1. INTRODUCTION

A vast variety of photochemical reactions are induced by ultraviolet (UV) radiation. Specifically, solar UV radiation triggers many atmospheric reaction and fragmentation processes that involve environmental trace gas species like ${{\rm O}_3}$, ${{\rm NO}_2}$, NO, and HCHO. In order to improve our understanding of the relevant reaction pathways, spectroscopic access to the UV spectral region is of paramount importance. Because most molecular gases show strong and congested absorption characteristics in the ultraviolet region [1,2], a high spectral resolution is required for complete state determination. At the same time, broad spectral coverage is desired to achieve high specificity and to simultaneously detect characteristic transitions of reactants and products of a photochemical reaction. Finally, rapid acquisition times can grant access to the exploration of reaction rates. So far, the combination of all three criteria–high spectral resolution (50 GHz), broad spectral coverage (${\gt}{30}\;{\rm THz}$), and short acquisition times (${\lt}{10}\;{\rm s}$)–has not yet been accomplished in the UV region. State-of-the-art techniques aiming at high spectral resolution involve scanning techniques, providing instrumental linewidths on the order of 100 MHz, i.e., resolving powers up to ${{10}^7}$, with measurement times of minutes to hours [3–8]. Alternatively, experimental observations aiming at a broad bandwidth and high spectral resolution have been shown to cover up to 533 THz within 120 s measurement time and exhibit a resolving power of ${9}{{.6 \times 10}^{3}}$ at a spectral resolution of 83 GHz [1,9,10].

In this work, we introduce ultraviolet dual comb spectroscopy (DCS) that simultaneously features fast acquisition, broad detection bandwidth, and high resolution as a novel tool suitable for studying complex photo-chemical reaction processes in gaseous media. DCS is an innovative spectroscopic method [11–14] that has proven its capabilities in numerous implementations operating in the visible spectral region across the infrared down to the THz domain [12,15–20]. Especially, mid-infrared DCS can be exploited for sensitive and accurate determination of rotational and vibrational transitions, the so-called molecular fingerprints [21–23].

In contrast, the UV region has so far been relatively unexplored by DCS, mainly due to the lack of readily available laser frequency comb sources [24–26]. Most recently, several groups are working on establishing DCS in the UV spectral region [27–30]. This is because introducing DCS with its rovibronic detection capabilities into the UV region, implying high photon energies, would additionally enable fingerprinting the electronic energy structure of matter and thus help to unravel a fundamental riddle in spectroscopy: the complex trinity of rotational, vibrational, and electronic excitation in gaseous media. Excitations involving electrons can be followed by various reaction pathways and their resulting different molecular components are highly relevant, like the ${{\rm NO}_x}$ cycle for atmospheric sciences [5].

 

Fig. 1. Experimental implementation of dual comb spectroscopy in the ultraviolet spectral region. (a) The outputs of two laser frequency combs (commercial Yb fiber laser oscillators), stabilized in their repetition frequencies ${{ f}_{{\rm rep}}}$ are seeding two pulse-picking Yb fiber amplifiers, reducing the repetition rates of the oscillator pulse trains by a factor of eight and supplying Watt-level average powers at ${\sim}{10}\;{\rm MHz}$ repetition rates. These two high-power near-infrared laser frequency combs are frequency upconverted via third harmonic generation in nonlinear crystals. Subsequently, the UV light is spectrally broadened in a solid core silica fiber. After spatial superposition, fast photodetectors (FPD) record the time-domain interferograms of the sample (S) and the reference (R) path. (b) Measured frequency upconverted laser spectra centered at ${{ f}_c} = {871.2}\;{\rm THz}$ with a FWHM of 2.6 THz and 3.1 THz. (c) Schematic representation of a dual comb spectrum after fast Fourier transformation (FFT). Computing the FFT of the low-pass-filtered (LPF) interferograms yields the downconverted optical transmission spectrum in the radio frequency (RF) domain. We calculate the downconversion factor $m$ by dividing the repetition rate ${{ f}_{\rm rep,II}}$ by the detuning of the two frequency combs $\delta$, which is used to convert the spectral information back to the ultraviolet region.

