Gas-phase single-shot thermometry at 1 kHz using fs-CARS spectroscopy

Sukesh Roy; Waruna D. Kulatilaka; Daniel R. Richardson; Robert P. Lucht; James R. Gord

doi:10.1364/OL.34.003857

Time-resolved coherent anti-Stokes Raman scattering (CARS) spectroscopy using femtosecond lasers has been successfully employed to measure gas-phase temperature in reacting flows involving both $H_{2}$ and hydrocarbon fuels [1, 2, 3]. However, time-resolved temperature measurements are not suitable for transient or turbulent reacting flows, where temperature varies rapidly across the spatiotemporal domain. The objective of this research effort is to demonstrate single-shot temperature measurements in reacting flows at 1 kHz.

Femtosecond coherent anti-Stokes Raman scattering (fs-CARS) spectroscopy permits the performance of thermometry and species-concentration measurements that are nearly independent of the local collisional environment [4, 5]. This feature, along with the data-acquisition bandwidth afforded by off-the-shelf femtosecond lasers, makes fs-CARS ideal for investigating various dynamical events in turbulent reacting flows. Single-shot gas-phase temperature measurements acquired with a chirped-probe pulse by probing the $H_{2}$ molecule were originally demonstrated by Lang and Motzkus [6]. However, measuring the gas-phase temperature by probing $H_{2}$ is not suitable for most reacting flow environments because of the low concentration of $H_{2}$ in such an atmosphere. For air-fed combustion, measuring the gas-phase temperature using $N_{2}$ molecule is more appropriate since $N_{2}$ is present throughout the combustion zone. To perform measurements in a nearly collision-free regime using the $N_{2}$ molecule, we focused our attention on the initial dephasing rate of the Raman coherence that is caused by the oscillations of various Raman transitions at slightly different frequencies [1, 4].

A schematic diagram of the experimental system is shown in Fig. 1 . A 1 mJ, 1 kHz, 85 fs, Ti:sapphire regenerative amplifier at $\sim 800 nm$ was used to pump an optical parametric amplifier (OPA) and also to provide the Stokes laser pulse with an approximate energy of $100 μ J$ /pulse. The frequency-doubled output of the OPA ( $\sim 675 nm$ with energy of $30 μ J$ /pulse) was used for the pump and probe beams. The probe beam was linearly chirped with a 30-cm-long SF-10 rod to extend the temporal width of the 80 fs pulse to $\sim 2.5 ps$ at FWHM. The chirped-probe pulse, where the red part of the spectrum arrives earlier than the blue part, allows one to map the temporal behavior of the Raman coherence into the spectrum of the CARS signal. The CARS signal was then detected with a 0.25 m spectrometer and an electron-multiplying charge-coupled-device (EMCCD) camera. Temperatures were evaluated from single-shot $N_{2}$ spectra when the probe beam was delayed by $\sim 2 ps$ with respect to the pump and Stokes beams.

Since the FWHM of the probe pulse is $\sim 2.5 ps$ , at a 2 ps delay a significant interference between the resonant and nonresonant signals will be present. Despite having a short temporal duration at the CARS probe volume, the nonresonant signal will be significantly chirped when dispersed at the spectrometer, causing an overlap in time with the resonant CARS signal at the EMCCD face. The effect of resonant and nonresonant signal interference on the chirped-probe CARS signal is shown in Fig. 2 . The modulation of the resonant CARS signal is due to rapid in and out-of-phase oscillations between various spectral components caused by the changing frequency of the chirped-probe pulse. The amplitude of the modulation of the CARS signal is significantly enhanced as a result of the interference of the resonant and nonresonant signals, as is evident in Fig. 2 where the nonresonant signal undergoes rapid in and out-of-phase oscillations with respect to the resonant CARS signal. The observed interference can be significantly reduced if the probe beam is delayed further. However, this will result in a significant reduction in the resonant CARS signal at flame temperature.

A least-squares-fitting code was developed to extract the gas-phase temperature by comparing the experimental single-shot $N_{2}$ CARS spectrum with the theoretical one calculated using Eqs. (1, 2, 3, 4, 5, 6). Here $E_{sig} (t)$ , $E_{pr} (t)$ , $E_{p} (t)$ , and $E_{S} (t)$ are the electric field amplitudes of the CARS, probe, pump, and Stokes pulses, respectively.

E_{sig} (t) = E_{pr} (t) P_{res} (t) + E_{pr} (t) P_{nres} (t),

P_{res} (t) = β [\int_{- \infty}^{t} E_{p} (t^{'}) E_{S} (t^{'}) d t^{'}] \sum_{i} {Δ N_{i} {(\frac{d σ}{d Ω})}_{i} cos (ω_{i} t + ϕ) exp (- Γ_{i} t)},

P_{nres} (t) = α E_{p} (t) E_{s} (t),

E_{pr} (t) = E_{0, pr} exp [- {(t - t_{0, pr})}^{2} / τ_{pr}^{2}] cos (ω_{0, pr} t - β_{pr} t^{2}),

E_{sig} (ω) = \int_{- \infty}^{+ \infty} [E_{pr} (t) P_{res} (t) + E_{pr} (t) P_{nres} (t)] exp (i ω t) d t,

S_{CARS} (ω) = {| E_{sig} (ω) |}^{2} .

