1. Introduction

Laser-produced plasmas provide an intense short-pulse source of XUV radiation that is of major interest both for fundamental and applied science in areas such as fusion research [1], X-ray laser research [2], soft X-ray spectroscopy [3], extreme ultraviolet (EUV) lithography and source development for water-window imaging [4].The spectra of laser-produced plasmas (LPP) provide detailed information on the transitions and electronic structure of highly ionized atoms as discussed in several recent papers [5–7]. Emission in the water-window spectral region between the oxygen K (O_K)-edge at 2.34 nm and carbon K (C_K)-edge at 4.38 nm is currently utilized for the imaging of biological objects and molecular structure [8,9].

For development of a LPP source with a suitable spectral emission range, the selection of target elements is, therefore, critical to maximize emission to develop the most efficient light sources for soft X-ray microscopy and high-resolution tomography. The emitted flux generally increases with the atomic number, Z, of the target, since the average ion stage attained increases with Z while the target concentration can provide a certain degree of control over the optical thickness $L_\nu ^{opt} = \int {\kappa _\nu ^{\prime}\,\textrm{d}l} $ of emission from a particular element [10]. Here $\kappa _\nu ^{\prime}$ is the absorption coefficient reduced by stimulated emission and integration is conducted along line from the emitting region to the plasma-vacuum boundary. Hence, depending on the requirements posed by the experiment, different target concepts can be chosen. The use of solid targets has been proven to be a flexible and easy to operate concept for a broad variety of materials [11]. According to the quasi-Moseley’s law, plasmas of higher-Z elements are expected to produce high output flux, which originates from unresolved spectral structure due to n = 4 − n = 4 transitions. It predicts that bismuth (Bi) is one of the most promising elements for use in an efficient water-window soft X-ray light source [12,13]. However, higher laser intensities are required to achieve electron temperatures in the 500 − 600 eV range needed for generation of highly charged ion emitters from such a high-Z plasma source.

Recent study suggested the feasibility of using the n = 3 − n = 4 (Δn = 1) transitions in the 2nd row transition elements as possible candidates for soft X-ray water-window sources [10,14]. The efficiency of laser energy transformation to emission out the plasma from these transitions is increased due to smaller reabsorption as their optical thickness is lower. As the emission from Δn = 1 arrays moves monotonically to higher photon energy with increasing degree of ionization, the radiation trapping amongst overlapping transition arrays is negligible and thus, it does not decrease the energy emitted out of the plasma. In addition, lower laser intensities and electron temperature of 150 − 300 eV are required to populate these transitions. Based on our previous studies [10,14], we identified transitions in Mo¹⁸⁺ and Mo²⁰⁺ that might be particularly suitable for use together with TiO₂/ZnO and Cr/Sc B₄C multilayer mirrors (MLMs) with reflectance peaks at 2.74 nm and 3.15 nm, respectively [15,16]. In addition, the spectral behavior of water-window soft X-ray emission from molybdenum (Mo) plasmas has also been observed from dual-pulse laser-produced plasmas [10]. Mo is a refractory metal that can withstand extreme temperatures without significantly expanding or softening. Alloys based on Mo offer high stability, high thermal conductivity and are thus very attractive for many important high-temperature applications such as in military equipment, aircraft, turbines and fusion reactors. The spectra from Mo plasmas have been well-analyzed because of their relevance for the above applications [17], and whose potential as a water-window source has been recently highlighted [14]. While the previous papers concentrated to the identification of the spectral lines [14] and to an enhancement of source emission by dual laser pulses [10], our present work is focused to the effects caused by conversion of 150 ps laser pulse of the wavelength 1064 nm to the visible second harmonics (532 nm) on the XUV emission from a Mo target. In addition, it is focused on evaluating the variation in water-window absolute photon output flux and spectral behavior.

