with the gas jet at the optimal phase matching position for high harmonics 0.8 mm behind the focus whereas the other spectra are taken at the laser focus and thus have pronounced plasma lines. The harmonics of argon show a modulation in the short wavelength range, which is magnified in the inset. A HHG minimum is identified at the 33rd harmonic, corresponding to a quantum energy of 51 eV. This minimum has been interpreted in the framework of the Cooper minimum known from photoionization [14, 15, 16]. A slight shift compared to the energetic position of the photoionization Cooper minimum is observed and our calibration method can be used to measure this shift to a high accuracy to shed further light on shift mechanism.
As in Fig. 2, all spectra are initially taken as a function of camera pixel (upper x-axis of Fig. 3) and the calibration we describe is used to establish the wavelength axis given by the lower x-axis of Fig. 3. The lines we use for calibration purposes are marked by arrows and their labels can be decoded with help of table 1. Three different mechanisms can be responsible for the emission lines we observe. An atom or molecule can be directly promoted to an excited electronic state of the ion which then relaxes by emission of VUV light. This mechanism requires laser-induced multi-photon resonances, and the probability for that step was measured to be small compared to indirect excitation mechanisms [28, 27]. This mechanism can play a significant role only in diatomic molecules like N2 , however the directly induced emission observed in Ref.  is not in the detection range of our spectrometer. The indirect mechanisms are recombination and collisional excitation by energetic electrons in the plasma. These were found to be dominant for rare gas atoms [28, 27]. In making line assignments we were guided by several past studies of emission lines from ultrafast laser induced plasmas [28, 29]. We performed a rough calibration of the spectrometer using the Al filter cutoff at 70 eV. The Kr7+ line pattern in our spectra was identified by comparison with the spectra in Ref. . A Grotrian diagram (Fig. 7 in Ref. ) shows the different transitions in the ion and we identify the 4p←5d, 4s←5p and 4p←4d emission in our spectra. Caution should be exercised when comparing spectra from laser induced plasmas with those using other excitation methods. As an example, while the Kr7+4p←5d and 4s←5p multiplets are of essentially equal amplitude in both our spectra and Ref. , the 4s←5p multiplet was found to have a greater amplitude by two orders of magnitude in an earlier study using an arc lamp source . This issue is discussed in Ref. . The N2 lines were identified with the help of . Since we have a higher resolution in comparison with that study, we can resolve the N22 and 3 lines at 57.47 and 58.21 nm respectively. The Ne and Xe lines were attributed based on the most intense lines visible in the laser induced plasma. The Xe7+ 4d 105s←4d 95s5p emission is peculiar, because the core excited state that fluoresces can only be induced by multielectron interaction. Due to the large intershell coupling between 5s and 4d electrons, two electrons are removed from the respective shells in a multiphoton ionization . Table 1 summarizes our attribution of the plasma lines to particular transitions including the wavelength of the line, the reference, and the position on our CCD detector in pixels. Since the wavelengths of the atomic transitions are known very accurately, the primary source of uncertainty is due to the determination of the position of each line on the detector. The position of the lines was determined by fitting a gaussian function to each line using the center of each gaussian as a fitting parameter. The fitting error of the gaussian centers is smaller than one pixel, with the exception of Kr3 and 4 that have 1 and 4.7 pixel errors.
The linewidth of the plasma emission line N22 is 0.45 nm at 57.47 nm central wavelength resulting in a resolving power of 125. The resolving power of a grating λ=Δλ cannot exceed the number of illuminated lines. We put a 5 mm aperture in front of the grating orthogonal to the beam. The plasma emission, which is emitted in the full 4π solid angle, is clipped to the size of the aperture. Considering a grazing angle of 19.4° for our 450 lines/mm grating, we calculate a theoretical resolving power of 6770. Usually this theoretical limit is never achieved because of grating and substrate imperfections. The resolving power of the grating is almost constant throughout the full spectral range. For the highest harmonics of Ar around 20–25 nm, we calculate a spectral resolving power of about 100. Ray tracing calculations by the grating manufacturer predict resolutions of 200 in the spectral range around 60 nm, 140 at 35 nm and 40 at 10 nm (with a 30×30 µm entrance slit and slightly different grating illumination due to a different mask) . Our observation of lower resolving power at long wavelengths is probably due to the fact that we did not optimize the grazing angle to the linewidth as described in Ref. . Movement of the gas jet away from the image plane causes some broadening of the spectral lines due to defocusing out of the object plane, but this is very small (5% of the
line width) because of the small distances involved. More importantly, the defocusing does not complicate the HHG calibration because it only effects the widths of the lines and not the line position.
