1. Introduction

Ultrabroadband fs-laser (5–20 fs) pulses provide a spectral bandwidth of 800–3000 cm⁻¹. Therefore, they are an excellent light source for spectroscopic applications. For example, the large bandwidth may be used to simultaneously excite multiple species in coherent anti-Stokes Raman spectroscopy (CARS). The typically required higher spectroscopic resolution for CARS may be obtained by pulse shaping techniques with spatial light modulators (SLMs) [1], or by a separate narrowband probe pulse.

For samples in the solid or liquid phase, the pulse energy of fs oscillators (∼nJ) is usually sufficient [1]. For gaseous samples, however, pulse energies of a few µJ are required [2,3]. Although gas-filled hollow-core fibers have been used for ∼20 years to generate ultrabroadband fs-pulses at µJ or mJ level [4], these pulses exhibit some limitations. The self-phase modulation (SPM), which is induced by the pulse propagation through the fiber, leads to a complex shape of the spectral intensity and phase [5]. Moreover, the spectral intensity shows considerable fluctuations on a shot-to-shot timescale, making the actual excitation efficiency hardly predictable [5]. Therefore, it is questionable if the Raman excitation induced by these pulses is reliable for all Raman shifts under investigation. Nevertheless, previous studies investigated the use of ultrabroadband pulses for CARS-based gas analysis in combustion, as this technique combines two essential features: (i) the CARS signal is independent from molecular collisions, when the Raman excitation is probed within a few picoseconds [6,7], and (ii) multiple gas species may be detected in a single spectrum.

In this regard, Roy et al., applied hollow-waveguide-based ultrabroadband single-beam CARS to detect N₂ [3] and CO₂ [8]. The probe pulse was generated by shaping a small part of the pump/Stokes pulse. However, the damage threshold of the shaping device limited these investigations to qualitative results. Furthermore, Bohlin et al., suggested a two-beam approach, using a sub-10 fs excitation pulse and a ∼90 ps probe pulse in a quasi-collinear configuration [9,10]. With this technique, the combustion relevant species CH₄, CO₂, H₂, and N₂ were detected [11]. For quantitative results, the authors suggest acquiring the resonant CARS signal and the nonresonant signal at the same time. In narrowband CARS, the nonresonant and resonant signals were recorded simultaneously and the nonresonant signal was used to normalize the resonant one for quantitative measurements [12]. The pulse-to-pulse temporal and spatial variations of the laser fields were corrected, but the authors argued that broadband implementations were not feasible due to the signal loss accompanying the polarization analysis. Nevertheless, Bohlin et al., measured mole fraction ratios in a methane/air flame at atmospheric pressure using ultrabroadband pulses and the nonresonant signal in argon as a reference measurement [13]. In a flame, however, controlled and reproducible conditions for the species concentration are difficult to achieve.

Therefore, this study aims at comparing concentration measurements in ternary gas mixtures with and without spectral referencing in pure argon. For this purpose, an oven with control on the temperature and gas concentration is used [14]. We implement high-pressure (up to 10 bar) quantitative concentration measurements based on two-beam ultrabroadband vibrational femtosecond/picosecond CARS (two-beam fs/ps CARS) in ternary gas mixtures for molecules with Raman shifts up to ∼3000 cm⁻¹ at room temperature. The ∼7 fs pump/Stokes pulses show high spectral stability on a shot-to-shot basis (rms spectral fluctuations ≤ 1.6%). The ∼2 ps probe does not only provide sufficient spectral resolution for the relevant vibrational lines but also provides a temporal window for which species-specific dephasing or molecular collisions can be neglected. These effects may dominate the high-pressure applications at larger delays. The excitation efficiencies are determined from nonresonant signal measured in pure argon for each elevated pressure. The high-pressure concentration measurements are investigated in detail and the quantified results with and without consideration of the excitation efficiency are compared.

2. Ultrabroadband two-beam fs/ps CARS

2.1 Experimental setup and theoretical simulation modelling

The experimental setup of the two-beam fs/ps CARS setup (Fig. 1) is described in detail elsewhere [15]. Briefly, a dual-output 200 kHz, optical parametric chirped pulse amplification system (venteon OPCPA, Laser Quantum GmbH, Konstanz, Germany) provides a ∼7 fs (E_pulse ∼11 µJ, 650-1100 nm) pulse, acting as both pump and Stokes beam and a ∼2 ps (E_pulse ∼ 0.9 µJ, 516 nm) pulse acting as probe. Within the OPCPA, the seed pulses are amplified in two BBO-based non-collinear parametric amplification (NOPA) stages.

 

Fig. 1. Sketch of two-beam CARS. DCM: double-chirped mirrors; LPDM: long pass dichroic mirror; BS: beam splitter; CM: concave mirror (f = 500 mm); CL: collimating lens; BD: beam dump; SPF: short pass filter (cutoff wavelength = 500 nm); FL: focusing lens (f = 150 mm). The spectrometer is equipped with a 1200 line/mm grating. The acquisition time of the CCD camera is 50 ms; 20 acquisitions are accumulated.

