Ultrafast background-free ro-vibrational fs/ps-CARS thermometry using an Yb:YAG crystal-fiber amplified probe

: A novel laser system for ro-vibrational spectroscopy using coherent anti-Stokes Raman Scattering in hybrid fs/ps regime is presented. A single Yb:KGW laser source is used as a master laser to generate the three CARS laser beams, namely the pump and Stokes femtosecond pulses and a 58 ps probe pulse. Master oscillator power ampliﬁer (MOPA) architecture is implemented to increase the probe output power using a custom two stage free space linear ampliﬁer. The probe is 0.37 cm − 1 in width and 100 µJ in energy to allow resolving the Q-branch ro-vibrational lines of N 2 and recording single shot CARS spectra at kHz repetition rate in ﬂames. An original and simple technique based on the study of the inﬂuence of probe delay and polarization has been setup to optimize nonresonant background rejection, with no loss in resonant contribution. CARS performances are reported for N 2 thermometry between 300 K and 3000 K, demonstrating state of the art precision. within the hybrid fs/ps CARS regime exploiting the inﬂuence of single and 8 Go The histograms of the best-ﬁt from a


Introduction
Laser diagnostics are very powerful for the noninvasive study of a large variety of media. Among other spectroscopic techniques, Raman scattering allows to efficiently probe the rotational and vibrational fundamental molecular levels, providing precise information (as composition, concentration, temperature, pressure) to characterize a medium [1,2]. In particular, coherent anti-Stokes Raman scattering (CARS) [3,4] is widely used to retrieve local information. It is applied to microscopy in condensed media [5,6], life sciences [7], metrology [8,9], but also to diagnose gaseous flows [10] such as combustion [1,11], plasma [12][13][14][15] and supersonic flows [16,17]. Especially in the case of reacting flows, these measurements are essential for the understanding and the reliable simulation of the physical processes taking place in presence of high temperature, pressure and turbulence. Among others, the temperature is a key parameter to describe these flows, since it governs the kinetic of chemical reactions [15]. Thanks to its ability to provide broadband ground state spectroscopy in a single shot, CARS thermometry is widely used [10], its precision and accuracy being still unrivalled.
CARS process (Fig. 1) is a non-linear 4-wave mixing interaction that relies on a two photon excitation of the ro-vibrational coherences of the medium by two lasers, namely pump and Stokes, whose frequencies ω P and ω S match a Raman active vibration ω αβ = ω P − ω S ( Fig. 1(b)). Here ω αβ refers to the frequency gap between two ro-vibrational states |α = |ν, J and | β = |ν , J , defined by their respective vibrational and rotational quantum numbers ν and J. Figure 1(a) shows the ro-vibrational levels fulfilling the selection rule ν = ν + 1 and J = J that are involved in the fundamental Q branch. The ro-vibrational coherence is then probed by a third laser beam, namely the probe, of frequency ω Pr , to generate an anti-Stokes signal of frequency ω AS = ω Pr + ω αβ (Fig. 1(c)). As in all nonlinear processes, wave-vectors fulfill the phase-matching condition for optimum amplification of the anti-Stokes beam. The anti-Stokes spectrum is composed of spectral lines whose relative amplitudes and widths, when properly resolved, provide information on the thermodynamic properties of the medium such as temperature, pressure or the relative concentrations of major species. The amplitude A(ν, J) of a line corresponding to the molecular transition |ν, J ↔ |ν + 1, J can indeed be expressed as [4]: where T is the temperature, σ eff (ν, J) is the Raman cross section of the transition, Q int (T) is the internal energy partition function, and ∆ρ(ν, J, T) is the population difference between the two ground energy levels involved in the Raman transition. The population of level |ν, J depends on temperature through Boltzmann equilibrium: where g(J) is the nuclear spin degeneracy factor, h is the Planck's constant, c is the speed of light and k is the Boltzmann's constant. In practice, temperature is retrieved by comparing experimental spectra to simulations through fitting procedures. The resonant third order nonlinear susceptibility χ R (3) (ω) is thus computed as the sum of complex Voigt profiles centered on the many rotational Raman lines inside few vibrational bands [4]. A constant term χ NR is also added to take into account the nonresonant (NR) contributions to the CARS spectrum: This NR signal is an important limitation of traditional CARS diagnostics in reactive media since it induces complex interferences within the CARS spectrum, perturbing its interpretation. CARS thermometry has traditionally used for long time ns-lasers operating at few Hz repetition rate [15]. Thanks to the recent development of ultrafast laser sources, ultra-short pulses regime (femtosecond or picosecond duration) as well as high repetition rates (MHz-kHz) are now available, allowing high speed measurements [18][19][20][21][22] in turbulent environments. Among many spectro-temporal regimes (ps-CARS, fs-CARS, CPP-CARS, etc.), the hybrid femto-picosecond (fs/ps-CARS) solution [23,24] appeared well appropriated to overcome the limitations of CARS diagnostics. In this regime, the pump and Stokes pulses have short duration (between few fs and few hundreds of fs), providing high peak powers and broad spectral bands excitation, while probe pulse is longer (1-100 ps), allowing well resolved spectroscopy. This allows increasing the measurement repetition rate up to kHz [19], the dimensionality to 2D instantaneous imaging [25], and the bandwidth to more than 4000 cm −1 [26] in single shot.
