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Abstract
We present an experimental study on the high-harmonic yields from the ions in the laser-ablated plumes of various metal targets (W, Mo, Cr, Cu, Ni, Fe, Ag and Mg) with the purpose of comparing their ion density and single-atom response. The harmonic yields as a function of medium length are measured and the results are fitted against a theoretical model to extract the coherence length, absorption length and strength single-atom response (in arbitrary units) of different harmonic orders for each target. It is found that the coherence lengths decrease monotonically as a function of harmonic order for all targets. Ion density of the generation media are estimated by the trend of the coherence length as a function of harmonic order. Qualitatively, targets with lower melting temperatures seem to produce laser-ablated plumes of higher ion density, vice versa. Also, the strength of the single-atom response of the metal ion species with only one electron in the outermost subshell are weak compared with the other targets considered in this study.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-harmonic generation (HHG) is one of the most important phenomena in strong-field atomic physics. It can be used to generate ultrashort, coherent extreme ultraviolet pulses [1,2] and has become an attractive tool in ultrafast science [3,4].
In atomic HHG, noble gases have been the most common choices for the generation medium, as they are easy to handle (simply by using gas jets or gas cells) and can withstand high driving laser intensity [5–7]. Using metal atoms in vapor form are much less convenient due to the demanding requirement of heating. In fact, HHG in metal vapors have been demonstrated only for alkali atoms which are easy to be vaporized such as Cs [8] and Rb [9]. Fortunately, laser ablation may be treated as a convenient alternative to effusive atomic beam [10,11] for the purpose of HHG. By focusing an intense laser pulse on a metal surface, a plasma plume containing metal atoms and ions with sufficient density can be readily formed [12]. This method drastically widens the choices of atom species for HHG as it is effective for most metals regardless of their thermal properties.
So far, more than twenty kinds of metals have been used to produce laser-ablated plasma plumes (LPPs) for HHG [13–16] and there are several techniques [17,18] to enhance the yield and stability of harmonics [19]. Significant variations in cut-off energy [20,21] and harmonic yield among different metal species [22,23] have been observed but the reasons are still not very clear. In particular, quantifying and understanding the difference in harmonic yield is not straightforward since the yield does not only depend on the single-atomic response of the target, but also the macroscopic properties of the medium which affect phase matching and absorption effects [5,24–27]. Moreover, unlike gaseous medium whose density can be adjusted and monitored rather precisely without much effort, the density of ions in LPPs are very difficult, if not impractical, to control and measure precisely. This causes another major difficulty in performing systematic comparison on HHG from different target species as the difference in ion density in different targets is hardly trackable.
In this work, we attempt to separate the effect of single-atom response from the macroscopic effect in order to obtain a relative comparison of the strength of single-atom response between eight different metal targets (W, Mo, Cr, Cu, Ni, Fe, Ag and Mg). These targets are selected in order to cover a wide range of harmonic cutoff. The goal is achieved by measuring the medium length Lmed dependence of harmonics yields, which vary like a damped cosine function due to the macroscopic effect of phase matching and absorption. Then the experimental yields are fitted against the theoretical formula derived by E. Constant et al. [24] which describes how high-harmonic yields depend on the strength of single-atom response, coherence length and absorption length of the medium. Note that the first quantity describes the property of individual atom, and the last two quantities reflect the macroscopic properties of the medium. By treating these three quantities as the fitting parameters, we obtain the strength of single-atom response (in arbitrary units) for all the targets in this study. In addition, the fitted values of coherence length could also be used to estimate the ion density of the laser-ablated plumes from the metals [28].
2. Experimental setup
In this experiment, a commercial Ti: sapphire chirped pulsed amplifier system (Spectra Physics: Sprifire Ace) with a center wavelength of 0.8 µm and a repetition rate of 1000 Hz is used. Before temporal compression, the amplified laser beam in the system is split into two. One of them is sent out of the laser system without compression (pulse duration = 210 ps); it is the heating pulse (HP) which is used to generate LPP from the metal sample surface. The other beam, which is temporally compressed to 35 fs, is the driving pulse (DP) for generating high harmonics in the LPP. A significantly longer optical path is built for the DP such that it is temporally delayed by ∼50 ns relative to the HP. The delay is fixed throughout the entire study for all targets.