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In this study, the temporal overlap between the seed and the pump pulse is moderately varied in the 1^st NOPA stage in order to arbitrarily tune the output spectrum of the pump/Stokes pulse. In this way, the day-to-day realignment of the OPCPA system is simulated. The pump/Stokes and probe beams are spatially overlapped by a long pass dichroic mirror and focused into a gas oven [14], using a concave f = 500 mm mirror. The duration of the pump/Stokes pulse at the focus is ∼10 fs, measured with an interferometer-based autocorrelator (Femtometer, Newport Corporation, Irvine, USA) under similar conditions as within the oven, e.g. with a sapphire optical window installed in the beam path. The temporal delay between the pump/Stokes and the probe pulse is adjusted using a motorized translation stage in steps of 100 fs. The zero delay is defined when the integrated nonresonant signal has the maximum level. All pulses have the same linear polarization.

In the following, we will show how the nonresonant signal measured in pure argon is used to get information about the Raman excitation efficiency for the molecules under investigation. The nonresonant polarization may be expressed as [16]

 

Fig. 2. Scheme for the determination of the excitation efficiency for a particular Raman shift. E_p, E_St, E_pr are the electric fields of the pump, Stokes and probe pulse, respectively. ω_R is the angular frequency at the spectral position of the Raman shift of the molecule. Ω and ω₁ are the integration variables according to Eq. (1).

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2.2 Shot-to-shot pump/Stokes spectrum stability

As discussed in the introduction, considerable fluctuations of the pump/Stokes spectrum may occur. This would significantly affect the feasibility of the current study, which determines the nonresonant and resonant signal from independent measurements. Therefore, we investigated the pump/Stokes spectrum in further detail. The typical pump/Stokes spectrum (Fig. 3(a)) was measured with a compact grating spectrometer (AvaSpec-ULSi3648, AVANTES, Netherlands) with integration time of 32 ms. In order to observe the shot-to-shot stability of the pump/Stokes spectrum, the pump/Stokes beam was focused into a spectrograph (Acton SP2300i, Roper Industries Inc., Saratosa, USA) equipped with a 300 line/mm grating and recorded using a triggered streak camera (OptoScope SC-10 system, Optronis, Kehl, German). A tunable ps-laser system (Ekspla PL2231 with PG401, Ekspla, Vilnius, Lithuania) was used to calibrate the wavelength scale in the range from 740 nm to 860 nm. Figure 3(b) shows 50 normalized single-shot pump/Stokes spectra. The blue line shows the averaged spectrum from the 50 single-shot measurements, and the grey shadow shows the standard deviation at each wavelength. The remaining part of the pump/Stokes spectrum shows a similar behavior, but lies out of the spectral window of a single measurement and is therefore not shown in Fig. 3(b). The measured shot-to-shot rms spectral fluctuations were ≤1.6%, which are considerably lower than the fluctuations determined for hollow-core fibers (7.8% for linearly polarized light [18]).

 

Fig. 3. (a) Typical pump/Stokes spectrum integrated over 32 ms. The blue shadow part indicates the spectral region where Fig. 3(b) is recorded in a separate measurement. (b) Averaged 50 single-shot pump/Stokes spectra centered at 800 nm. The grey shadow shows the standard deviation of the 50 single-shot spectra. The spectra are normalized to their maximum values in the measured spectral range.

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3. Results and discussion

Figure 4(a) shows the CARS signals (37.5% CO₂, 50.0% N₂, 12.5% CH₄) and the nonresonant responses measured in pure argon at 1.7 bar for two measurements (M1, M2) with different spectra of the pump/Stokes pulse. For comparable signal strength, the nonresonant responses and the CARS signals are all normalized at the Raman shift of N₂ (Δν_R ∼ 2330 cm⁻¹). At the Raman shift of CH₄ (Δν_R ∼ 2917 cm⁻¹), the nonresonant signal of M2 is larger than that of M1. Correspondingly, the CH₄ CARS signal from M2 shows a ∼ 2 times higher intensity than that of M1. Similar ratios between M1 and M2 are observed at the Raman shifts of CO₂ (Fermi dyads at Δν_R ∼ 1388 cm⁻¹ and Δν_R ∼ 1285 cm⁻¹). Thus, clear correspondence between the nonresonant signal and the CARS signal is displayed in Fig. 4(a).

 

Fig. 4. (a) The CARS signals in a gas mixture of 37.5% CO₂, 50% N₂, and 12.5% CH₄ at ∼2.2 ps delay together with the nonresonant responses measured in pure argon at zero delay at 1.7 bar and room temperature. NR: nonresonant response; M1: measurement 1; M2: measurement 2. (b) Concentration measurements with and without considering the nonresonant response (NR) for measurement 1 (M1) and measurement 2 (M2) for two different pump/Stokes spectra at 1.7 bar and room temperature. The bars show the averaged results from 5 CARS spectra at probe pulse delays of 1-3 ps. Error bars show the standard deviations. Black lines indicate the concentrations expected from the settings of the mass flow controllers.

