1. Introduction

Since the first demonstrations of high-order harmonic generation (HHG) by short pulse lasers [1, 2], the coherent and ultrashort pulse radiation have been achieved in the extreme ultraviolet (XUV) and soft x-ray regions. Many studies for the extension of the HHG cutoff energy have demonstrated during last two decades [3–5]. Recently, the maximum cutoff energy of HHG has been extended up to 3.5 keV [6]. The highest possible (cutoff) photon energy of high harmonic is described by E_c ≈ I_p + 3.17 U_p, where I_p is the ionization potential and U_p is the pondermotive energy [7]. U_p=e ² E ²/4mω ²=9.33×10^-14 I _L λ ², where e and m are electron charge and mass, and E, ω, I _L, and λ are the field’s amplitude, frequency, laser intensity, and laser wavelength, respectively. To obtain the highest possible cutoff energy, one has to increase the ponderomotive energy or the ionization potential of the nonlinear medium. The pondermotive energy strongly depends on the laser intensity (I _L). However if the gas medium is ionized before the peak of the I _L, the cutoff energy is defined by the saturation intensity (I _S<I _L). Therefore the higher ionization potential material is useful for extending the cutoff energy. In particular, the ionization potential of the ions from alkali metals is the highest among other materials, therefore the HHG by using the laser plasma produced on the surfaces of alkali metals has been demonstrated [8–10]. However the maximum photon energy of the harmonic was 64.92 eV using the laser plasma potassium ions with irradiating the subpicosecond KrF excimer laser at the wavelength of 248 nm [8]. The harmonic cutoff energy was further extended up to 105 eV by using the lead ions irradiated by the KrF laser [10]. At the same time, in the case of Ti:sapphire laser (λ=800 nm), the maximum cutoff energy of HHG achieved in previous studies was 42.6 eV by using the laser plasma containing sodium and potassium ions [10]. These cutoff energies from ions by using laser plasma were lower than that from neutral atomic by using gas medium although the ionization potential energy was higher than that of neutral. Furthermore, the plateau was not observed in those studies.

Recently, we have obtained the 63^rd harmonic at the photon energy of 98 eV (wavelength: 12.63 nm) using laser-ablation boron ions with irradiating the femtosecond laser pulse [11]. The plateau-like distribution of high-order harmonics was observed in these experiments. The 63^rd harmonic radiation was occurred from the interaction of the femtosecond laser pulse with the single charged ions. To increase the harmonic yield, the enhancement of the single harmonic due to the multiphoton resonance with the strong radiative transitions has been realized using the indium and tin single charged ions [12,13]. In this paper, we report the first observation of the 71^st harmonic generation at a photon energy of 110 eV with conversion efficiency of 1.6×10^-7 using a laser-ablation vanadium plume. This obtained cutoff energy is the highest one among the previously reported data of the HHG from laser-ablation plasmas used as the nonlinear media. We attribute the origin of the 71^st harmonic generation to the interaction of laser pulse with the double charged ions.

2. Experimental setup

The schematic of experimental setup was described in our previous paper [14]. The pump laser was a commercial, chirped pulse amplification laser system (Spectra Physics: TAS-10F), whose output was further amplified using a homemade three-pass amplifier operating at a 10 Hz pulse repetition rate. A pre-pulse was split from the amplified laser beam by a beam splitter before a pulse compressor. The pre-pulse energy was 17 mJ with pulse duration of 210 ps. A main pump pulse output at a center wavelength of 795 nm had the maximum energy of 17 mJ and the pulse duration of 150 fs. A cylindrical lens focused the pre-pulse onto a solid target placed within a vacuum chamber, which generated a laser-ablation plume containing the low-charged ions. Vanadium, silver, titanium, lead, and germanium were used as the nonlinear media in these experiments. The size of the line focus on the target surface was 100 μm width and 3 mm long, and the intensity of the pre-pulse was varied in the range of 1.6×10¹⁰ W cm^-2. The main pulse was focused onto the ablation plume by a spherical lens (focus length of 200 mm), 100 ns after pre-pulse irradiation. When the delay was changed from 20 to 100 ns, the cutoff energy from these ablation plumes was not big difference. Therefore the delay was fixed at 100 ns in this experiment. The intensity of the main pulse at the plasma plume was 6.8×10¹⁴ W cm^-2. The confocal parameter of the femtosecond laser pulse was 10 mm. The spectrum of the generated high-order harmonics was analyzed by the grazing incidence spectrometer with a gold-coated Hitachi 1200 grooves/mm flat-field grating. A gold-coated grazing incidence cylindrical mirror was used to image translation of the harmonics onto the detector plane. The XUV spectrum was detected by using a micro-channel plate with a phosphor screen read-out (Hamamatsu, model F2813-22P), and the optical output from the phosphor screen was recorded using a CCD camera (Hamamatsu, model C4880). The details of an absolute calibration of the spectrometer were described elsewhere [15].

