1. Introduction

Coherent anti-Stokes Raman scattering (CARS) is a powerful gas-phase diagnostic tool for probing of flames, high-speed flows, and plasmas. Typical CARS instruments for gas-phase diagnostics utilize Nd:YAG and dye laser systems with nanosecond-scale pulse durations and repetition rates on the order of 10 Hz [1]. These workhorse systems provide reliable thermometry, species, and pressure measurements [2–4]. Nevertheless, the 10-Hz repetition rate of nanosecond pulsed lasers does not permit time-resolved measurements in turbulent flows; measurements are impacted by uncertainty in nonresonant background and collision-broadened linewidths; and the broadband dye lasers employed as Stokes sources for single-shot data are plagued by chaotic mode noise and phase fluctuations [5], which ultimately limits the precision of the measured thermochemical parameters.

Femtosecond-class laser systems are enabling new developments that overcome the above limitations in CARS of gas-phase systems. Commercial Ti:Sapphire amplifiers operate in the 1-10 kHz range, where the energy containing scales of many turbulent flows reside. Improved measurement precision is possible because near-transform-limited broadband femtosecond pulses exhibit minimal spectral-amplitude and spectral-phase noise, and are a superior alternative to chaotic broadband dye sources [6, 7]. This low-noise pump/Stokes preparation of the Raman coherence, when combined with the introduction of a time-delayed probe beam, permits effective time-gated elimination of nuisance nonresonant background signals. Probe delays as short as a few ps allow for collision-free measurements at modest pressures [1, 8]. At higher pressures, linewidth data can be obtained in situ by direct observation of the ps-scale decay of the Raman-resonant polarization [9, 10]. Practical combustion thermometry using femtosecond CARS of vibrational Raman resonances in N₂ has been demonstrated using both bandwidth-limited [11] and broadband temporally chirped [12, 13] ps probes with single-laser-shot precision as good as 1% in some cases [7].

When femtosecond pump and Stokes preparation is used, pure-rotational CARS (R-CARS) offers several distinct advantages to vibrational CARS (V-CARS) for gas-phase measurements. R-CARS is well-known to offer more precise thermometry at temperatures up to 1200 K, and the longer decay time of rotational Raman polarizations (~100 ps at 1 atm) makes time-gated suppression of nonresonant background more practical. R-CARS is also a more straightforward approach than V-CARS for simultaneous temperature and multiple-species detection in the femtosecond regime because most species of interest have rotational Raman frequencies on the order of a few hundred cm⁻¹, which is well within the bandwidth of lasers with 50-100 fs pulses. Vibrational resonances for different species are often separated by 1000 cm⁻¹ or more, rendering singe-shot multi-species detection using a single fs pump/Stokes combination less practical. These advantages have motivated several recent studies of R-CARS utilizing femtosecond pump/Stokes excitation with time-delayed bandwidth-limited ps probing [8, 9, 11, 14, 15]. These “hybrid” fs/ps R-CARS approaches have been demonstrated in pure N₂ and O₂ as a quantitative temperature diagnostic at both atmospheric and elevated pressures [8, 14, 15], and for time-domain detection of self-broadened rotational linewidths [9]. Recent reports [16, 17] of fs/ps R-CARS spectra in air are the first measurements with the technique in a gas mixture; qualitative changes in the spectra with temperature and the relative change in measured O₂/N₂ ratio with pressure were examined. In each of these hybrid R-CARS experiments, temporal locking of the preparation and probe pulses was achieved by using a single fs laser to provide all three pulses, and subsequently removing bandwidth from the probe using either a 4f pulse shaper [9, 18] or a Fabry-Perot etalon [15, 18]. These bandwidth-carving approaches to ps probe-beam generation limit the available probe-beam energy and, ultimately the R-CARS signal strength. Recent work in our laboratory [19] has focused on high-energy ps probe beams using sum-frequency generation of second-harmonic pulses from temporally chirped 800-nm beams. This new approach to probe-beam generation has extended hybrid R-CARS to flame temperatures, where temperature and quantitative O₂/N₂ measurements have been extracted from the high-temperature CARS spectra.