The optical setup for HHG is schematically shown in Fig. 1. The HP is first focused by a cylindrical lens with a focal length of 200 mm. It is then imaged onto the metal sample surface by a 2:1 telescope. An adjustable slit is placed at the focal plane of the cylindrical lens to truncate the line focused laser beam. By adjusting the slit width, the length of HP on the sample surface, thus the length of the LPP, can be precisely controlled [29].The HP intensity at the sample surface is estimated to be about 15 GW/cm2. On the other hand, the DP, with a maximum estimated intensity of 240 TW/cm2, is focused by a convex lens and propagates parallel to the sample face. The ions in the LPP are driven by the DP and the generated high-harmonics are measured by a home-built spectrometer consisting of an entrance slit, a concave mirror, a 1200 grooves/mm flat field grating, a microchannel plate with a fluorescent screen and a CCD camera. Each raw harmonic spectrum is the accumulated result of a certain number of laser shots. Then, the spectral intensity is divided by the number of laser shots. That is, each presented harmonic spectrum below represents the averaged harmonic signal detected per laser shot.
3. Results and discussion
High-harmonic spectra at various length of LPP medium are measured for all the selected metal species in this study. As an example, Fig. 2 shows the results for Cu. More than 20 spectra at different medium length ranged between 0.2 and 1.4 mm are stacked together and presented all together as the false color map in Fig. 2(a). To display the variation more clearly, spectra at three of the medium length values (0.3, 0.5 and 0.7 mm) are shown in Fig. 2(b). We extract yield of each harmonic order as a function of medium length. The results for three of the harmonic orders (25th, 31st and 37th) are displayed in Fig. 2(c).
Fig. 2. HHG in plasma plume of Cu. (a) Harmonic spectra as a function of medium length. (b) Harmonic spectra at three of the medium lengths: 0.3mm, 0.5mm, 0.7mm. (c) The harmonic yields as a function of medium length for three of the harmonic orders: 25th, 31st and 37th. The dots are the data from the experiments. The lines are obtained by fitting experimental data according to Eq. (1).
According to E. Constant et al. [24], the medium length Lmed dependence of the number of emitted qth harmonic photons Nout on axis per unit length is given by
Treating Lcoh, Labs and Aq/σq as the fitting parameters, the data of harmonic yields for different order are fitted to Eq. (1). For instance, the fitted curves for the data of the 25th, 31st and 37th order are shown by the solid lines in Fig. 2(c). Note that a shorter period of the cosine-like variation implies a shorter coherence length, vice versa. The fitted values of Lcoh, Labs and Aq/σq for different harmonic orders are shown in Fig. 3(a)-(c), respectively. The decreasing trend of Lcoh as a function of harmonic order can be understood by the general properties of phase-matching. In HHG, the four main factors that contribute to phase-mismatch are the neutral-atom dispersion, the plasma dispersion, the laser Gouy phase and the intensity-dependent phase [28,30,31]:
Fig. 3. According to Eq. (1), the fitted parameters of Cu from Fig. 2. (a) Lcoh (b) Labs and (c) Aq/σq. The dots are the parameters, the error bars are the 95% confidence limits and the dash line in Fig. 3(a) is fitted by Lcoh = π/(a1q + a2).
Assuming plasma dispersion is the most significant term among the first three terms, as suggested in Ref. [29], the fitted value of a1 can be used to estimate the plasma density ρe since a1 = ρee2/(2meε0ω0c). With this method, the plasma density, thus the ion density, in the LPP of Cu is estimated to be 1.1 × 1017/cm3. The other two fitted parameters, Labs and Aq/σq, are shown in Fig. 3(b) and (c), respectively.
The same measurement and fitting procedures are applied for the other eight metal targets, and the spectra are presented in Fig. 4 (for Ag, Ni and W), Fig. 5 (for Fe and Mg), and Fig. 6 (for Cr and Mo). In each figure, the false color maps in the top column shows the raw spectra at all Lmed; the middle column shows the spectra at three selected Lmed; and the bottom column shows the dependence of harmonic yield on Lmed for two of the selected harmonic orders.
Fig. 4. Results of HHG from with the targets with relatively high harmonic cut-off energies. Harmonic spectra as a function of medium length for (a) Ag, (b) Ni, (c) W. Harmonic spectra at three different selected medium lengths for (d) Ag, (e) Ni, (f) W. The harmonic yields as a function of medium length for two of the harmonic orders for (g) Ag, (h) Ni, (i) W. The dots are the data from the experiments. The lines are obtained by fitting experimental data according to Eq. (1).