Figure 4B shows wavelength of the attributed transition versus pixel number as symbols for the respective sample gases. Since a general polynomial law for VLSG is not known, we fit the data deliberately by a fourth order polynomial in agreement with Ref. . The fit is plotted as the grey line in Fig. 4B. The linear correlation coefficient (Pearson’s r) for the fit is equal to 0.99999, extremely close to a complete positive linear correlation (r=1). The calibration function is λ=b 0+b 1×pixel+b 2×pixel 2+b 3×pixel 3+b 4×pixel 4, with b 0=9.21453 nm, b 1=0.06709 nm/pixel, b 2=-2.90425×10-5 nm/pixel2, b 3=5.51872×10-8 nm/pixel3, and b 4=-3.1681×10-11 nm/pixel4.
To estimate the accuracy of the calibration, we plot the difference between the reference wavelength from table 1 and the fourth order fit as solid squares in Fig. 4A. All values apart from N21 lie in a 0.1 nm interval around zero, which means that an unknown single line can be calibrated to an accuracy of ±0.1 nm. For comparison we indicate the zone that corresponds to the spectral width of a 2 pixel region by the two solid lines. This corresponds to a reading uncertainty of ±1 pixel from the camera. It can be seen, that the differences are either contained in the zone or are lying very close to it. We also fitted our calibration data by a linear function. The difference between the reference wavelength from table 1 and the linear fit as open circles in Fig. 4A. It is obvious from the differences, that the fourth order polynomial fits the data better than the first order function.
The wavelength accuracy of an unknown line is limited by two factors. If the the line is known to arise from a single transition then the accuracy of the wavelength is given by the calibration error of ±0.1 nm. Addressing the second factor, the resolution limited linewidth of our spectrometer ranges from 0.25 nm for short wavelengths to 0.45 nm for longer wavelengths. Two lines can be resolved only if their maxima are spaced by at least half the linewidth, meaning that the wavelength accuracy for adjacent lines is not better than the spectrometer resolution. In the low harmonics around the N22 line, the calibration uncertainty of ±0.1 nm corresponds to ±0.04 eV. In the high harmonics around 25 nm it corresponds to ±0.2 eV. The resolution criterion for line separation corresponds to 0.2 and 0.5 eV for the low and high energies, respectively. Throughout the spectral range the calibration and line separation give an accuracy for an unidentified spectral line that is better than the calibration with harmonics that has an error of ±1.5 eV. Our results were measured with a relatively low dispersion instrument having 450 lines/mm. The accuracy is expected to scale with the resolution.
A method of quickly and accurately calibrating high harmonic spectra using emission lines from laser induced plasmas has been described. This method can easily be implemented in typical laboratory HHG setups. The source medium (gas jet or cell) is typically located in the diverging part of the laser beam due to the optimized HHG phase matching there. The higher intensities and decreased HHG phase matching encountered by positioning the source medium in the laser focus enhances plasma lines, which, once identified, are known spectrally to a very high accuracy. Thus, one can switch from ‘HHG mode’ to ‘calibration mode’ simply by driving the source medium into the focus with a step motor without making other changes to the laser setup. We use several different gases as source media and find that all gases studied exhibit identifiable lines. Krypton and N2 provide the majority of the identifiable lines. A wavelength calibration is made by a fourth order fit between the known wavelength of the plasma lines and their position on a CCD detector. The accuracy is found to be better than the calibration method using only high harmonics. Accurate HHG calibrations are becoming increasingly important as more research focuses on using HHG amplitude and phase to gain information about the transient orbital structure of the source molecules.
We thank H. Merdji for insightful discussions. Supported by the U.S. Department of Energy Division of Basic Energy Sciences through the SLAC National Accelerator Laboratory.
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