In this work, we perform a practical assessment of the diagnostic utility of an etalon-based hybrid fs/ps R-CARS setup of the type used in [15], where the accuracy and precision of temperature and O₂/N₂ concentration measurements is systematically evaluated for temperatures from 290 to 800 K. The primary focus of the study is thermometry, although an assessment of O₂/N₂ ratio measurement in air over the full range of temperatures is also made. Two different etalon-generated probe beams are utilized: (1) a frequency-narrow (2.11 cm⁻¹ FWHM) 7-ps-duration probe that permits resolution of individual rotational line structure in many cases; and (2) a second probe with 1.5-ps duration (5.3-cm⁻¹ FWHM) that allows us to investigate the feasibility of measurements at coarser spectral resolution and a 3 × increase in probe-beam energy.

2. Experiment hardware and setup

The layout of our hybrid fs/ps rotational CARS system is shown in Fig. 1. A “single-box” Ti:Sapphire amplifier (Spectra Physics Solstice) provided 3.1-mJ, 100-fs duration pulses at 1-kHz repetition rate. The amplifier output spectrum was centered near 800 nm, with a bandwidth of 180 cm⁻¹ FWHM. The 800-nm beam was split into three parts to form pump, Stokes and probe beams. A half-waveplate and polarizer combination was used to limit thepump and Stokes beam energies to 40 and 53 μJ/pulse, respectively, in order to minimize the impact of stimulated Raman pumping [20], semi-permanent molecular alignment, and laser-induced ionization [21] associated with high preparation pulse energies. Picosecond-duration, frequency-narrow probe pulses were generated by inserting Fabry-Perot etalons into the probe-beam path, as first demonstrated for sum-frequency generation spectroscopy [22], and more recently applied to hybrid fs/ps CARS [15, 18]. The available energy in the probe beam line was limited to 500 μJ/pulse by using a fixed-ratio beam splitter to minimize the risk of optical damage to the etalons. A spectrally narrow 7-ps duration probe was obtained using two etalons with free-spectral ranges (FRS) of 455 and 13 cm⁻¹ in succession, while a coarser, 1.5-ps probe could be generated using the 455 cm⁻¹ FSR etalon only. Probe-beam energies were 4 μJ/pulse for the double-etalon setup, and 12 μJ/pulse for the single-etalon arrangement. Each of the three lasers beams was routed to a time-of-flight delay line and then relayed to a 500-mm focal length beam-crossing lens in a carefully phase-matched folded BOXCARS [23] geometry. Spatial isolation of the resulting CARS signal from the nearly frequency degenerate background laser radiation was obtained by careful alignment of apertures in the CARS collection optics path and by a tight 50-μm entrance slit on the 0.32-m imaging spectrometer used to detect the CARS signal with ~1 cm⁻¹ instrument resolution. An electron-multiplying CCD camera (Andor Newton) was directly mated to the spectrometer to provide shot-averaged and single-shot detection at rates up to 250 Hz in our demonstration experiments.

 

Fig. 1 Essential elements of the fs/ps rotational CARS experiment.

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Time-domain characterization of the probe pulse intensity profile was obtained by mechanically scanning the probe-beam delay through the ~100-fs nonresonant polarization induced by the pump and Stokes pulses in argon. Probe cross-correlation data are shown in Fig. 2 for both the single-etalon (black lines) and double-etalon (blue lines) configurations. The power spectra (squared magnitude) of the Fourier transform of the cross-correlation data are also shown to provide an estimate of the frequency content, assuming that the probe pulses are transform limited. In the single-etalon configuration, the probe pulse exhibits the expectedbehavior reported by Stauffer et al. [15], with a rapid ~300-fs rise from zero to maximum intensity followed by a nearly exponential decay with a ~1.5-ps time constant. The Fourier transform of the single-etalon cross-correlation data reveals a Lorentzian-like shape with 5.3 cm⁻¹ FWHM bandwidth. Insertion of the 13 cm⁻¹ FSR etalon further narrows the Fourier-transform bandwidth to ~2.1 cm⁻¹, but introduces a complex shape to the probe. The double-etalon probe pulse exhibits the same rapid rise as in the single-etalon setup, but consists of a train of pulses, all with a rapid sub-picosecond rise and a ~2.5-ps exponential decay, with the pulse maxima separated by roughly 2.5 ps. This pulse train is similar to the behavior described by Lagutchev et al. [22] for input pulses with coherence length less than the etalon gap. The resulting Fourier-transform spectrum reveals low-energy side lobes atop an otherwise Lorentzian lineshape.

 

Fig. 2 Probe-beam cross-correlation data (left) and Fourier transform spectra (right).