The CARS signal is modeled [27] by a convolution of the susceptibility by the probe spectrum complex amplitude S probe (ω), with a dephasing term proportional to the probe delay τ [28]: Its spectral behavior is strongly influenced by the probe spectrum and many efforts have been made in order to engineer its spectral and temporal properties. Pulse shaped probes properly delayed from the pump/Stokes excitation ( Fig. 1(d)) have been implemented to remove NR contributions such as unfolded four photon interaction ( Fig. 1(e)) mainly appearing when the three laser pulses overlap in time [29][30][31]. In this powerful hybrid regime, one main experimental challenge is to produce the femtosecond pump and Stokes pulses as well as the picosecond probe pulse that have very different time and spectral properties. Although some impressive setups use two different laser sources [25,26], many setups are based on a single laser for the sake of simplicity and synchronization of the pulses. Various filtering techniques have been implemented in order to generate the narrowband probe out of a broadband initial laser pulse. Based on linear filters, such as commercial filters [32], 4-f pulse shapers [33,34], Fabry-Perot etalons [35,36] and volume Bragg gratings [37], experimental setups had to deal with the energy loss associated with spectral narrowing. Nonlinear techniques were also used to produce a narrow probe more efficiently and overcome this limit. They are mostly based on second harmonic bandwidth compression in crystals, using long crystals [38] or inversely chirped pulses in commercial modules (SHBC LightConversion) [14,39]. However, respective bandwidths of 10 cm −1 and 3.5 cm −1 are achieved with those techniques, which is too high for ro-vibrational resolution in N 2 . Thus a compromise had always to be found between the spectral resolution of the CARS spectrum and the pulse energy to achieve single shot measurement.
In this paper, we report on the development of a new experimental setup in which a master oscillator power amplifier (MOPA) architecture is used. The probe output power is increased using a custom amplifier (Fibercryst). This architecture allows us to engineer the spectral properties of the probe pulse separately from its energy. A gain in energy by a factor of 100 has been achieved compared to the previous implementation [37]. Spectra of hot gaseous media were obtained in single shot measurements with good enough resolution and signal to noise ratio (SNR) to distinguish ro-vibrational structure. Influence of probe delay and polarization are investigated in order to set up a novel technique to optimize NR background rejection. Temperature measurements are carried out in ambient air, in a pre-mixed stoichiometric methane-air (CH 4 /air) flame (McKenna burner) and in an oxyacetylenic (C 2 H 2 /O 2 ) torch at 1 kHz repetition rate. State-of-the-art precision is demonstrated in the 300-3000 K temperature range.