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In this work, we perform fast and broadband UV DCS of formaldehyde (HCHO). HCHO plays a primary role in tropospheric chemistry and is the most abundant and most important organic carbonyl compound in the earth’s atmosphere [31]. Due to its high environmental relevance and multifaceted absorption characteristics, HCHO has been studied spectroscopically for decades under different experimental conditions aiming either at a high spectral resolution, broad spectral coverage, or high sensitivity [3–5,9,32–34]. We demonstrate the coalition of those important spectroscopic criteria with single-trace DCS in the UV, i.e., one interferogram only. Averaging multiple DCS traces enables a higher signal-to-noise-ratio (SNR). As a result of averaging, longer apodization windows are possible, achieving an improved spectral resolution but with the same SNR when compared to the single-trace spectra. Finally, we exploit the strong UV absorption cross section enabling single-trace acquisition for real-time UV DCS realizing ad-hoc monitoring of the HCHO concentration in our sample cell.

2. METHODS

A. Experimental Scheme

Figure 1(a) illustrates the experimental setup, employing two ytterbium-based frequency comb oscillators. Their outputs are centered at a wavelength of 1030 nm, and their repetition rates are stabilized to ${{ f}_{\rm rep,I}} = {80}\;{\rm MHz}$ and ${{ f}_{\rm rep,II}} = {80}\;{\rm MHz} + {6}\;{\rm Hz}$. After amplifying the average power in a pulse-picking fiber amplifier and reducing the repetition rates by a factor of eight, we generate the third harmonic of the amplified frequency combs by a collinear, two-step nonlinear upconversion process (see Appendix A). Figure 1(b) shows the resulting Gaussian-shaped UV spectra centered at ${{ f}_c} = {871.2}\;{\rm THz}$ (344 nm wavelength) with a full width at half maximum (FWHM) of 2.6 THz and 3.1 THz. Then, we inject the UV beams into a 10-cm-long solid-core silica fiber for spectral broadening.

For dual comb experiments, the two spectrally broadened output beams are superimposed using a 50:50 beam combiner. The two frequency combs with detuned repetition rates correspond to two pulse trains with a sweeping delay between consecutive pulses. This optical delay is analogous to the varying pathlength difference in Fourier-transform spectroscopy using a scanning-mirror interferometer, resulting in a downconverted heterodyne signal. The obtained time-domain interferogram has its largest value at zero delay between the two pulses due to maximum constructive interference. After the fast Fourier transformation (FFT) of the interferogram, we obtain a spectrum in the radio frequency domain at ${ f}_c^{{\rm RF}}$, which can be converted back to the ultraviolet region by multiplying it with the downconversion factor ${m} = {{ f}_{\rm rep,II}}/\delta$, with $\delta$ being the repetition rate detuning [see Fig. 1(c)].

After the combiner, one output is sent through a multi-pass sample cell yielding an interaction path length of 2.3 m and focused onto a fast photodetector. The second beam exiting the combiner is focused directly onto a second fast photodiode for referencing. We record both dual comb interferograms simultaneously (see Supplement 1).

B. Nonlinear Spectral Broadening in the UV Region

To extend the spectral coverage, we employ nonlinear spectral broadening via self-phase modulation in a silica fiber. Figure 2(a) shows the spectral evolution of the 168-fs-long UV input pulses simulated by solving the generalized nonlinear Schrödinger equation to find the optimum fiber length [35]. We determine a 10-cm-long fiber to yield maximum spectral coverage while keeping the pulse short. Using this fiber length, we characterize the gain in spectral bandwidth by measuring the output spectrum with a grating spectrometer at different input pulse energies [see Fig. 2(b)] and observe symmetric broadening of the input spectrum in excellent agreement with the simulation. The maximum bandwidth is achieved for an input pulse energy of 3.5 nJ. Higher output powers are advantageous as we are mainly limited by detector noise (see Supplement 1). However, at higher input pulse energies non-reversible photodarkening of the fiber occurs [36]. The spectral bandwidth at the 6.5 µW/THz level agrees with the simulation and scales logarithmically with input pulse energy [see inset Fig. 2(b)]. We achieve a maximum bandwidth of $\Delta {\rm f} = {50.3}\;{\rm THz}$ and a spectral broadening factor of 12.5, surpassing previous results in the UV by a factor of two [37,38]. For UV DCS absorption experiments, we use an input pulse energy of 1.7 nJ, resulting in a spectral coverage of 35.7 THz, which extends over three full vibronic absorption bands of formaldehyde centered at 861 THz, 874 THz, and 885 THz [see Fig. 2(b)].