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3. Rotational CARS modeling

CARS spectra are calculated by adapting methods similar to those outlined in [8, 12]. We consider the electric fields of all laser beams and the resulting CARS signal in the time domain. For the probe time delays of interest here, we need only consider the Raman-resonant part of the signal because the nonresonant signal is negligible when the probe pulse is introduced at sufficient time delay for the pump and Stokes pulses to decay to zero. Our calculation assumes transform-limited pump and Stokes pulses with infinite bandwidth, so that all Raman transitions are pumped with equal efficiencies. The experimental spectra are normalized by a nonresonant CARS spectrum recorded in argon at zero probe delay to account for finite laser bandwidth and departure of the preparation pulses from transform-limited behavior. Under these conditions, the time-dependent Raman-resonant polarization is given by,

At the low, 290-800 K, temperatures investigated, we only consider rotational transitions in the ground vibrational level. Values of ${\gamma }_k^2$are referenced to N₂. Drake and Rosenblatt [26] tabulate values of ${\gamma }_{O_2}^2/{\gamma }_{N_2}^2$that range from 2.26 to 2.64. We have set ${\gamma }_{O_2}^2/{\gamma }_{N_2}^2$ = 2.370 in this work. This value was determined to achieve reasonable agreement between fitted O₂/N₂ concentration ratios and the known value of [O₂]/[N₂] = 0.2683 when fitting room-temperature R-CARS spectra obtained with the 7-ps probe.

With knowledge of the Raman-resonant polarization, χ, the CARS electric field at a probe-beam delay of τ is calculated in the time domain from,

The experimental spectra are background subtracted for stray light and normalized by nonresonant CARS spectra from argon. The resulting processed spectra are normalized to unit maximum and fitted using a nonlinear least-squares algorithm where the temperature and O₂/N₂ ratio are fitting parameters along with wavenumber axis shifting and stretching parameters and an intensity offset. The probe pulse delay is permitted to vary within a ± 0.5-ps window to account for uncertainty in the measured delay. Fitted probe delays exhibit standard deviations of 3.5% of the mean value for single-shot spectra across a wide range of temperatures when using the 1.5-ps probe at 3.4-ps nominal delay. Standard deviation in the fitted delay is 1.9% of the mean when using the 7-ps probe at 800 K and 2.8-ps nominal delay. Sensitivity of the fitted temperatures and O₂/N₂ ratio to these observed levels of probe delay uncertainty is determined to be less than 1%.

4. Results and discussion

4.1 Time-dependent behavior of air spectra at room temperature

A spectrogram constructed from hybrid fs/ps R-CARS spectra recorded with probe delays scanned from 0 to 20 ps in room-temperature air (292 K), and using the 1.5-ps duration probe, is shown in Fig. 3. Experimental data are the average of 100 laser shots at each probe delay, and are shown on the top of the Figure with the theoretical prediction shown below. For reference, the temporal evolution of the rotational coherence, χ(t) given by Eq. (1), is provided below the spectrograms. Only the imaginary part of Raman-resonant χ is plotted, as the real part is zero. The visual comparison between the measured and calculated spectrograms is excellent; the simple model of Eqs. (1)–(5) predicts the complex behavior of the rotational Raman transients in a quantitative manner. Introduction of a second gas into the mixture results in spectrograms which are less regular than those reported by Stauffer et al. [15] for pure N₂. The character of the spectrum exhibits distinct changes when the fast rising edge of the probe pulse crosses the recurrence peaks in χ(t), with peaks in the spectrum shifting their position and even disappearing at some probe delays. This behavior arises from the complex beating of the rotational polarization with the probe electric field, as well as interference between contributions from O₂ and ortho/para N₂ to the total rotational wavepacket.

 

Fig. 3 Room-temperature specta for air in the single-etalon probe configuration with a 1.5-ps/5.3-cm⁻¹ probe beam.

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The quantitative agreement of our model and room-temperature experiments is demonstrated by least-squares fits to the measured spectra at the three probe delays indicated by the vertical, dashed lines on the experimental spectrogram of Fig. 3. The fitted temperatures range from 285.5 K to 291.5 K, within 2.2% of the measured room temperature. Fitted O₂/N₂ ratios are within 3.5% of the expected value of 0.268 for air for probe delays of τ = 1.6 ps and 3.4 ps, with a 9% inaccuracy at τ = 4.2 ps, where a sudden and abrupt change in the spectrogram occurs as the probe rising edge is aligned with a recurrence peak, and the lowest quality fits were achieved. Increased sensitivity of the fitted spectra to probe delay may be expected when the probe is coincident with time-domain recurrence features. This sensitivity seems to impact the measured temperature and concentration, which may be an artifact of the multi-parameter fitting routine or small changes in relative beam path lengths resulting from environmental effects.