The three metal targets presented in Fig. 4 (Ag, Ni and W), and the Cu shown in Fig. 2, are the ones with relatively high harmonic cut-off energies. On the other hand, Fe and Mg in Fig. 5 have lower cut-off energies. As for Fig. 6, Cr and Mo are two interesting targets exhibited resonance features which have been investigated extensively [14,29,32,33]. For an investigation on comparing the harmonic cut-off between different targets, the readers may refer to a recent publication by the authors [34]. Note that the harmonic cut-offs of some targets shown in this work appear to be slightly lower than that presented in [34]. It is just because in this experiment we need to avoid saturation of pixels in our CCD camera for majority of the harmonic orders, and therefore we have to keep the overall harmonic signal moderate at the expense of the visibility of the highest few orders close to the cut-off.
Fig. 5. Results of HHG from the targets with relatively lower harmonic cut-off energies. Harmonic spectra as a function of medium length for (a) Fe, (b) Mg. Harmonic spectra at three different selected medium lengths for (c) Fe, (d) Mg. The harmonic yields as a function of medium length for two of the harmonic orders for (e) Fe, (f) Mg. The dots are the data from the experiments. The lines are obtained by fitting experimental data according to Eq. (1).
Fig. 6. Results of HHG from the targets with resonance enhancement features. Harmonic spectra as a function of medium length: (a) Cr, (b) Mo. Harmonic spectra at three selected medium lengths: (c) Cr, (d) Mo. The harmonic yields as a function of medium length for two of the harmonic orders: (e) Cr, (f) Mo. The dots are the data from the experiments. The lines are obtained by fitting experimental data according to Eq. (1).
As mentioned, the fitting procedures for Cu are applied for all the other targets. The fitted values of Lcoh as a function of harmonic orders for them are shown in Fig. 7(a)–(h), respectively. Similar to Fig. 3(a), the dashed lines are the fitted curves in the form of Lcoh = π/(a1q + a2) for estimating plasma density from the trend of Lcoh. The estimated ion density for all targets are summarized in Fig. 8. It is a plot of melting point of the metal against the inverse of plasma density. Note that the specific heat capacities of these metals are very similar to each other. Although the process of forming plasma plume from a solid metal by laser ablation is vastly different from simply heating a solid metal from solid to gaseous form [35,36], it is not unreasonable to expect that, given a fixed amount of energy deposited into the material, the amount of matter in the ablated plume is larger for material with lower melting point, vice versa. Such a trend can be seen in Fig. 8 qualitatively. That is, the melting point increases with the inverse of ion density.
Fig. 7. Lcoh as a function of the harmonic order for the metal of (a) Ag, (b) Ni, (c) W, (d) Mo, (e) Cr, (f) Fe and (g) Mg. The dots are Lcoh deduced from Figs. 4–6, the error bars are the 95% confidence limits, and the dash lines are fitted by Lcoh = π/(a1q + a2).
Fig. 8. The plot of melting point of the metal against the inverse of ion density. The ion density is estimated from a1, which is derived from Fig. 3(a) and Fig. 7.
Finally, we present the comparison of Aq/σq between different targets in Fig. 9. Each panel shows the comparison for one harmonic order only. The results from the 21st harmonic up to the 31st harmonic are presented. Note that it is very likely that the measured harmonic spectra are mostly contributed by ions rather than neutral atoms. It is because the neutral atoms of metals have very low ionization potentials and so could only withstand very low driving laser intensity [34]. In other words, the results reflect the Aq/σq values of ions rather than neutral atoms. Also, note that the particularly low Aq/σq value of Mo at the 21st order, which is not shown in Fig. 9(a) and the high Aq/σq value of Cr at the 29th order are due to resonance effects [32,33].
Fig. 9. Aq/σq of the different metals for harmonic order: (a) H21, (b) H23, (c) H25, (d) H27, (e) H29, (f) H31.
Identifying the physical origin of the differences requires in-depth theoretical investigation and is beyond the scope of this work. Qualitatively, it seems that the targets with only one electron in the outermost subshell (Mg+, W+ and Fe+) tends to have weaker response.
4. Conclusion
In summary, we measured the harmonic spectra from LPPs of eight different metals as a function of the medium length. Using the theoretical formula derived by E. Constant et al. [24], we extracted the three parameters: Lcoh, Labs and Aq/σq for every targets. From Lcoh, we estimated the ion density of each target and found that the plasma density depends to the melting point of metal materials. We also found that the single-atom response of the metal ion species with only one electron in the outermost subshell are weak compared with the other targets considered in this study.
Funding
National Natural Science Foundation of China (12004380, 62121005); Innovation Grant of Changchun Institute of Optics, Fine Mechanics and Physics; Jilin Provincial Science & Technology Development Project (YDZJ202102CXJD002); Development Program of the Science and Technology of Jilin Province (20200802001GH).
Disclosures
The authors declare no competing financial 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.
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