 

Fig. 2. Direct spectral broadening in the ultraviolet region using a silica fiber. (a) Calculated propagation-distance-dependent gain in spectral coverage [35]. Red dotted line: fiber length of 10 cm leading to maximum bandwidth and minimal deterioration of the temporal pulse shape. (b) Bottom: output spectra of a 10-cm-long fiber at different pulse energies of the UV seed laser. Dotted lines: simulated (Sim.) output spectra using the same pulse energies as input parameters. Black solid line: input spectrum measured directly in front of the fiber. Inset: the spectral bandwidth of measurement and simulation are in excellent agreement and scale logarithmically with the input pulse energy. The bandwidth is defined at the 6.5 µW/THz level, which corresponds to the noise equivalent power of the fast photodetectors (NEP FPD, black dashed line; see Supplement 1). The maximum spectral coverage of 50.3 THz was achieved for 3.5 nJ input pulse energy, accomplishing a broadening factor of 12.5. Top: absorption cross section of formaldehyde [1]. The broadened spectrum fully covers the absorption bands centered at 861 THz, 874 THz, and 885 THz, respectively, i.e., the ${4}_0^2$, ${4}_0^3$, and ${2}_0^1{4_{0}^{1}}$ vibronic branches of the electronic transition $\tilde{A^1}A_{2}-\tilde{X^1}A_{2}$.

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3. RESULTS

A. Dual Comb Interferometry in the Near-UV Spectral Region

The resulting interferogram is recorded by an oscilloscope and depicted in Fig. 3(a). Figure 3(b) shows a close-up view of the centerburst, which reveals oscillations arising from the interference of the two detuned pulse trains. After the FFT of the 100-µs-long interferogram, we obtain the downconverted laser spectrum in the radio frequency domain [see Fig. 3(c)].

 

Fig. 3. Dual comb signals generated from two interfering UV frequency combs. (a) Time-domain interferogram generated by two UV frequency combs and recorded with a fast oscilloscope. (b) Close-up view of the interferometric centerburst with characteristic oscillations arising from the interference of the detuned pulse trains. Red: 3-µs-long super-Gaussian apodization time window. (c) Downconverted laser spectrum, centered at ${ f}_c^{{\rm RF}} = {2.8}\;{\rm MHz}$, obtained after the fast Fourier transform (FFT) of the 100-µs-long time trace. The spectrum covers ${{\Delta f}^{{\rm RF}}}= {1}{\rm .28\;MHz}$ (FWHM) in the radio frequency domain. (d) Spectrogram generated by calculating the short-time fast Fourier transformation (STFFT) for different apodization time window positions displayed with linear colorscale. For window position $|\tau |\; \gt \;{2}\;\unicode{x00B5}{\rm s}$, temporal wings are observed, which form an elliptic pattern around the center part (indicated by black dashed line).