Experimental setup
The experimental setup is described in Fig. 2. A commercial single all-solid state laser source is used to generate the three interfering laser beams. The Yb:KGW regenerative amplifier (Pharos, LightConversion) emits a 1 mJ, 150 fs pulse train at 1030 nm at a repetition rate between 1 and 5 kHz, and exhibits a 8 nm FWHM spectrum. A commercial optical parametric amplifier (OPA) module (Orpheus, LightConversion) is used to produce a tunable idler radiation from 1030 nm to 2700 nm. The idler is frequency doubled in a commercial second harmonic generation (SHG) module (Lyra, LightConversion) and provides a Stokes pulse 15 µJ in energy and 150 fs in duration at 583.5 nm. In the Orpheus module, a residual part of the 515 nm radiation produced to pump the OPA crystals is extracted, generating a 100 µJ pulse which is used as the pump. The synchronization of the pump, Stokes and probe pulses is achieved thanks to motorized delay lines on pump and probe paths. The recombination of the beams is done through a dichroic parallel plate. Beams are focused using a 300 mm focal-length achromatic lens in a folded BOXCARS phase matching geometry [40]. All beams are re-collimated and the incident light is rejected in bandpass filters. The generated anti-Stokes beam is recorded through a 750 mm spectrometer (Acton), equipped with an electron-multiplying back-illuminated CCD camera. Single shot anti-Stokes spectrum is thus displayed over a 2220-2360 cm −1 spectral window. The whole experimental scheme is arranged in a compact and transportable setup (occupied area <1 m 2 ) that can be easily placed next to the medium to probe.
The main novelty of the described setup is represented by the original architecture we use to produce the probe pulse. Our goal is to produce from a femtosecond laser a probe pulse that is narrow enough to resolve ro-vibrational lines and intense enough to allow single shot measurement. As in traditional filtering spectral narrowing is obtained at the expense of laser energy, we implement an innovative laser architecture based on spectral shaping at fundamental laser wavelength followed by an amplification stage. A 300 µJ residual part of 1030 nm radiation is spectrally narrowed and phase-shaped using a combination of a Fabry-Perot etalon (FPE) and a volume Bragg grating (VBG) [37]. The 1.4 µJ resulting pulse is then seeded into an optical amplifier to produce a 250 µJ pulse at 1030 nm that is doubled with a 40% efficiency through SHG in a LBO crystal to produce a 100 µJ probe pulse at 515 nm.
The amplification module is a unique master-oscillator power-amplifier (MOPA) system based on Yb:YAG crystal-fiber technology (Fibercryst) [41,42]. It is a free space linear amplifier that uses two crystalline fibers pumped by 980 nm laser diodes to provide a 180 amplification factor at 1030 nm. The first fiber is used in single pass, while the second one is used in a double pass scheme. The use of crystalline fibers provides high gain, due to the long interaction, and low nonlinear effects, keeping the spectral purity. A 250 mW output beam, exhibiting Gaussian circular profile, is obtained starting from a 1.4 mW seed input at 1 kHz. Yb:YAG amplifiers represents a valuable alternative to Nd:YAG systems that are commonly used to amplify picosecond pulses [43]. This latter, in fact, provide high amplification factor, but the spectral width of the gain band is narrow and centered at 1064 nm, which is not compatible with the ultrashort pulse generation (< 200 fs) needed for the first stage of the experiment.
The probe pulse is characterized in the spectral and temporal domain to allow appropriate CARS signal simulation. The temporal profile is measured by scanning the pump-probe delay while recording the CARS amplitude in argon [16]. Argon signal results from instantaneous superposition of a short pump/Stokes excitation (∼150 fs FWHM) with a long probe pulse (tens of picoseconds FWHM). Thus, by scanning a suitable probe delay range (∼300 ps), the probe temporal profile is sampled. A 58 ps (FWHM) asymmetric pulse is measured, as illustrated in Fig. 3(a). A slight intensity modulation is attributed to the residual spectral comb structure due to the free spectral range of the FPE. A Fourier Transform of the temporal profile is then calculated, assuming a flat temporal phase. The intensity (solid line) and the phase (dotted line) of the resulting spectrum are given in Fig. 3(b). The phase exhibits a step profile, and the intensity shows a 0.37 cm −1 FWHM Voigt profile. The achieved narrowband width is thus well suited for N 2 Q-branch spectroscopy at flame temperature.

