1. Introduction

The excitation of inner-shell electrons contains a wealth of physical information about electron dynamics in atomic and molecular system [1,2]. However, the excitation of the inner-shell requires high energy, which is beyond the scope of the traditional light source. Recently, the development of high-order harmonic generation (HHG), with its cut-off energy constantly expanding to the high-energy region, has provided an alternative approach to the study of the electronic structure and dynamics of the inner-shell of atoms and molecules [3–7]. The HHG can be described as a semiclassical three-step model: the active electrons first tunnel through the potential barrier, then accelerate in the presence of laser field, and finally recombine with parent ions to emit high-energy photons [8]. In this model, if electrons are emitted from the inner-shell, the ionization process are generally accompanied by an ultrafast rearrangement of the electronic cloud [9], which may lead to the participation of the neighboring, inner, or outer shell in the photoionization and compounding process [10].

A typical example is that heavy neutral atoms such as Xe have a large and broad photoionization cross section near a photon energy of 100 eV [11–14], which is commonly referred to as “the giant resonance.” The enhancement of HHG in atoms due to giant resonance has attracted widespread attention with the promising application in studying the electronic structure and multielectron correlations effects of the inner-shells of atoms and molecules. This enhancement was initially predicted by Frolov et al. [15] and was first experimentally observed by Shiner et al. [14]. They indicated that the 100 eV peak is due to the influence of 4d electrons, which have a large photoionization cross-section in this region owing to a shape resonance. Later, Trallero et al. [16]and Cheng et al. [17] based on the quantitative rescattering (QRS) theory, investigated experimentally and theoretically the giant resonance in the HHG, respectively. Zhang et al. [12] theoretically proposed a different interpretation of giant resonance, attributing it to the increase in magnitude of the modulus of radial part of the wave function in momentum space and suggested that circularly polarized laser light could be used to generate the similar structure in photoelectron spectra. In addition, Faccialà et al. [18] investigated the features in the HHG of Xe with a two-color driving field, where symmetry between neighboring subcycles is broken and each trajectory is split in two resulting in two cutoffs that are energetically well separate. They shown the upper branch is enhanced due to the collective excitation involving the 4d, 5s, and 5p shells in Xe. Bray et al. [11] performed simulations of giant resonance based on a simplified approach and identified the role of inner-shell correlation effects.

In this work, the 4d-5p resonance absorption peaks in Xe are observed simultaneously during the HHG driven by a two-cycle, intense, infrared (IR) laser field with a wavelength of 1.75 µm. In addition, 3d-4p resonance absorption peaks are also detected in Kr. These absorption peaks show periodic variations similar to the the intensity of harmonic signal when changing the carrier-envelope-phase (CEP) of driving laser pulses and the delay of the two-color laser field. This periodic variations indicate that the absorption peaks and harmonics are simultaneously modulated by the laser field and carry information about the collective multi-electron effects involving inner-shell electrons. The 4d-5p absorption peaks of Xe were also previously observed by transient absorption spectroscopy, although not directly during the generation of high harmonics [19–21]. As the absorption target pressure continue to increase, the absorption peak depth will increase all the way, while the intensity of harmonic signal peaks at an optimum gas pressure and fades subsequently. The appearance of this phenomena can be ascribed to two distinctive mechanisms that HHG will be suppressed by phase mismatching at a pretty high gas pressure, while the absorption peak intensity is enhanced by the incremented particles number.

2. Experiment method

As illustrated in Fig. 1, the infrared femtosecond driving pulse is generated by a home-built three-stage optical parametric amplifier (OPA) pumped by a commercial Ti: sapphire laser system (Coherent LEGEND-HE-Cryo, 40 fs, 800 nm, 1 kHz, 10 mJ pulse energy). The OPA can deliver a 50 fs (full width at half maximum) laser pulse with central wavelength at 1.75 µm and single pulse energy of 1.7 mJ. After the OPA, the laser pulse will be guided into the argon-filled hollow fiber (HF) and then passes through a dispersion compensator (a pair of fused silica wedges). Finally, a CEP-stabilized 1.0 mJ/12 fs laser pulse with central wavelength at 1.75 µm is generated [22]. Subsequently, the CEP-stabilized few-cycle laser pulse is focused by a concave silver mirror (CM, with a focal length of 210 mm) into a noble gas filled stainless-steel tube with an inner diameter of 1.8 mm to generate the harmonics. The energy before the concave mirror is ∼0.8 mJ and the peak intensity is ∼ 6.6×10¹³W/cm², estimated by the cutoff energy E = Ip+3.17Up. The spectrometer consists of a flat field grating (Hitachi, 001-0266, 1200 lines/mm) and a soft X-ray CCD (PI, PIXIS-XO: 2 KB) to record the HHG spectra. The grating is located approximately 237 mm away from the harmonic source and is shielded from the IR fundamental laser by a 150-nm-thick aluminum film. In the spectrometer, the harmonic source is directly regarded as a spot light and is reflected by the grating; thus, its resolution is very high, and loss is low compared with the traditional soft X-ray spectrometer.