2. Experimental apparatus

A Q-switched Nd:YAG laser operating at 1064 and 532 nm with full width at half maximum (FWHM) pulse durations of 150 and ∼ 130 ps, respectively, irradiated bulk Mo targets. The laser system consisted of the master oscillator power amplifier (MOPA). The seed pulse which was produced by a Q-switched oscillator at a wavelength of 1064 nm was compressed by backward stimulated Brillouin scattering (SBS) using a tetrachloromethane (CCl₄) liquid cell with loose focusing. The backscattered pulse was injected to the amplifier. Second harmonic pulse conversion was achieved by use of a K*DP crystal. The stabilities of the pulse energy were pm 5% and 8% at 1064 and 532 nm, respectively. The beam profile was nearly Gaussian. The maximum pulse energies were 220 mJ at 1064 nm and 160 mJ at 532 nm, resulting in an efficiency of 73% for conversion to the second harmonic. A lens with a focal length of 10 cm was used and the focal spot diameter for the two wavelengths was the same, approximately 40 µm, due to different beam divergences. The maximum focused laser power density achieved was about 10¹⁴ W/cm². A solid density planar target of Mo was placed at the center of the vacuum chamber with the vacuum pressure of the order of 10⁻⁴ Pa. The linearly polarized laser beam was incident normally on the target surface. The critical electron densities are 1 × 10²¹ and 4 × 10²¹ cm^-3 for the laser wavelengths of 1064 and 532 nm.

A flat-field grazing incidence spectrometer with an unequally ruled 2400 grooves/mm grating (made by Shimadzu) variable line space grating was positioned at 30° with respect to the incident laser axis. The time-integrated spectra, recorded in the 1 − 8 nm wavelength range, were detected by a thermoelectrically cooled back-illuminated X-ray charge-coupled device (CCD) camera. The spectrometer was wavelength calibrated using known lines from silicon and nitrogen ions. The resulting calibration uncertainty was approximately 0.01 nm. The response of the grating and the X-ray CCD camera were calibrated using synchrotron radiation with a reflectometer installed at the BL-11D beamline of the Photon Factory at KEK [18].

3. Results and discussion

In Fig. 1, we compare the spectra of the emission from Mo, recorded with 1064 nm and 532 nm laser pulses, at a laser pulse energy of 160 mJ (corresponding to the maximum for 532 nm laser wavelength). Spectra recorded at pulse energies down to 20 mJ, for each laser operation, were found to contain essentially the same features but to have significantly lower intensities. At the lowest pulse energies, the features were extremely weak and signal to noise ratio was too low to make unambiguous identification of the features. At each energy value we recorded spectra from three shots, and averaged the spectra. The strongest discrete structure in the water-window soft X-ray spectral range (2.3 − 4.4 nm) is due to overlapping 3dⁿ − 3d^n-14f, 3p − 4s, 3p − 4d, 3s − 4p (n = 3 − n = 4, Δn = 1) lines. Transitions of the type 3p − 4d, emitted from stages with an outermost 3p subshell, are responsible for the shorter wavelength emission, while at longer wavelengths, distinct line groups appear due to 3dⁿ − 3d^{n- 1}4p transitions. Satellite lines from transitions of the type 3d^{n- 1}4l − 3d^{n- 2}4l4f also contribute in the water-window soft X-ray region lying on the low energy side of the 3 d − 4f arrays. The emission spectra of Mo have previously been classified in detail [10,14]. The spectral intensity in the shorter wavelength ranges 1.5 − 2.5 nm and 3.6 − 6 nm is higher for the shorter laser wavelength.

 

Fig. 1. Mo spectra from 150 and 130 ps, λ = 1064 and 532 nm LPP recorded in the wavelength region 1 − 6 nm at 160-mJ laser energy, corresponding to a laser intensity 8.5 × 10¹³ W/cm². The spectrum at 220-mJ laser energy (laser intensity 1.1 × 10¹⁴ W/cm²) (red) at the laser wavelength of 1064 nm and the spectrum at 80-mJ (energy for the laser wavelength of 532 nm (blue). The contributions from different transitions come from 3d − 4p, 3d − 4f, 3p − 4s, and 3s − 4p transitions.

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Here, the photon flux in the spectral peaks was around 4 × 10¹³ photons/nm/sr. The contrast of intensity between the spectral peaks regions outside the peaks is lower for the second harmonic probably due to more intense satellite emission and higher optical thickness. We also compared the variations of spectral emission recorded for a range of energies for 532 nm and 1064 nm, while the intensity increases with laser energy, the appearance of the short wavelength features dominate for 532 nm at 160 mJ (laser power density: ∼ 8.5 × 10¹³ W/cm²) as compared with 1064 nm at 220 mJ (1.1 × 10¹⁴ W/cm²). Thus, we see that despite inevitable energy losses, laser wavelength conversion may lead to emission enhancement in certain spectral ranges. When the emission spectrum for 532 nm and laser energy of 160 mJ is compared with lower laser energy of 80 mJ, larger decrease in the emitted energy is observed for shorter emission wavelengths below 1.8 nm than for longer wavelengths above 2.2 nm.