Results
We have performed CARS measurements in ambient air, in a pre-mixed stoichiometric methaneair (CH 4 /air) flame (McKenna burner), and in an oxyacetylenic (C 2 H 2 /O 2 ) torch. Typical single shot spectra are shown in Fig. 4. Typical NR spectrum of argon is also shown (dotted line) to figure out the overall bandwidth of the coherent excitation. In ambient air (blue line) the spectrum is narrow and is restricted to the first rotational lines of the fundamental band (ν = 0 → ν = 1, ν being the vibrational quantum number). In flames (CH 4 /air in green, C 2 H 2 /O 2 in red), different vibrational bands are observed (ν = 0 → ν = 1,ν = 1 → ν = 2,ν = 2 → ν = 3) with many rotational lines (J ∼ 0 − 40, J being the rotational quantum number). The influence of temperature on the profile behaviour is driven by the Boltzmann population distribution in the ro-vibrational manifold of levels. As expected, when temperature increases, the amplitude of the high vibrational bands increases (ν ≥ 1), and the rotational lines distribution shifts towards higher J values. Signal to noise ratio (SNR) was found to be 1800, 130 and 75 in the spectra recorded in ambient air, CH 4 /air flame and O 2 /C 2 H 2 flame respectively. It decreases when T increases since the number of molecules n per volume unit decreases and CARS signal intensity scales as n 2 . Also, NR background contributions become predominant in the flames spectra due to the decrease of the resonant contribution, and to the production of species leading to stronger NR contributions (CO 2 , H 2 O. . . ). The rejection of NR background is an important issue to solve in order to have a proper measurement of temperature. In this paper, we propose a simple and original technique to accomplish this goal within the hybrid fs/ps CARS regime by exploiting the influence of probe polarization and delay.
Probe polarization and delay [31,33] have been two experimental strategies traditionally used to reject NR background. In the traditional 60°crossed-polarization scheme [3,40,44], NR rejection is obtained with attenuation (of a factor 16) of the resonant contribution The effect of probe delay has been also widely investigated [28,45], demonstrating that this parameter can be tuned to emphasize or minimize some particular spectral features of the CARS spectrum. However, since the interference pattern is highly influenced by the probe spectral shape, it is necessary to measure it for each new experimental condition in order to properly characterize the light-matter interaction.
Pump and Stokes beams being vertically polarized, we call parallel-configuration when the probe polarization is vertical and crossed-configuration when the probe polarization is horizontal. In the CH 4 /air flame, we find that NR contribution to the N 2 CARS spectrum is attenuated using crossed-configuration with nearly no effect on the resonant signal. Figure 5 shows the spectra recorded in parallel-configuration when the pump-probe delay τ is scanned between −50 ps and 300 ps using a motorized delay line. The picture exhibits the coherent beating between the various rotational lines that modulates the signal decay mainly driven by the coherence lifetime, as previously described [28,37,45]. Around τ = 0 ps, pump and probe overlap in time and NR background is observed. We have searched for the specific probe delay that minimizes the NR background together with the first fundamental band-head, since it is particularly relevant for flame diagnostics. Indeed, in some experimental cases, for instance in heterogeneous media, that measurement strategy acts in favor of hot zones that may interfere with cold ones through the measurement volume [37]. In our case, we have found an optimized delay of τ = 50 ps that fulfills the two above conditions. For this reason, it will be referred throughout the paper as the reference value.
