The deep ultraviolet (DUV), or “UV-C,” is defined as wavelengths less than 280 nm [1] where earth’s atmosphere completely absorbs incident solar radiation and photon energies can directly damage cellular structure. This spectral region also contains a large density of strong atomic and molecular electronic transitions in a wide range of neutral and ionized elements, with many transitions originating from ground and low-energy states. Accurate measurements of atomic and molecular transitions in the DUV are important for fundamental science based on atomic and nuclear theory, such as models used in theoretical astrophysics to study atmospheric chemistry, stellar evolution, or even in testing potential variability of fundamental constants from quasar absorption spectra [2]. The DUV also enables access to Rydberg transitions directly from ground states, often used for benchmarking quantum theory [3], as well as a low-energy isomeric nuclear transition in ${^{{229}}{\rm Th}}$, whose direct excitation was recently observed and is being actively pursued by many groups as a next generation nuclear clock [4]. Optical diagnostics at DUV wavelengths are also important for technological advances such as characterization of low-temperature plasmas used in a broad range of applications from processing and etching in the semiconductor industry to plasma medicine [5]. Despite all these opportunities, there are significant gaps in spectroscopic information for this region compared to the visible (VIS) and near-infrared (NIR), partly due to the challenges of performing high-resolution optical emission spectroscopy (OES) or absorption spectroscopy (AS) with tunable lasers in the DUV.

In this Letter, we introduce dual-comb spectroscopy (DCS) as a new approach for broadband and high-resolution absorption spectroscopy in the DUV. DCS has commonly been employed across the VIS to mid-IR spectral regions for high-resolution studies of atomic and molecular transitions in applications ranging from remote sensing of greenhouse gasses to spectral lidar [6,7]. The ability to rapidly probe broad spectral regions with high resolution enables one to distinguish congested and overlapping spectral features while performing time-resolved studies such as combustion dynamics [8] or observation of transient species [9]. Recent preliminary work in the near-UV shows the growing interest in pushing DCS to shorter wavelengths [10–12]. Here, we establish DUV DCS by exploiting the high peak powers provided by the frequency comb pulse trains combined with efficient and readily available nonlinear crystals to access the DUV and perform time-resolved studies on transient plasmas.

Laser-produced plasmas (LPPs), which are created by laser ablation of condensed media into a plasma phase, provide a powerful tool for analysis of solid materials and more generally for spectroscopic studies of atomic, ionic, and molecular species in plasma conditions [13]. Key parameters in LPP characterization include plasma temperatures and electron densities, both of which evolve rapidly in time over many orders of magnitude. OES has been used extensively to characterize LPP properties. Fitting relative intensities of emission lines to a Boltzmann distribution is used to determine excitation temperatures ${T_{\rm{ex}}}$ for neutral and ionized species, and Stark broadening/shift measurements are used to determine electron density ${n_e}$ [13]. However, OES measurements are limited to early times in LPP evolution when temperatures are high enough to produce sufficient emission for detection. In addition, instrumental linewidth limits ${n_e}$ measurements to early times when Stark broadening exceeds the resolution limit. Saha-Boltzmann analysis has been used to determine ${n_e}$ in LPPs using OES; however, it is also limited to early times when emission signals are strong [13]. Because experimental information on LPPs has primarily been obtained using OES, there is very little information on LPP properties such as ${n_e}$, charge/ionization state, and whether local thermodynamic equilibrium (LTE) conditions are satisfied for times later than about 10 µs [14].

In contrast, AS can probe LPP properties over time scales much longer than OES by measuring atomic transitions from low-lying energy levels including the ground state. AS also yields direct quantitative measurement of number densities [13,15]. AS has been used to measure atomic state densities, total column densities, ${T_{\rm{ex}}}$, and kinetic temperatures for LPP systems over ${\sim}1 {-} 1000\;\unicode{x00B5}{\rm s}$ time scales [13]. Neutral and ion number densities and ${T_{\rm{ex}}}$ for uranium [16] and yttrium [15] have been measured using AS out to 20 µs after LPP formation. However, to the best of our knowledge there is no information on ${n_e}$ at later times in LPP evolution.