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The gas concentrations determined for CO₂, CH₄ and N₂ are shown in Fig. 4(b). The determinations are implemented from CARS spectra at probe delays of 1-3 ps. For these probe pulse delays, the CARS signal evolution does not depend on the gas mixture or pressure up to 50 bar [7]. In this regard, the influence from the species-specific dephasing rates can be neglected. The orange bars show results without considering the nonresonant response, while the green bars show results after the excitation efficiencies are determined from the nonresonant response. As displayed in Fig. 4(b), for measurement M1, referencing the excitation efficiency from the nonresonant response is essentially necessary. One may notice, however, that the concentrations for CO₂ and N₂ in M2 are quite similar to the values without considering the nonresonant response. This is because the nonresonant responses of M2 at ∼1388 cm⁻¹ and 2330 cm⁻¹ have already comparable intensities (Fig. 4(a)). Therefore, spectral referencing may not be necessary when the Raman shifts under investigation are not too large and the excitation efficiency may be adjusted to a smooth profile. In this regard, we have recently demonstrated concentration measurements for molecules with Raman shifts up to 2330 cm⁻¹ (N₂) without spectral referencing [15]. In view of our own experience as well as ultrabroadband spectra from both OPCPAs [19] and Ti:Sa based laser systems [5], it seems unlikely that a sufficiently smooth profile for large Raman shifts such as for H₂ (∼4161 cm⁻¹) can be achieved. For processes with unknown species or molecules with Raman shifts $ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} $2330 cm⁻¹, spectral referencing is presumably necessary for accurate concentration measurements based on our current setup.

Concentration measurements under higher pressures are further explored. Figure 5(a) shows one example of the referenced nonresonant responses in pure argon at 1.7 bar, 5 bar and 10 bar. From the peak centered around 2180 cm⁻¹, spectral broadening is observed as the pressure is increasing, indicating that the pump/Stokes pulse is presumably subject to SPM [20]. Based on the measured nonresonant responses in pure argon at 5 bar and 10 bar, the results of concentration measurements in a gas mixture of 37.5% CO₂, 50% N₂, and 12.5% CH₄ are shown in Fig. 5(b). Overall, the deviations from the concentration settings of the mass flow controllers are still small compared to measurements without taking the nonresonant response into account (Fig. 4(b)). This is particularly the case for CH₄, which has the highest Raman shift. The same seems to hold for N₂ with a slight increase from 5 to 10 bar, but in the opposite direction. For CO₂, however, there is a clear decrease of the accuracy from 5 to 10 bar. This may be explained by the observation that the change of the nonresonant response from 1.7 bar to 10 bar at the Raman shift of CO₂ (∼1388 cm⁻¹) is more pronounced compared to the one of CH₄ or N₂ (Fig. 5(a)). Therefore, the error which is caused by changing the gas from argon to the actual composition (CH₄, CO₂, N₂) may be larger for CO₂ than for the other gas species.

 

Fig. 5. (a) The nonresonant responses in argon at zero delay measured at 1.7 bar, 5 bar, and 10 bar at room temperature. The grey dotted lines indicate the positions of the Raman shifts for CH₄, N₂ and the peak at 1388 cm⁻¹ of the Fermi dyad of CO₂. (b) Concentration measurements at 5 bar and 10 bar in a gas mixture of 37.5% CO₂, 50% N₂, and 12.5% CH₄. The bars show the averaged results from 5 CARS spectra at 1-3 ps delay. Error bars show the standard deviations. Black lines indicate the concentrations expected from the settings of the mass flow controllers.

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A possible solution is to use the same or at least similar gas concentrations for the acquisition of the nonresonant signal. Ideally, the acquisition of the nonresonant signal should be obtained simultaneously with the CARS signal from the same gas composition. By combining proper-oriented polarizers and analyzers, the nonresonant signal may be split from the resonant CARS signal [12]. This technique may experience considerable loss of the measured CARS or nonresonant signal intensity [12,21]. Moreover, it is still questionable if the two paths of the CARS signal and the nonresonant signal experience the same alignment into the detection devices. This will be the focus for our future work. Besides, the standard deviations (error bars in Fig. 4(b) and Fig. 5(b)) of subsequent measurements at different probe pulse delays are small throughout this study. We attribute this behavior to the high stability of the pump/Stokes spectrum generated by the OPCPA (Fig. 3(b)).

4. Conclusion

In summary, we have quantified the excitation efficiency correction required for two-beam ultrabroadband fs/ps CARS by comparing concentration measurements with and without spectral referencing from the nonresonant spectrum recorded in pure argon. The high spectral stability of the ultrabroadband pump/Stokes pulse allows for this separate spectral referencing. In this regard, our two-beam ultrabroadband CARS system provides the potential of simultaneous concentration and temperature measurements for the most relevant gasification or combustion species for high-pressure applications up to 10 bar. For higher pressures, either the different amount of SPM generated by the different gas species may come into play, or simultaneous measurements of the resonant and nonresonant signal may be more suitable.