P_{res} (t)

and

P_{nres} (t)

describe the induced polarization of the resonant Raman and the nonresonant four-wave mixing signal. In Eq. (2),

Δ N_{i}

and

{(d σ / d Ω)}_{i}

are the population difference and Raman cross section for each Raman transition i, respectively. The phase factor ϕ is used to account for the different phase of the resonant and nonresonant responses to the pump-Stokes excitation. The scaling parameters α and β are varied to obtain the best fit between theoretical and experimental spectra; the phase factor ϕ is also varied for best fit. It is assumed that the pump and Stokes pulses are transform-limited (TL) such that the various Raman transitions are oscillating in phase at time

t = 0

. After impulsive excitation by the pump and Stokes beams, the polarization for each Raman transition oscillates with angular frequency

ω_{i}

. The polarization for individual transitions decays as a result of dephasing collisions with a rate constant

Γ_{i}

, the Raman linewidth, but at time scales much longer than a few picoseconds. Since the CARS signal was detected with a spectrometer-coupled CCD camera, the time-dependent theoretical signal is converted to the spectral domain using Eq. (5), and the intensity of the CARS signal

S_{CARS} (ω)

is calculated using Eq. (6).

Measurements were initially performed in a heated gas cell. Figure 3a shows a single-shot spectrum of $N_{2}$ at 900 K when the probe beam was delayed by $\sim 2.0 ps$ and its least-squares fit compared with the theoretical spectrum. The theoretical temperature was found to be within 2% of the set value. The probability density function (PDF) of 1000 single-shot spectra at 900 K is shown in Fig. 3b. The mean temperature and precision of the single-shot thermometry approach based on the heated-gas-cell measurements are found to be within $\sim 1 %$ and $\sim 3 %$ of the set value, respectively. The accuracy and the precision of the single-shot fs-CARS measurements are similar to the one observed for traditional ns laser-based CARS spectroscopy. The presence of nonresonant signal did not significantly affect the accuracy of the temperature measurements. Temperature measurements were also performed in an atmospheric pressure, nearly adiabatic $H_{2}$ –air flame stabilized over a Hencken burner. The single-shot spectra and associated PDFs of 1000 spectra for equivalence ratios of 0.5 and 1.0 with a probe-beam delay of $\sim 1.5 ps$ are shown in Fig. 4 . The least-squares fit of the experimental and theoretical spectra are also shown in Figs. 4a, 4b, respectively. For a temperature range of $\sim 1000 - 2400 K$ , the accuracy and precision are found to be within $\sim 1 % - 6 %$ of the adiabatic flame temperatures and $\sim 1.5 %$ of the mean temperatures, respectively. It should be noted that the theoretical temperatures depend significantly on laser parameters such as the temporal and spectral shapes of the pulses, the ratio of the resonant to nonresonant signals, and the probe time delay with respect to the pump and Stokes beams. The temporal profiles of the laser pulses are assumed to be Gaussian and TL because of the unavailability of instruments for properly characterizing them.

In conclusion, single-shot temperature measurements using fs-CARS signal of $N_{2}$ were demonstrated in a heated gas cell and in a near-adiabatic laboratory flame. These measurements along with high-bandwidth $(> 1 kHz)$ lasers will pave the way for addressing the dominant instability modes, ranging from 200 Hz to 10 kHz, and their interactions in turbulent reacting flows.

Funding for this research was provided by the Air Force Research Laboratory (AFRL) under Phase II SBIR contract FA8650-09-C-2918; by the AFRL Nanoenergetics Program; by the Air Force Office of Scientific Research (Dr. Julian Tishkoff and Dr. Tatjana Curcic, Program Managers); by the National Science Foundation (NSF), Combustion and Plasmas Program, under award 0413623-CTS; and by the U.S. Department of Energy (DOE), Division of Chemical Sciences, Geosciences, and Biosciences, under grant DE-FG02-03ER15391.

Fig. 1 Schematic diagram of single-shot fs-CARS experimental apparatus.

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Fig. 2 Theoretically calculated resonant and nonresonant components of the fs-CARS signal, showing different modulations.

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Fig. 3 (a) Experimentally measured single-shot fs-CARS spectra along with the least-squares theoretical fit and (b) PDF of extracted temperatures for 1000 consecutive laser shots in a heated gas cell at 900 K.

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Fig. 4 Experimental and theoretical single-shot fs-CARS spectra in a $H_{2}$ –air flame stabilized over a Hencken burner for (a) $Φ = 0.5$ and (b) $Φ = 1.0$ . The corresponding temperature PDFs for 1000 consecutive laser shots are also shown in panels (c) and (d).

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Gas-phase single-shot thermometry at 1 kHz using fs-CARS spectroscopy

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Optics Letters