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We perform a sliding-window analysis of the centerburst to characterize the time dependency of our dual comb spectrum [see Fig. 3(d)]. For each window position, the interferogram trace is apodized using a 3-µs-long super-Gaussian time window with subsequent FFT. The intense part of the spectrum up to the ${{1/e}^2}$ value is contained in a 4-µs-long time interval centered around zero delay. For window positions $\tau \; \lt \;{2}\;\unicode{x00B5}{\rm s}$, we observe a temporal wing, which emanates from the uncompensated chirp after spectral broadening via self-phase modulation in the fiber (see Supplement 1). For DCS, we adjust the average power in front of each fiber to compensate for the different transmissions through the individual optical paths, yielding a balanced signal strength after the beam combiner. This asymmetric fiber input configuration results in a tilted spectrogram with unequal intensity distribution of the temporal wings (see Supplement 1), not affecting the data analysis as the contributions are identical for both sample and reference paths.

B. Ultraviolet Dual Comb Spectroscopy of Formaldehyde

Figure 4(a) compares the UV-DCS recorded absorbance spectrum of HCHO to values reported by Bass et al. [1]. The absorbance spectrum exhibits congested absorption characteristics with several vibronic excitation bands featuring rotational substructure superimposed to the electronic transition driven by the UV photons [see Fig. 2(b) top] [1,39]. Within only 1620 µs apodization time (corresponding to six single traces of 270 µs duration each; see Supplement 1) we achieve 50 GHz spectral resolution, i.e., a resolving power of ${1}{{\rm .8 \times 10}^{4}}$, across the entire 35.7 THz bandwidth covering three vibronic branches of the molecule. The measurement unveils a plethora of narrow lines arising from rotational states allowing to assign the full set of quantum numbers to the rovibronic transition as exemplified for six prominent resonances in Fig. 4(a) [40].

 

Fig. 4. Fast and broadband UV DCS resolving rotational energy levels of formaldehyde. (a) UV absorbance spectrum of formaldehyde measured by DCS (blue) and by Bass et al. (black) [1], both clearly revealing the rotational substructure of the energy levels. The dual comb trace was obtained by averaging six traces resulting in a total apodization time of 1620 µs (total acquisition time of 8 s). The high resolution allows the assignment of all relevant quantum numbers to the absorption peaks implying characterization of the complex trinity of rovibronic energy states [40,41]. These three types of transitions induce a non-planar orientation (electronic excitation) of the formaldehyde molecule together with a superposed vibrational and rotational motion [39]. (b) Single-trace absorbance spectrum measured with DCS (blue) and a grating spectrometer (GS, orange), both achieved with the same acquisition time window of 100 µs. The DCS curve yields more than a factor of four higher spectral resolution, featuring single-trace sampling of electronic fingerprints resolving rotational states, e.g., the absorption peak at 874 THz. (c) Real-time DCS series during evacuation of the sample cell pre-filled with formaldehyde as an application of real-time gas concentration monitoring. Lineout: expected absorbance (red dots) at 874 THz together with the value of the DCS peak absorbance (blue dots). After 50 s and 152 s the valve to the reservoir is opened intentionally to introduce abrupt changes in the sample concentration. This is observed in the dual comb signal, demonstrating the instant response of our UV DCS monitor.

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Figure 4(b) corroborates the resolving power of our UV-DCS concept even further. For single-trace dual comb spectroscopy the measurement time can be faster than the inverse of the repetition rate detuning (here, 1.3 s; see Supplement 1), which defines the duration between consecutive interferograms. Here, we record one single trace in 100 µs achieving 134 GHz spectral resolution (see Supplement 1). This reduced acquisition time window is sufficient to resolve the rotational absorption peaks, e.g., at 874 THz corresponding to the rotational level with $K^{\prime\prime}=3$ and $J^{\prime\prime}=15$ in the ${4}_0^3$ vibronic band of the $\tilde {A^{1}} {A_{2}}{\text-}\tilde {X^{1}}A_{2}$ system (see Supplement 1 Table 1), thus demonstrating fast acquisition and high spectral resolution simultaneously. In comparison, this rotational substructure cannot be identified using a state-of-the-art grating spectrometer recording with 640 GHz resolution under identical experimental conditions (blue and orange lines, respectively).