Similar room-air spectrograms for the 7-ps duration probe beam obtained in the double-etalon configuration are shown in Fig. 4. This high-resolution probe pulse provides better-resolved O₂ and N₂ contributions to the spectrum. The longer time duration of the higher spectral resolution probe results in the simultaneous probing of a greater number of recurrence features, but significant time-dependent changes to the spectrum are still observed. Fitted temperatures in air are within 2.3% of the monitored room value with O₂/N₂ ratios within less than 1% of the known air composition.

 

Fig. 4 Room-temperature specta for air in the double-etalon probe configuration with a 7-ps/2.1-cm⁻¹ probe beam.

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4.2 Furnace-heated air: shot-averaged spectra

CARS spectra were recorded for air in a tube furnace for temperatures from 292 K to 798 K for both single- and double-etalon probe beam-line configurations, and with the probe beam delay fixed in each case. The spectra were averaged for 100 to 1,000 laser shots to optimize signal-to-noise ratio in the data. Higher loss of probe beam energy when twoetalons were used resulted in lower single-shot signal-to-noise ratio. Shot-averaging provides a means to compare the performance of the technique for the two probe beams used. Measured furnace spectra obtained using the 1.5-ps duration, 5.3-cm⁻¹ linewidth probe are shown along with theoretical fits for 6 different temperatures in Fig. 5. These spectra were recorded with the probe delay fixed near τ = 3.5 ps, and the fitted delays are generally within 40 fs of a mean fitted value of τ = 3.42 ps. The best-fit temperature, O₂/N₂ ratio and probe delay are shown on each plot along with temperature indicated by a thermocouple that was placed into the furnace gas after the conclusion of the CARS experiments. Fitted temperatures are accurate to within ± 2% of thermocouple measurements, which is comparable to the accuracy reported for nanosecond rotational CARS by Seeger and Leipertz [27]. Fitted O₂/N₂ ratios range from + 8.4% to −10% of the known value, and a systematic decrease in measured O₂/N₂ with increasing temperature is observed.

 

Fig. 5 Fits to CARS spectra obtained in tube-furnace-heated air in the single-etalon probe configuration with a 1.5-ps/5.3-cm⁻¹ probe beam at a nominal probe delay of 3.5 ps.

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Fits to the temperature-dependent air spectra for the 7-ps duration, 2.1-cm⁻¹ linewidth probe at a fixed delay near τ = 2.8 ps are shown in Fig. 6. Similar quality fits are seen at this finer probe resolution, with the fitted temperature generally within 1-3% of thermocouple readings. CARS-measured temperatures are higher than the thermocouple data for T < 600 K and lower at higher temperatures. Measured O₂/N₂ ratio is within 2% of the known value, which is superior to the results obtained with the 1.5-ps probe, albeit with a similar systematic trend toward lower O₂/N₂ observed with increasing temperature.

 

Fig. 6 Fits to CARS spectra obtained in tube-furnace-heated air in the double-etalon probe configuration with a 7-ps/2.1-cm⁻¹ probe beam at a nominal probe delay of 2.8 ps.

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4.3 Furnace-heated air: single-laser-shot data

Randomly selected single-laser-shot spectra are shown in Fig. 7. Spectra recorded using the 1.5-ps probe are shown in plots a-d, with spectra taken using the 7-ps probe provided in plots e and f. The 3 × increase in probe-beam energy available in the 1.5-ps probe provides increased signal-to-noise ratio relative to the higher resolution 7-ps probe. Temperature histograms were constructed from ensembles of 500 to 1000 single-shot measurements at each furnace setting, and plotted for the same conditions as the spectra of Fig. 7 in Fig. 8. The results of our single-shot data campaign are summarized in Table 1, where six furnace settings are reported for spectra obtained with the 1.5-ps probe, and two for the finer resolution 7-ps probe. The precision in the single-shot temperature data is quantified by the ratio, σ_T/$\overline{T}$,where σ_T is the standard deviation of the histogram data and $\overline{T}$ is the corresponding mean. Based upon this metric, the precision in our single-shot temperature data is outstanding at the higher signal levels afforded by the 1.5-ps probe beam. Values of σ_T/$\overline{T}$range from 0.8% at room temperature to 1.9% at 773 K, with the metric hovering just above 1% for all temperatures in between. This level of temperature-measurement precision compares very favorably to values reported for nanosecond rotational CARS, where “typical” values of 3-4% are common fromroom conditions to flame temperatures [27]. Temperature-measurement precision is degraded to ± 3.7 and ± 2.6% at furnace settings of 521 and 773 K, respectively, when the more frequency narrow 7-ps probe is used. We presume that this is a result of the above-mentioned decreased signal-to-noise in the spectra shown in Figs. 7(e) and 7(f), and not due to the intrinsic nature of the high-resolution spectra. Single-shot O₂/N₂ statistics in air are additionally compiled in Table 1. The mean values range from O₂/N₂ = 0.25 to 0.275, or −7.3% to + 2.5% of the true value in air. When using the 1.5-ps probe, the standard deviation of the O₂/N₂ measurement ranges from 1.1 to 4.3% of the mean, with degraded levels of precision observed with the 7-ps probe.