 

Fig. 1. Schematic diagram of the experimental setup. HF: hollow fiber; CM: concave mirror; CCD: charge coupled device.

Download Full Size | PDF

3. Results and discussions

We use different gases in our experiment to generate high-order harmonics and observe resonance absorption peaks only in Xe and Kr. The gas density and target position are optimized for harmonic generation. Figure 2(a) and Fig. 2(b) show the original HHG spectra from Xe and Kr taken by the CCD, respectively. Horizontal axis of the original HHG spectra is the photon energy, and the vertical axis is the spatial angle distribution of the HHG signal. Figure 2(c) and Fig. 2(d) show the spectra from integrating the CCD image vertically (blue solid line), and the absorption curve of the aluminum film (black dashed line) obtained from the internet (http://henke.lbl.gov/optical_constants). The insets show the magnified spectra covering the positions of the absorption peaks. Here, we define the absorption peak depth as the difference between the actual harmonic intensity and the fitted curve at the same photon energy. The fitted curve, shown as the red dotted line in the insets, approximates the unabsorbed harmonic intensity. The distinction between absorption peaks and harmonics is mainly based on the the absorption depth. It can be seen from the harmonic curve on the Fig. 2(a) and Fig. 2(b) that the harmonic is a continuous spectrum. When the absorption depth of the absorption peak is enough, it can be clearly distinguished. When the absorption depth is too small, it will be difficult to distinguish.

 

Fig. 2. Experiment HHG spectra from Xe at a pressure of 80 torr (a) and Kr at a pressure of 100 torr (b). In (c) and (d), the blue solid line is the intensity of harmonic signal from integrating the CCD image vertically, and the black dotted line is the absorption curve of aluminum film. Inset: solid blue lines shows the amplification of the intensity, and the red dotted line is the fitted harmonic intensity.

Download Full Size | PDF

As shown in Fig. 2 (a) and (c), the most striking spectrum feature is the three evident absorption peaks labeled as A, B, and C, located at 55.45 eV, 56.14 eV, and 57.43 eV respectively, which are consistent with the observed transition energies for the Xe⁺ (5p^{-1 2}P → 4d^{-1 2}D) resonances [21,23,24]. The absorption depths of peaks A, B, and C are 44.16%, 12.12%, and 4.92%, respectively. A clear cut, the L-edge of aluminum, can be observed at ∼72.3 eV. The absorption edge in the spectrum shows that the resolution of our spectrometer is 0.86 eV, which is comparable to the theoretical result by calculating the transmission curve of 150-nm-thick aluminum. In the same way, we can see two absorption peaks labeled D and E in Fig. 2 (b) and (d). The locations of peaks D and E are 79.71 eV and 80.3 eV, which coincide with the resonant transition energy of Kr⁺ (4p^{-1 2}P →3d^{-1 2}D) [25,26]. The absorption depths of peaks D and E are 14.88% and 1.38%, respectively. The locations of absorption peaks, appearing in the HHG spectra, indicate that they originate from the inner-shell transitions, which suggests that electrons can take a path different from that predicted by the three-step model. In other words, the resonance absorption associated with the collective multielectron effects involving inner-shell electrons. In addition, the resolution improvement of spectrometer and the use of ultrashort pulses are key to observing clear absorption peaks in HHG spectra. Our results show that the home-made spectrometer has a high resolution and can observe the resonance absorption of the inner shell during the HHG, which could not be observed previously.

In the next section, we analyze the characteristics of the absorption peaks using Xe as an example. Shiner et al. used similar driving laser parameters in Ref. [14] to study the high-harmonic spectra of Xe to beyond 160 eV, which reported the 4d-5p resonance transition in Xe. They experimentally observed the giant resonance due to inelastic scattering in HHG, meaning that the returning 5p electrons kick out the 4d electrons. The process is shown in Fig. 3, there are two possible paths that electrons can take. After tunnel ionizing from the valance shell, an electron accelerates in the continuum and recombines with the original hole, following the three-step model indicated in path 1. As shown in paths 2 and 3, the returned electron can also promote an electron from the 4d shell to the 5p shell by inelastic scattering, while the returned electron combines with the hole left in the 4d shell. In addition, based on the result of Trallero et al. [16], it is clear that the giant resonance occurs when the driving laser intensity exceeds 1×10¹⁴ W/cm². However, the intensity in our experiment can only reach up to ∼ 6.6×10¹³W/cm² and this is why we did not observe the giant resonance. Our experimental results, as shown in Fig. 2, indicate that the HHG process of path 1 is accompanied by a resonance absorption process that matches the energy of path 3, so that the electron transition does occur between the valence 5p and inner 4d shell. However, the inter-shell transitions are excited owing to the resonance absorption of harmonic photons rather than inelastic scattering of electrons. The appearance of absorption peaks is also the result of the collective multielectron effect and indicates that both Xe and Xe⁺ play a role in the HHG process, which cannot be described by the three-step model.