We have previously used DCS in the VIS-NIR to perform high-resolution, broadband, and time-resolved atomic and molecular absorption spectroscopy in LPPs [17,18]. Here, we apply DCS in the DUV to obtain time-resolved absorption spectra across multiple transitions in neutral (Fe I) and singly ionized (Fe II) iron atoms in a LPP. Analysis of state column densities indicates that Fe I and Fe II atoms remain in LTE at late times of LPP evolution (20–50 µs), with both ionization states following Boltzmann distributions at similar excitation temperatures. Based on comparison of Fe I and Fe II column densities, the LPP average electron density is determined from 10 to 50 µs in the LPP. In particular, probing Fe II transitions from low-energy levels in the UV enables measurement of electron densities at ${\sim}{10^{14}} {-} {10^{16}}\; {{\rm cm}^{- 3}}$ levels, and at longer time delays than would be possible using OES, providing valuable new information over these time scales with low temperatures and electron densities.

Figure 1(a) shows a simplified experimental schematic. The frequency combs used here are based on two home-built mode-locked ytterbium fiber lasers. The optical spectra are centered near 1060 nm with 30 nm bandwidths. A portion of each output is used to stabilize the combs via two CW reference lasers at 1050 and 1064 nm to establish high mutual coherence, as described previously [17]. When phase-locked, Comb 1 has a repetition frequency of 77.85 MHz and a difference frequency from Comb 2 of 455 Hz. The combs can be amplified up to 50 W power levels; however, in the present experiment only 2 W are needed. Each output is frequency doubled in 0.5 mm thick barium borate (BBO) crystals to near 530 nm and subsequently frequency doubled again by 7 mm thick BBO crystals to near 265 nm. The length of the second pair of BBO crystals limits the phase-matched optical bandwidth of UV light to less than 0.5 nm (${\sim}2\;{\rm THz} $). Adjustment of the crystal angle allows tuning the center wavelength across a span of 5 nm. In this way, the BBO crystals provide optical filtering for high signal-to-noise DCS while allowing broad tunability. Figure 1(b) shows examples of measured spectra in the DUV region of 260.5–263.5 nm.

 

Fig. 1. (a) Schematic of the experiment with two stages of second harmonic generation and a symmetric (collinear) DCS configuration to probe the LPP. (b) Examples of “reference” (black) and “signal” (red) dual-comb spectra (50 µs delay) over tuning range used for the experiments. Reference and signal spectra are normalized and vertically offset for clarity.

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Laser ablation is performed using a commercial Nd:YAG $Q$-switched laser with 350 mJ pulse energy, 5 ns pulse duration, and 10 Hz repetition rate. Ablation pulses are focused through the top window of a vacuum chamber toward an iron metal sample. At the metal surface, the ablation beam diameter is ${\sim}1.5\;{\rm mm} $, delivering a pulse fluence of ${\sim}20\; {{\rm J/cm}^2}$. Experiments are performed under 100 Torr flowing Ar to minimize oxidation reactions in the LPP [18]. A motorized stage translates the sample at 0.14 mm/s to reduce formation of deep craters.

The two UV combs are overlapped spatially before the plasma in a symmetric (collinear) configuration that maintains common-path propagation through the turbulent LPP and maximizes absorbance signal strength [6]. Then, the beams are focused through anti-reflection coated windows of the vacuum chamber to probe the LPP at 3 mm above the metal sample, and then focused onto a silicon photodetector. A 10 nm bandpass UV filter reduces detection of LPP emission. A field programmable gate array timing system adjusts the delay $\tau$ between the laser ablation pulse and the zero-path difference (ZPD) position of the “signal” dual-comb interferogram (IFG) to probe the LPP at delays from $\tau = 10$ to 150 µs, with a timing jitter ${\sim}1\; \unicode{x00B5}{\rm s}$ [17]. For each signal IFG, a “reference” IFG immediately preceding the ablation is also recorded for normalization in post-processing.