C. Real-Time Monitoring of Gas Concentration Changes

To demonstrate the potential of UV-DCS for rapid-update environmental monitoring, we monitor the pressure variation in the gas sample cell [see Figs. 4(c) and S5]. While acquiring dual comb interferograms consecutively as they re-occur after 1.3 s, we track the pressure of formaldehyde to compute the expected absorbance change. The absorbance at 874 THz precisely follows the calculated reference points, with a single-trace noise equivalent absorption of ${\rm NEA} = \;{5{ .9 \times 10}^{- {4}}}{{\rm \;cm}^{- 1}}{{\rm \;Hz}^{- 1}}$ (pressure 0.21 mbar; see Supplement 1). A standard computer derives the absorbance spectrum from the interferograms in less than 200 ms, rendering the update rate fully applicable for real-world applications, e.g., the formaldehyde emission monitoring in the wood and textile industry where, typically, HCHO concentration levels up to 4000 ppm, i.e., partial pressure of 4 mbar at atmospheric conditions, accumulate [42,43]. The temporal resolution of UV DCS can be dramatically improved to the femtosecond scale by the implementation of pump-probe schemes [44,45]. Since UV DCS is capable of rapid fingerprinting the electronic energy structure, online monitoring of ultrafast complex reaction pathways on the femtosecond scale comes into reach.

4. DISCUSSION

For quantitative comparison, we define the parameter $M_{\rm T}=\Delta f/(\delta f \cdot \sqrt {T})$ with the bandwidth $\Delta { f}$, the spectral resolution $\delta {f}$, and the acquisition time ${T}$, in analogy to the work by Newbury et al. [46]. The quality factor ${\rm QF=SNR}\cdot M_{\rm T}$, with SNR being the signal-to-noise ratio in the frequency domain (see Supplement 1), is determined to a value of ${5}{{\rm .9 \times 10}^{3}}\sqrt {{\rm Hz}}$ for the averaged case. Thereby, we achieve a QF about three times higher than another recent UV dual comb system employing photon counting [47]. Notably, the work by Xu et al. successfully targets at high spectral resolution while the experiments presented here focus on a broader spectral coverage. Hence, a fair comparison remains difficult due to the different parameter space of the two demonstrations (see Supplement 1).

Future developments aim at increasing the repetition rate, which will allow faster gas monitoring by using higher detuning values. Consequently, the waiting time will be reduced when using apodization windows shorter than the re-occurrence time (see Supplement 1). Limitations to the repetition rate in our setup arise due to the influence on the nonlinear processes, especially the conversion efficiency of frequency upconversion and spectral broadening. A higher repetition rate results in lower pulse energies and with that in a decreased conversion efficiency. For experiments in the NUV, this can be compensated for by higher average powers of the fundamental radiation. Further development of the spectral broadening scheme will be required with increased repetition rates. Another possibility to eliminate waiting time is to periodically invert the detuning frequency of the two combs. For this approach, no adjustment of the broadening scheme would be necessary [48]. In order to investigate formaldehyde at urban abundances, the sensitivity has to be increased. This can be achieved, for example, by combining UV DCS with enhancement cavities [7,49].

In conclusion, this work constitutes the first demonstration of DCS in the ultraviolet spectral region utilized for broadband real-time monitoring of formaldehyde. Our system features an unprecedented combination of short acquisition time windows on the µs timescale together with GHz spectral resolution over tens of THz spectral bandwidth in the near-UV and expands the application possibilities of DCS dramatically. Since all molecular species absorb strongly in the UV, our approach can be expanded to analyze other samples, including ${{\rm NO}_2}$ and ${{\rm O}_3}$.

We observe the trinity of electronic, vibrational, and rotational transitions in the complex absorption spectrum of formaldehyde revealing rotational state resolution while covering a full spectral bandwidth of 35.7 THz. The demonstration of real-time monitoring of the HCHO concentration forms the basis to investigate reaction pathways and rates in trace gas mixtures. The chosen example of HCHO plays an important part in the interrelated chemistries of ozone and the ${{\rm HO}_x}$ and ${{\rm NO}_x}$ cycles and highlights that UV-DCS will enable detailed insights into the photochemistry of our troposphere [31].