 

Fig. 7 Fits to single-laser-shot CARS spectra at several temperatures in tube-furnace-heated air: 1.5-ps/5.3-cm⁻¹ probe (top and middle), and 7.0-ps/2.1-cm⁻¹ probe (bottom).

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Fig. 8 Temperature histograms obtained from fits to single-laser-shot fs/ps rotational CARS spectra.

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Table 1. Summary of fitting results for single-laser-shot spectra.

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We believe that the reason for the observed improvement in temperature-measurement precision relative to nanosecond CARS is a result of the low-noise pump/Stokes driving offered by the nearly transform-limited femtosecond preparation pulses. This results in very low levels of spectral amplitude and phase noise when compared to nanosecond broadband dye lasers. This high-quality preparation of the Raman coherence yields very repeatable spectral envelopes, as illustrated in Fig. 9, where 1000 single-shot spectra are overlaid on a single set of axes at furnace settings of T = 292 K and 473 K. The spectra have been normalized to unit maximum to remove shot-to-shot intensity fluctuations while preserving the spectral shape. It is seen that the spectral envelopes are essentially identical over all 1000 laser shots in each case. The shot-to-shot repeatability is particularly striking at T = 292 K, where signal levels are highest.

 

Fig. 9 One thousand single-laser-shot spectra normalized to the peak CARS intensity at temperatures of 292 K and 491 K. The spectra highlight the low level of noise due to near-transform-limited pump/Stokes preparation.

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5. Summary and conclusion

The results of our study are summarized graphically in Fig. 10, where fitted temperature and O₂/N₂ ratio from both shot-averaged and single-laser-shot spectra are plotted against the furnace thermocouple reading. Data points for single-shot results represent the sample mean, while error bars (where visible) represent a single standard deviation of the single-shot results. Temperature-measurement accuracy was generally within 2.5%. Best thermometry results were obtained using the 1.5-ps/5.3 cm⁻¹ probe, where CARS photon yields were higher as a a result of the increase in retained probe bandwidth and energy. Using this low-resolution probe, a single-shot temperature measurement precision of 1% was demonstrated fortemperatures from 290 to 700 K and 1.9% near 800 K. Temperature accuracy was retained in shot-averaged spectra when a 7-ps/2.1 cm⁻¹ probe was used, with some degradation in the single-shot precision that we presume is due to lower CARS photon yields associated with this lower energy probe. O₂/N₂ concentration ratios were most accurate when the low-energy, high-resolution 7-ps probe was utilized, with some systematic trend toward lower O₂/N₂ with increasing temperature for both probe resolutions. Single-shot precision in O₂/N₂ was 1-4% for the 1.5-ps probe and 4-8.6% for the 7-ps probe.

 

Fig. 10 Summary of fitted temperatures and O₂/N₂ ratios.

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This study demonstrates the utility of the hybrid fs/ps CARS approach for practical, high-precision and background-free diagnostics in a gas mixture. Use of etalons and other bandwidth-limiting pulse shapers limits the available picosecond probe-beam energy, providing a practical limit on probe linewidth and on the highest temperature measureable with these bandwidth-carving approaches. The coarse resolution in the 1.5-ps probe beam does not appear to limit the potential of the technique for thermometry, but with some decreased accuracy in the concentration measurements reported here. Even coarser probe-beam resolutions may still provide adequate thermometry, and an upper limit on probe bandwidth has yet to be assessed. We are currently working on methods to increase the energy content in frequency-narrow probe beams [19] and extend the technique to flame temperatures with a more systematic evaluation of concentration measurement capability.