 

Fig. 3. Schematic diagram of the steps for harmonic generation and resonance absorption. Path 1: Harmonics emission through usual three-step model. Path 2: The returning electron recombine to the hole in the inner 4d shell and emit harmonics. Path 3: The electron transition occurs between the valence 5p and inner 4d shell.

Download Full Size | PDF

To gain further insight into this physical process, we investigate the absorption peak by varying the CEP of driving laser and the delay of two-color laser field. It is well known that the CEP of few cycle laser field can significantly affect the HHG process [6,7], multiphoton ionization [8] and above-threshold ionization [27]. In order to elucidate the underlying mechanism of the resonance absorption during the HHG from Xe, we control the CEP of driving laser by changing the relative position of the fused silica wedges and observe the variation of the absorption peak depth. Taking the absorption peak at 55.45 eV as an example, we study the dependence of the absorption peak depth on the CEP of driving laser and compared the depth with the harmonic intensity. In Fig. 4 (a), the blue dots represent the change in the absorption peak depth, and the red triangles represent the change in the intensity of harmonic signal. The blue solid line and red dotted line are the fitting curves of the absorption peak depth and of the harmonic intensity, respectively. The intensity varies periodically with the CEP, which is consistent with the results of [21]. The absorption peak depth also varies periodically and is consistent with the variation of the harmonic intensity.

 

Fig. 4. The depth of absorption peak at 55.45 eV (blue dot) and the intensity of the harmonic signal (red triangle) as a function of CEP (a) and the relative delay of orthogonally polarized two-color laser field (b).

Download Full Size | PDF

In order to introduce the two-color laser field, we use 0.1-mm-thick BBO crystal and 0.8-mm-thick CaCO₃ crystal to control the delay of orthogonally polarized two-color (OTC) laser field. The BBO crystal is used to generate the second-harmonic, and the CaCO3 crystal tune the relative delay of OTC laser field [28]. As shown in Fig. 4 (b), the intensity of harmonic signal is modulated periodically as a function of the relative delay where the red triangle represents the change in the harmonic intensity and the red dotted line represents the fitting curves. A positive delay indicates that the 1800 nm pulse comes first. The intensity of harmonic signal has a period of T_{1800 nm}/4 (T_{1800 nm} = 6 fs), which is consistent with previous studies [28,29]. The absorption peak depth at 55.45 eV (red dotted line) has the similar period of the harmonic intensity. These similarities indicate that the 4d-5p resonance absorption occurs approximately simultaneously with the HHG process. In addition, for the OTC field, the electrons released from every half-cycle can return only at certain delays and recollide with its parent ion with emission of photons, while at other delays, most of the electrons are shifted by the field so that they miss the ion core. In this process, the hole generated by tunneling ionization from the valance shell and harmonic generated by recombine provides the conditions for the resonance absorption of the inner shell. And a strong modulation of the absorption is obtained by controlling the pump laser field.

In addition to the above-mentioned laser field modulation, we also change the gas pressure and observe the variation of the absorption peak depth. As shown in Fig. 5, we can clearly see that the depth of absorption peak at 55.45 eV has the similar trend as the intensity of the harmonic signal when the pressure gradually increases from 20 torr to 120 torr. However, when the pressure is further increased to 200 torr, the intensity of the harmonic signal begins to weaken, and the absorption depth still increases. The intensity of the harmonic signal with pressure is influenced by the phase matching condition. With the increase in pressure, the balance between the neutral gas dispersion and equal particle dispersion is gradually broken, and the phase matching condition is destroyed, resulting in a decrease of the harmonic intensity. However, the variation of the absorption peak depth is mainly influenced by the number of particles involved in the 5p-4d resonance transition. With increasing pressure, the number of particles involved in the 5p-4d resonance transition keeps increasing, which leads to a continuous increase in the absorption depth.

 

Fig. 5. The depth of resonance absorption peak (the blue solid line) and the intensity of harmonic signal (the red dotted line) at 55.45 eV as a function of the pressure.

Download Full Size | PDF

4. Conclusion

In summary, we investigate the specific resonance absorption structures involving the excitation of the inner-shell electrons from Xe and Kr. Our experiment detects distinct absorption peaks in the HHG spectra and the locations of these absorption peaks indicate that they originate from the inner-shell transitions, which suggests that electrons can take a path different from that predicted by the three-step model. Apart from recombining with parent ions directly, returning electron can take an alternative path to excite an inner shell electron and fill up the vacancy. In other words, the absorption peaks during the HHG process, come from collective multi-electron effects. The correlation of these observed absorption peaks with the HHG is experimentally investigated by changing the laser CEP and the relative delay of OTC laser field. The depth of resonance absorption displays a different dependence on gas pressure compared with the intensity of HHG, which suggests that resonance absorption is mainly dictated by the number of particles involved in the 5p-4d resonance transition. Hopefully, our results will trigger more progressive theoretical studies on the essence of the HHG spectra of the heavy neutral atoms and pave the way to uncover the physical mechanism of the collective multielectron effects involving inner-shell electrons in the HHG.