3. Results and discussion

Figure 1 shows the typical spectra of HHG from the laser-ablation vanadium and silver plumes irradiated by femtosecond laser pulses. The high-order harmonics up to the 71^st order at the photon energy of 110 eV were observed using the laser-ablation vanadium plume. The harmonics disappeared by changing the polarization of femtosecond laser pulse from the linear to circular. This tendency shows that these radiations should be generated from HHG. The conversion efficiency of the 71^st harmonic was 1.6×10^-7. Using the laser-ablation silver plume, the 59^th harmonic at the photon energy of 92 eV was observed. The plateau and cutoff were observed in both spectra.

 

Fig. 1. HHG from the (a) vanadium and (b) silver plumes irradiated by femtosecond laser pulse. The spectrum (a) was recorded by the accumulation of 100 shots. The spectrum (b) was recorded by the accumulation of 10 shots. The 71^st harmonic at the photon energy of 110 eV was obtained using the laser-ablation vanadium plume.

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In our previous work, the maximum cutoff energy linearly depended on the second ionization potential of laser-ablation plume [15]. Therefore we can expect the observation of higher photon energy harmonic by using the target with higher ionization potential. Previously, the maximum cutoff energy (98 eV) was obtained by using the laser-ablation boron target because the high second ionization potential of this material (24.12 eV). The second ionization potential of silver (21.04 eV) is less than the one of boron, therefore the cutoff energy obtained from the silver plume was 92 eV in these experiments. At the same time, although the second ionization potential of vanadium is only 14.65 eV, the 71^st harmonic with photon energy of 110 eV was observed in the case of vanadium plume. This cutoff energy is the highest one observed during the HHG from the laser-ablation plume used as a nonlinear medium. We attribute the generation of the 71^st harmonic to the interaction of femtosecond pulses with the doubly charged ions. The third ionization potential of vanadium is 29.31 eV, which is higher than the second ionization potential of boron. Therefore the observation of cutoff energy by using the vanadium plume is higher with regard to the boron plume.

To investigate the ionization conditions in the laser-ablation vanadium plume, we measured the emission of the plasma at the wavelength range of 280–500 nm as can be seen in Fig. 2. The emission of the V III, V II, and V I ionic transitions [16] was observed at the conditions of the observation of 71^st harmonic. In particular, the emission from V III transitions at the wavelength of 367.99, 370.53, and 471.49 nm were obtained, and therefore, from the analysis of plasma spectra, we confirmed the presence of doubly and singly charged V ions in the laser-ablation plume.

 

Fig. 2. The vanadium plasma spectrum at the wavelength range of 280–500 nm.

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To analyze the characteristics of the laser-ablation plume at the delay of 100 ns, we carried out the simulations using the HYADES code [17]. These data are presented in the Table 1. By increasing the prepulse intensity, the ion density in the plasma enhanced. At the prepulse intensity of 1.6×10¹⁰ Wcm², the ionization level and the ion density were estimated to be 1.07 and 3.6×10¹⁷ cm^-3 , respectively. These calculations confirmed the presence of doubly and singly charged ions and neutrals at the ion density of about 10¹⁷ cm^-3 in the laser-ablation vanadium plume.

It was difficult to define exactly the saturation intensity for vanadium ions in our experiments. To calculate the cutoff energy, we estimated the I _s of the low-charged vanadium ions by using the expression for the barrier-suppression ionization [18] I _BSI = c(I_p)⁴/128πe ⁶ Z_i² = 4×10⁹×(I_p)⁴/Z_i², where Z _i is the degree of ionization. The I _BSI of the singly and doubly charged vanadium ions was calculated to be 4.6×10¹³ and 3.3×10¹⁴ W cm^-2 , respectively. If the highest harmonic from vanadium plasma was obtained from the interaction of laser pulses with the singly charged ions, then the cutoff energy calculated from the relation E_c≈I_p + 3.17 U_p = 23.35 eV is quite far from our experimental data (110 eV). At the same time, in the case when doubly charged ions were responsible for highest harmonic generation in vanadium plasma, the estimations give the cutoff energy of 91.75 eV, which is closer to the experimental data. From this estimation, we concluded that the higher harmonics from vanadium plasma were originated from the doubly charged ions.