Figure 2 shows the charge separated spectra from Mo¹⁴⁺ to Mo³⁴⁺ ions. In order to identify the observed spectral features, calculations of the level structure and radiative rates of Mo ions was carried out using the flexible atomic code (FAC) [19]. The FAC has proven to be a versatile tool for the accurate calculation of numerous atomic radiative and collisional processes [20–22]. In our previous study, the observed spectra are compared with theoretical UTA profiles calculated using the Cowan code [23]. The results are essentially identical.

 

Fig. 2. Compared measured spectra in 1 − 3 nm region and calculated emission spectra of Mo for 150 and 130 ps, 1064 and 532 nm Nd:YAG laser produced plasma at a power density of 8.5 × 10¹³ W/cm². Normalized gA values with arbitrary units of possible transitions in the region of observation for Mo¹⁵⁺ − Mo³⁵⁺ ions calculated by the FAC: 3p − 4d, 3p − 4s, 3s − 4p, 3d − 5p, 3d − 5f, 3d − 4f, and 3d − 4p transitions.

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We do see in Fig. 2 that contribution from open 3s or 3p subshell ions to the emission from plasma produced by the 1064 nm laser is very minor while the contribution of these ions is very significant for the shorter laser wavelength. This implies that the plasma ionization degree is higher for the shorter laser wavelength. This is most probably caused by significantly higher laser absorption efficiency at the shorter laser wavelength. Collisional (inverse bremsstrahlung) absorption will be dominant at intensities of a few times 10¹³ W/cm² and the absorption coefficient is proportional to plasma density. As the density scale length at the critical density will be of order 10 − 20 µm the laser absorption will be below 50% for the fundamental wavelength while absorption of over 80% could be expected for the second harmonic [24]. The higher electron density at 532-nm irradiation will also help to increase population of autoionization states leading to more intense satellites [25] and it will also lead to a certain reduction of resonance line emission due to the higher plasma optical thickness, which keeps the overall emission in the same ballpark as that of the 1064 nm plasma. Opacity effects are generally less in picosecond (ps) plasmas, as the emission from ps plasmas generally arises from the lower-density, expanding plume itself.

Higher spectral intensity of the shorter wavelength emission from plasma produced by the second harmonics laser may be caused by higher mean ion charge $\bar{q}$. In order to verify this assumption, we have carried out simulations via the FLYCHK [26] code. The FLYCHK results presented in Fig. 3 for the presumed characteristic plasma scale length of 20 µm show slightly higher mean ion charge for denser plasmas relevant for the laser wavelength of 532 nm at the same plasma temperature. If optically thin plasma is assumed, mean charge is slightly lower in both cases; however, qualitatively the result is the same. FLYCHK result predicts the same mean ion charge $\bar{q}$ for temperature 450 eV at density 4 × 10²¹ cm^-3 as for temperature 700 eV and density 10²¹ cm^-3. The population of higher ionization states may be also influenced by super-Maxwellian electron distribution caused by collisional laser absorption. The modification of electron distribution depends on the parameter ${\alpha _L} = \bar{q}\,\textrm{v}_{osc}^2/\textrm{v}_{Te}^2$, where v_osc is electron oscillation velocity ion laser field and v_Te is electron thermal velocity. The exponent m of the distribution function is approximated by the scaling formula [27] $m = 1 + 3/(1 + 1.66/\alpha _L^{0.724})$ with m = 2 (Maxwellian distribution) for α_L=0 and m = 5 for α_L→∞. In our experiment α_L = 1.18 for the longer laser wavelength (6 × 10¹³ W/cm², 600 eV) leading to m = 3.2 while for the shorter laser wavelength α_L is 4 × lower and m = 2.6. Consequently, fewer electrons are present at the tail of electron distribution for the longer laser wavelength which decreases the rate of collisional ionization to high charge states leading to less intense emission at shorter wavelengths.