To underline this and point out the influence of polarization, CARS spectra measured in parallel and crossed probe configuration, at τ = 0 ps and τ = 50 ps, are shown in Figs. 6(a) and 6(b) respectively. During experiments, care was taken to use an achromatic half-wave plate in front of the spectrometer to maintain horizontal signal polarization inside the device and thus eliminate polarization effects due to the detection grating. At τ = 0 ps, the two polarization configurations exhibit different behaviour. In the parallel case, NR background is clearly visible in the 2340-2360 cm −1 spectral range, and a hole is located in the wing of the first vibrational band (∼2335 cm −1 ) as a typical signature induced by complex interferences between resonant and NR contributions. In the crossed case, CARS spectrum appears immune from NR distortions. Due to the attenuation of the NR contribution, the amplitude of the stronger J lines (J>18 at T = 2000 K) of the fundamental and hot band is lower, but the fundamental bandhead amplitude remains approximatively constant. At τ = 50 ps, the spectral behaviour exhibits a strong reduction of the fundamental bandhead (low rotational quantum number J) due to destructive interference of the neighboring ro-vibrational lines. However, the amplitude of the hot ro-vibrational lines (high rotational quantum number J) remains similar than at τ = 0 ps, since a higher line spacing in this spectral range results in constructive interferences at this particular probe delay [28,37,45]. Furthermore, no difference is anymore observed between the parallel and crossed spectra since negligible NR contribution is expected at this delay. Therefore, in both strategies, NR background rejection is achieved at very low cost in resonant signal amplitude. To emphasize the NR rejection by using crossed-polarization configuration, the evolution of the CARS spectra as a function of probe delay is shown in both configurations in Figs. 7(a) and 7(b) for N 2 , and in Fig. 7(c) for Ar in parallel-configuration. N 2 spectra have resonant (ω< 2330 cm −1 ) and NR (broadband) contributions, while Ar signal is purely NR. In the three pictures, a clear trade-off can be seen at about 40 ps delay, which is the position of the probe rising edge. From Fig. 7(c) it is clear that NR signal is only visible for τ< 40 ps. Therefore, a mainly resonant spectrum is obtained at probe delays τ> 40 ps. Spectra obtained in parallel-and crossed-polarization become identical for higher delays (> 40 ps) leading to the same resonant information in the two polarization configurations. However, they differ notably around zero delay, more particularly in the ω> 2330 cm -1 region, where NR signature is evidenced. NR contribution is nearly zero for crossed-polarization, while it is important in parallel case. In Fig. 7(d), the evolution of the logarithmic CARS amplitude of a single rotational line J = 36 is plotted as a function of τ. That specific frequency is marked with an arrow in Figs. 7(a)-7(c). In the two polarization cases, the intensity of the N 2 line rises when the delay grows from negative values, since the probe is in advance compared to the pump. For τ< 40 ps, the two plots exhibit a quasi-linear dependence, due to the exponential decay of the coherence. A modulation is also observed due to the beating between neighboring rotational lines. However, for τ< 40 ps the CARS signal in parallel-polarization (blue line) follows the fast decaying trend of Ar signal (black line) [31]. This NR signature is largely attenuated in crossed-polarization (red line).
The crossed-polarization case thus produces a CARS signal that appears with a significant reduction of NR background. Similar polarization arrangement was already used in femtosecond CARS [46][47][48], and NR contribution were still observed and phase shaping technique was added to improve its rejection. As derived in [3,49,50] the CARS susceptibility is given by the susceptibility tensor element χ 1111 = 1 24 (3σ NR + 4a) in the parallel case, where σ NR is the NR electronic contribution and a the isotropic Raman contribution, assuming that the anisotropic Raman contribution is negligible in the Q-branch of N 2 . In the crossed probe polarization case, the susceptibility reduces to χ 1212 = 1 24 (σ NR + 2a). Thus, the NR contribution to the susceptibility is divided by 3, leading to an attenuation factor of 9 in CARS intensity. Let us notice that the vertical scale in Figs. 6 and 7 gives the CARS intensity. In our experiment, an 8-factor attenuation is measured on argon CARS spectra. However, no attenuation of the resonant contribution was observed in N 2 CARS spectra while, from the above formulas, susceptibility it is expected to be reduced. In a future work, we intend to perform a more detailed study of the polarization impact on resonant and NR contributions in order to fully understand this beneficial effect.
Temperature measurements have been performed with our hybrid CARS system in single shot at 1 kHz repetition rate in ambient air, the pre-mixed CH 4 /air flame and in the C 2 H 2 /O 2 torch. The position of the probe volume is located at about 2.5 mm and 20 mm above the burner, for the CH 4 /air flame and in the C 2 H 2 /O 2 torch respectively. In Fig. 8, spectra are recorded in parallel-polarization at zero probe delay τ. In the CH 4 /air flame, performances of crossed-polarization and 50 ps probe delay are also investigated. In this case, the precision of the CARS measurement is evaluated. In the diffusion flame, which is a strongly fluctuant medium, CARS probability distribution is larger and influenced by the turbulent nature of the flame. Typical spectra are shown in Fig. 8. For each case, the best fitted spectrum is calculated, as well as the residuals between simulation and experiment.