Signal and reference IFGs are processed via a method used for single-sided IFGs in Fourier transform infrared spectroscopy [19], giving a frequency resolution of 1.2 GHz (see Supplement 1). For each time delay and spectral window, 500 signal and reference IFGs are recorded and the single-beam spectra (SBSs) are averaged. Figure 1(b) shows examples of signal and reference SBSs for six spectral windows, obtained at a delay of 50 µs, yielding a figure of merit of $4.3 \times {10^5}/\sqrt {\rm s}$ [6] (see Supplement 1). Absorbance spectra are computed according to $A(\nu) = - \ln [{{\rm SBS}_{\rm{sig}}}(\nu)/{{\rm SBS}_{\rm{ref}}}(\nu)]$, as described previously [17]. The absolute frequency stability of the CW reference lasers enables all separately measured spectral windows to map to a common frequency axis. The absolute optical frequency is then determined using a single shift of this axis to match positions of known Fe I and Fe II absorption lines.

Figure 2 shows examples of experimental absorbance spectra from regions in different spectral windows, for time delays of 10, 30, 65, and 100 µs. Three Fe I and two Fe II transitions are shown, with the lower energy levels for the transitions labeled. Transitions originating from higher energy levels decay faster than those from lower energy levels for both Fe I and Fe II, consistent with a decreasing LPP temperature. Many Fe I and Fe II transitions are observed within the six spectral windows; however, peaks with low SNR and peaks with high absorbance are both difficult to quantify accurately and are not used for the further analysis described below. In total, six Fe I transitions and three Fe II transitions across the six spectral windows are selected for analysis. Voigt profiles are fit to measured absorbance peaks using procedures described previously [17]. Examples of spectral fits are shown in Fig. 2, and the fit residual shown yields a noise equivalent absorbance of 0.02 (see Supplement 1). The area of an absorbance peak determines the measured column density ${n_i}L$ of the lower state in the transition according to ${n_i}L = {\rm Area}/({\tilde \sigma _0}{f_{\textit{ik}}})$, where ${\tilde \sigma _0} = \frac{{{e^2}}}{{4{\epsilon _0}{m_e}c}}$ is the integrated absorption cross-section constant and ${f_{\textit{ik}}}$ is the transition oscillator strength. Transition parameters are obtained from the Kurucz online database [20], with uncertainties in ${f_{\textit{ik}}}$ of 10%–50%.

 

Fig. 2. Example experimental absorbance spectra at 10, 30, 65, and 100 µs after ablation. Multiple Fe I and Fe II transitions are observed, labeled by the lower energy level of each transition. Spectral fits are shown by the shaded regions, and an example fit residual is shown in the inset.

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Fig. 3. Time-dependent plasma properties. (a) State column densities of two Fe I and two Fe II energy levels. (b) Total column densities of Fe I (open) and Fe II (filled) obtained from Boltzmann analysis. (c) Excitation temperatures of Fe I (open) and Fe II (filled) obtained from Boltzmann analysis.

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Figure 3(a) shows state column densities for two Fe I and two Fe II energy levels. The temporal behaviors of the state column densities are consistent with the qualitative observations from Fig. 2 but provide additional information for quantitative analysis. Using the state column densities from the six Fe I transitions and three Fe II transitions, absorption Boltzmann plots are constructed for each ionization state. All Boltzmann plots exhibit good linearity (see Supplement 1), indicating that LTE appears to be a valid assumption. Figure 3(b) shows the total column density and Fig. 3(c) shows ${T_{\rm{ex}}}$ for Fe I and Fe II obtained from the Boltzmann analysis of each ionization state.

The results in Fig. 3(b) indicate that the Fe II total column density decreases monotonically with time, while the Fe I total column density initially increases before a slower decay at later times. These behaviors are consistent with electron-ion recombination during early stages of LPP evolution, followed by a slower decrease in Fe atom number density due to diffusion and molecule/particulate formation. The results are also consistent with measurements on LPPs containing yttrium using OPO-based absorption spectroscopy in the VIS spectral region [15].

Figure 3(c) shows ${T_{\rm{ex}}}$ time evolution for Fe I and Fe II. Except for the earliest time delay of 10 µs, ${T_{\rm{ex}}}$ for Fe I and Fe II agrees within their uncertainties, again supporting the existence of LTE conditions and plasma homogeneity. The higher apparent Fe II excitation temperature at 10 µs is possibly due to spatial variations in temperature along the measurement path, combined with an increased ion density in higher-temperature regions. Similar behavior has been noted in both emission [21] and absorption [15] measurements.