 

Fig. 3. Calculated mean ion charge $\bar{q}$ of Mo as a function of electron temperature assuming coronal equilibrium and electron density of 1 × 10²¹ and 4 × 10²¹ cm^-3 for the fundamental wavelength and second harmonic wavelengths at a plasma scale length of 20 µm.

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Additionally, we have carried out one-dimensional (1-D) simulations for the present experimental conditions using our two-temperature hydrodynamic code PETE [28] with SESAME local thermodynamic equilibrium (LTE) equation of state (EoS) [29] and the ionization model from BADGER library [30]. Our results show a laser absorption of 32% for the fundamental wavelength while the calculated absorption was over 60% for the second harmonics. The results of 1-D simulations show that the maximum electron temperatures around critical densities are similar for both laser wavelengths (higher by 10% for longer laser wavelength). The maximum value of approximately 700 eV is moderately overestimated as energy losses due to transverse expansion and transverse energy transport are naturally omitted in this 1-D model. Small difference in electron temperatures for different laser wavelengths is rather surprising result in contradiction with the traditional scaling T_e ∼ (Iλ²)^3/5 derived by Colombant and Tonon [31] for small radiation losses which is not our case. The intensity in the scaling is the absorbed intensity and the temperature difference is partially relaxed by higher absorption (twice according to our simulations) and slightly higher intensity for the shorter laser wavelength. Paper [32] reported a decrease in maximum temperature from to 250 eV for 1064 nm laser wavelength to 160 eV for 256 nm for significantly longer for ns laser pulse and low Z nitrogen plasmas. Detailed two-dimensional simulations [33] for dense krypton gas jet, 1064 nm laser wavelength, 170 ps pulse duration and intensity 10¹⁴ W/cm² reported the maximum electron temperature of ∼800 eV which compares well with our simulation result.

For more detailed comparison of the spectral structures, we display in Fig. 4 the relative spectral intensity enhancement. The enhancement of the intensity in the wavelength region between 1 − 2 nm was observed for 3p − 4s, 3s − 4p, 3p − 4d, and 3d − 4f transitions in various ionic charge states from Mo²²⁺ to Mo³⁰⁺. This enhancement is tentatively explained by higher laser absorption for the shorter laser wavelength.

 

Fig. 4. Relative difference (I₅₃₂ − I₁₀₆₄) / I₁₀₆₄ of spectral intensities emitted from plasmas produced by the 1064-nm (I₁₀₆₄) and 532-nm (I₅₃₂) laser pulse irradiation.

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Figure 5 presents the output emission flux integrated over the water-window soft X-ray spectral region as a function of laser energy for both laser wavelengths. It is demonstrated that the output is higher for the shorter laser wavelength in the whole laser power density range studied of 1 × 10¹³ to 1.1 × 10¹⁴ W/cm². The total number of photons reached the value of 7 × 10¹³ photons/sr for the second harmonic at laser power density of 8.5 × 10¹³ W/cm². The data indicate tendency for saturation at laser intensities above 7 × 10¹³ W/cm² that is most probably caused by the emission shift to wavelengths shorter than water-window spectral range. For the longer laser wavelength, the maximum total number of photons in the water-window spectral range was 9 × 10¹³ photons/sr at a laser power density of 1.1 × 10¹⁴ W/cm² at 1064 nm.

 

Fig. 5. Comparison of number of photons emitted in the water-window soft X-ray spectral region (2.3 − 4.4 nm) from Mo targets at different laser energies of 150-ps, 1064-nm and 130-ps, 532-nm lasers.

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4. Conclusions

We have demonstrated the differences in the spectral emission in the soft X-ray spectral range 1 − 6 nm from Mo plasmas produced by lasers of different wavelengths. The most prominent features of the soft X-ray spectra were identified by comparison with results from atomic structure calculations using the FAC code as well as from previous results. The higher density of emitting plasmas produced by the laser second harmonic leads to lower contrast of intensity between the spectral peaks and the region outside them probably due to more intense satellite emission and higher optical thickness. Higher populations of higher ion charge states leading to enhanced emission at shorter wavelengths are observed and tentatively explained by higher laser absorption at the shorter laser wavelength and by a modest increase of mean ion charge with electron density. The absolute photon intensities of the spectra in the water-window spectral region from Mo LPPs were also determined to be (7 − 9) × 10¹³ photons/sr. The emission below 2 nm may be enhanced by greater laser wavelength conversion despite inevitable laser energy losses.