In order to retrieve the temperature, a fitting procedure has been performed for each experimental spectrum by using a Python routine. Good fits are obtained at low computational cost using only two free parameters: the temperature T and the NR amplitude a NR . Around 15 seconds are necessary to estimate the temperature value from a single spectrum using a personal computer with a 2.7 GHz processor and 8 Go of RAM. The histograms of the best-fit temperature from a set of 900 consecutive single laser-shot spectra are shown in Fig. 8(f). The measurements statistics extracted from these measurements are summarized in Table 1.

Medium
Optical configuration Measurement polarization τ(ps) Concerning the target temperature, in ambient air T 0 = 300 K is taken, while in CH 4 /air flame T 0 = 2075 K is taken according to [51] for a measurement volume located at 2.5 mm above the burner, and T 0 = 3000 K is taken in the acetylene/oxygen torch.
Mean values T and standard deviations σ are calculated over 900 consecutive single shot measurements. Accuracy is calculated by considering the relative difference between the measurement and a target temperature T 0 . State of the art precision (1.2%) and accuracy (1.5%) have been achieved in the CH 4 /air flame with parallel-polarization and zero probe delay [52]. Similar precisions have been obtained for crossed-polarization and delayed probe (σ = 50 ps) but slightly shifted value of the mean temperature and better accuracy. This outlines the benefit of NR background minimization and confirms the efficiency in using the 50 ps probe delay (Fig. 7(d)). In ambient air, worse precision (4.2%) and accuracy (2.3%) are obtained since the spectrum gets very narrow at low temperature with very few ro-vibrational structures to fit. The bias observed in the measured mean temperature value is thus due to calibration errors of some parameters such as probe delay that greatly influences the temperature estimation. In the C 2 H 2 /O 2 flame, histogram also exhibits a degraded precision (2.9%) which may be the result of temperature fluctuation inside the turbulent torch. The higher temperature and lower N 2 concentration within the probe volume are probably also degrading the SNR and thus affecting the measurement precision. The accuracy inside the torch has been calculated to 4.8% given a temperature of T 0 = 3000 K. However this value is not very reliable since the temperature inside the torch is not accurately known.

Conclusion and perspectives
We have demonstrated a MOPA based laser architecture that allows generating the three laser beams needed for fs/ps-CARS interaction out of a single femtosecond laser. This architecture involves a filtering stage and a custom optical amplifier to allow independent spectrum shaping and energy tuning of the femtosecond pulse. The produced probe pulse is intense and spectrally narrow enough to allow single shot measurements of N 2 spectra at flame temperature with a good ro-vibrational resolution. An original and low-cost technique for NR background rejection based on the optimization of probe polarization and delay have been demonstrated. Spectra have been recorded in ambient air, CH 4 /air flame and C 2 H 2 /O 2 flame at 1 kHz repetition rate. The performance of the temperature measurement has been investigated versus polarization and delay of the probe pulse. State of the art 1% precisions have been demonstrated in the 300-3000 K temperature range. To our knowledge, this is the first time that hybrid fs/ps-CARS spectrum of N 2 is recorded in kHz single shot measurements in flames with a fine ro-vibrational resolution.
The achieved results open the way to several perspectives, concerning both applications and technical improvements. For instance, measurement of the rotational T rot and vibrational T vib temperatures in a single laser shot is possible thanks to the good resolution of the ro-vibrational spectra. This can be of great interest in order to probe non-equilibrium media such as plasma and supersonic flows. Furthermore, the authors are planning to study the influence of collisions in a high pressure burner (1-20 bar) in order to undertake a measurement campaign in a high pressure real combustion facility, in the near future. Moreover, it would be very interesting to test the single shot performances, by increasing the repetition rate up to 5 kHz, which is consistent with our laser and amplifier performances, in order to efficiently probe unsteady phenomena and, further on, access to the turbulence timescale. Finally, a more detailed study of the polarization effect on NR contribution would be of great interest.