In LTE, the Saha equation relates populations in successive ionization states of a given element to the electron temperature ${T_e}$ and number density ${n_e}$ [22]. For uniform conditions along the measurement path, the Saha equation can be expressed as

 

Fig. 4. Path-averaged electron density ${\tilde n_e}$ determined from the Saha equation (red squares), from ${n_{\rm{II}}}L$ with ${L} = {1}\;{\rm cm}$ (black circles), and from ${n_{\rm{II}}}L$ with ${L} = {0.25 - 2}\;{\rm cm}$ (shaded). Dashed line shows ${n_e}$ from the McWhirter criterion.

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The ${\tilde n_e}$ in Fig. 4 determined from the Saha equation is near ${10^{14}}- {10^{15}}\; {{\rm cm}^{- 3}}$ from 20 to 50 µs. Previous determination of ${n_e}$ in LPPs using OES has typically been limited to times ${\lesssim} 5{-} 10\;\unicode{x00B5}{\rm s}$. Direct comparison of our measurement to prior OES studies is difficult due to variations in LPP conditions; however, previous measurements of ${n_e}$ using OES and Stark broadening/shifts or Saha-Boltzmann methods showed ${n_e} \sim {10^{16}}{-} {10^{17}}\; {{\rm cm}^{- 3}}$ at 4–10 µs [23–25]. The results here show electron densities continue to decrease as the LPP cools, reaching ${\sim}{10^{14}}\; {{\rm cm}^{- 3}}$ at 50 µs.

The McWhirter criterion ${n_e} [{{{{\rm cm}}^{- 3}}}] \ge 1.4 \times {10^{14}} \sqrt T {(\Delta E)^3}$, with $T$ and $\Delta E$ (the largest energy gap between upper and lower energy levels) in eV, specifies a minimum ${n_e}$ for a plasma to be in LTE, by requiring (de)population rates of atomic energy levels via electron collisions to be much larger than radiative rates [14]. OES studies have shown that the LPP eventually reaches a condition of low ${n_e}$ such that the McWhirter criterion is no longer satisfied [14]. Figure 4 shows that ${\tilde n_e}$ is below the McWhirter criterion (dashed line) at 20–50 µs after ablation, consistent with extensions of prior OES observations to these time delays. However, as discussed, our results also show that the energy level populations for Fe I and Fe II both follow Boltzmann distributions described by the same ${T_{\rm{ex}}}$, supporting that these two species are indeed in LTE at these times. The McWhirter criterion assumes that collisions with heavy particles (atoms) are negligible relative to collisions with electrons, but the results here suggest this may not be the case during the later times probed by AS.

Calculation of ${n_e}$ using the Saha equation assumes ${T_e} = {T_{\rm{ex}}}$; however, this may not be valid under low ${n_e}$ conditions. Therefore, Fig. 4 also shows ${\tilde n_e}$ calculated directly from the measured Fe II total column density, ${n_{\rm{II}}}L$, assuming a charge-neutral LPP with a length of 1 cm, which is reasonable for the ablation conditions [26]. The shaded region in Fig. 4 shows ${\tilde n_e}$ for lengths 0.25–2 cm as a reference. The ${\tilde n_e}$ calculated from the Saha equation and from ${n_{\rm{II}}}L$ are in good agreement, increasing confidence in both approaches. In the future, direct measurement of LPP size [15] would reduce uncertainty in ${n_e}$ determined from ${n_{\rm{II}}}L$. Because calculating ${n_e}$ from measured ${n_{\rm{II}}}L$ requires fewer assumptions than the Saha equation, this approach may give a more accurate and precise probe of low electron densities at late times of LPP evolution.

In summary, this work presents the first demonstration of DCS in the DUV. Measurement of broadband, high-resolution, and time-resolved spectra enables quantitative determination of Fe I and Fe II $nL$ and ${T_{\rm{ex}}}$ in the LPP, in turn used to probe ${n_e}$ at two orders of magnitude lower density than typically obtained using OES. Given the large number of strong transitions from low energy levels in neutral and ionized (including multiply ionized) atoms and molecules that can be probed, DCS in the DUV provides a promising approach for understanding charge properties of LPPs and other low-temperature plasma/gas sources. Future studies will push DCS to even shorter wavelengths in the vacuum ultraviolet ($\lt 190\;{\rm nm}$) utilizing intracavity high-harmonic generation [27,28], as was demonstrated recently [29].