Table 1. Calculations of the laser-ablation vanadium plume characteristics (electron density, ionization level, and ion density) as the functions of prepulse intensity.

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To investigate the nature of the HHG from the doubly charged ions in another ablation plumes, we measured the harmonic spectra using titanium, lead, and germanium. Table 2 shows the maximum cutoff energy of the HHG from these plumes irradiated by the femtosecond laser pulse. The second ionization potentials of titanium, lead, and germanium are 13.58, 15.03, and 15.93 eV, respectively. Furthermore the third ionization potentials of these materials are 27.49, 31.94, and 34.22 eV, respectively. Using these targets, the cutoff energies were found to be 95.4 eV, 54.59 eV, and 38.99 eV, for titanium, lead, and germanium, respectively.

Table 2. Maximum observed cutoff energies of the HHG from the titanium, vanadium, lead, and germanium plumes and their second and third ionization potentials.

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These results contradict with our hypothesis that higher ionization potentials generally lead to higher cutoff energies, since, for example, the second and third ionization potentials of germanium are higher than for vanadium, while the cutoff energy of germanium was measured to be only one-third of vanadium. The above results show that simple comparison of ionization potentials alone cannot definitively predict the relative cutoff harmonics among different atomic species. From above discussion one can conclude that the HHG from the titanium and vanadium plasmas were probably originated through the interaction of short pulses with doubly charged ions. At the same time, the cutoff energies of the harmonics generated in lead and germanium ablations were lower with regards to the titanium and vanadium ablations because the HHG from the former species occurred from the interaction between the femtosecond laser pulse and singly charged ions.

The relevant degree of ionization here is not that of the plasma produced by 210 ps pulse, which can recombine prior to the arrival of the 150 fs pulse. This parameter rather the degree of ionization reached in the plasma resulting from field-ionization of the plasma by the short pulse. In that case, one expects higher cutoff energies than those observed for all elements studied (except for vanadium and titanium).

The processes that determine harmonic generation from plasma plume are complex and may involve various factors that are not considered for gas harmonics. For example, the nonlinear media is already weakly ionized for plasma harmonics, whose level of ionization depends on the prepulse intensity. If the free electron density is too high, it can induce phase mismatch between the pump laser and the harmonics, or defocusing of the pump laser. Both of these effects can reduce or stop HHG. Recent time-resolved plasma spectroscopy experiments with the harmonics generated from gold plasma have shown that, at the conditions of the observation of highest cutoff, the plasma is cold enough so that there is no emission from the Au I ion, just before interaction with the main pump laser [19]. If one increases the prepulse intensity, the plasma ionization level increases, which was indicated by the increase of the Au I emission. Under such conditions, harmonic generation was either reduced or completely stopped.

Laser-ablation itself is a complex phenomenon, especially at relatively low laser intensities used for plasma harmonics. The behavior of laser-ablation will change considerably, depending on the equation of state, ionization potential, and cohesive energy of the material. Therefore, we attribute the different cutoff energies observed for titanium, vanadium, germanium, silver, and lead to this difference in the plasma behavior for different materials. Consequently, although the laser intensity of the laser generating harmonics is high enough for producing doubly charged ions, the higher harmonics from doubly charged ions were not obtained by using germanium, silver, and lead.

4. Conclusions

In conclusion, we observed the 71^st harmonic at the photon energy of 110 eV with the conversion efficiency of 1.6×10^-7 by using the laser-ablation vanadium plume irradiated by the femtosecond laser pulse. By measuring the spectra of laser plasma and calculating the ionization conditions and harmonic cutoffs in the laser-ablation plume, we concluded that the higher harmonics occurred from the interaction of the femtosecond laser pulses with doubly charged vanadium ions. At the same time, our studies of other plasmas showed a complex behavior of harmonic cutoff energies from these species. Further extension of the cutoff energy on HHG may be achieved in doubly charged ions by searching the appropriate targets for plasma formation.