Polarization suppression of the nonresonant background in femtosecond coherent anti-Stokes Raman scattering for flame thermometry at 5 kHz

Daniel R. Richardson; Devashish Bangar; Robert P. Lucht

doi:10.1364/OE.20.021495

1. Introduction

We report femtosecond (fs) coherent anti-Stokes Raman scattering (CARS) temperature measurements performed at 5 kHz while suppressing the nonresonant background using polarization techniques. Polarization suppression of the nonresonant background is a well established technique with nanosecond CARS. Performing nonresonant background suppressed measurements with chirped-probe-pulse (CPP) fs CARS is challenging due to the broadband nature of the pump and Stokes pulses as well as the complex interaction of the nonresonant background and the resonant CARS signal. By suppressing the nonresonant background, measurements are performed at zero probe time delay which are not obscured by the large nonresonant background which exists at this probe time delay. Such measurements aid in understanding the intricate physics of broadband pulse excitation of Raman transitions, and help reveal the influence of temperature and pulse timing. Understanding the physics of light-matter interactions with high peak power, short temporal duration, broadband laser pulses is essential to the development of new laser diagnostics techniques for reacting flow measurements. The measurements presented here will aid in the continued development of a high-fidelity theoretical model for comparison to future CPP fs CARS experimental measurements. The use of polarization suppression techniques with fs CARS may improve the accuracy of future measurements performed in turbulent flows by decreasing the influence of fluctuations in the nonresonant susceptibility, e.g. fluctuations in the gas phase composition at the probe volume.

Femtosecond laser systems with repetition rates on the order of several kHz and fundamental pulse energies on the order of several mJ are now commercially available. The use of such laser systems for measurements performed on a single-laser-shot basis has the potential to provide temporal resolution that cannot be achieved using conventional Nd:YAG laser systems with repetition rates on the order of 10 Hz. The use of ultrafast lasers diagnostics in reacting flows has been recently reviewed [1,2].

Coherent anti-Stokes Raman Scattering (CARS) is a third-order nonlinear optical process that has been used for a wide variety of measurements as it is sensitive to chemical composition, spatially resolved, and nonintrusive. A variety of ultrafast CARS diagnostic techniques and measurements have been demonstrated in reacting flows including: ps CARS [3,4], hybrid fs/ps rotational CARS for single-laser-shot flame thermometry [5], hybrid fs/ps CARS with an asymmetric probe pulse [6], hybrid fs/ps CARS at elevated pressure [7], probe-time-delayed ps CARS for hydrogen thermometry [8], single-beam CARS with a 7-fs pulse [9], one-dimensional quantitative measurements using ps CARS [10] and fs CARS [11]. Recently, CARS has been applied for measurements of glucose concentration levels in blood [12] and phonons in single-walled carbon nanotubes [13]. A wide variety of CARS microscopy techniques have been developed [14,15]. The broadband nature of ultrafast pulses has been recently used for combustion related measurements [16,17].

In CARS, the pump and Stokes fields excite Raman coherence in the medium, and the probe field is scattered from this coherence. Using broadband ultrafast pulses, many Raman transitions are efficiently excited [18]. The initial decay of the Raman coherence, due to the dephasing of the many Raman transitions, is sensitive to temperature but insensitive to the collisional environment up to pressures of several atmospheres [19]. The decay of the Raman coherence can be mapped to the frequency of the CARS signal by using a chirped-probe pulse (CPP) [20]. By comparing theoretical and experimental CPP fs CARS spectra, temperature measurements can be performed [21].

The nonresonant background generated by four-wave-mixing is spectrally and temporally overlapped with the resonant CARS signal. Typically, the nonresonant background is undesirable as it can obscure weak CARS signals or complicate CARS spectral analysis. The development of methods to suppress or eliminate the nonresonant background is an active area of research. Polarization suppression of the nonresonant background can be achieved by controlling the polarization of the pump, Stokes and probe pulses so that the nonresonant background and the CARS signal have different polarizations. The nonresonant background can then be blocked using an analyzer in the CARS signal beam path [22]. Other methods to eliminate the nonresonant background include coherent control of the phase and polarization of the input fields [23], preparation of an interface between resonant and nonresonant media [24], delaying the probe pulse [5,10,25,26], collecting radiation at limited angles [27], modifying the input laser field geometry [28], epi-detected CARS [29] (which is has not been demonstrated in gases), heterodyne techniques [30], and signal processing [31]. For this study, polarization suppression of the nonresonant background was chosen because the other techniques limit the pulse energies that can be used, are not feasible in gas-phase samples, or reduce the resonant CARS signal disproportionately, especially at high temperatures.

2. Experimental system

We report here single-laser-shot temperature measurements using CPP fs CARS with polarization suppression of the nonresonant background. The laser system is shown in Fig. 1 . The output of a 5-kHz, 60-fs, 2.4-mJ/pulse, 800-nm laser system (Legend Elite Duo, Coherent, Inc.) is split to form the Stokes and probe pulses as well as to pump an optical parametric amplifier (OPA). The frequency doubled output of the OPA near 675 nm forms the pump pulse. An energy level diagram for the CARS process with the Raman resonance of diatomic nitrogen near 2330 cm⁻¹ is shown in Fig. 2 . In the laser system, a pulse shaper (Silhouette, Coherent, Inc.) is located between the oscillator and amplifier. The pulse shaper modifies the spectral phase and amplitude of the pulses before the amplifier to achieve near Fourier transform limited pulses of the desired temporal duration after amplification. The probe pulse is directed through a 30-cm long glass rod to introduce chirp, with the red frequency components arriving at the probe volume first. The CPP duration is estimated to be 3 ps. Translation stages are used to control the relative timing of the pulses. The pump, Stokes, and probe pulse energies are controlled by half-wave plates and thin-film polarizers.

Fig. 1 Five-kHz fs laser system and chirped-probe pulse fs CARS experimental diagram.

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Fig. 2 CARS energy level diagram. The pump and Stokes pulses are tuned to the rovibrational Raman transitions of nitrogen near 2330 cm⁻¹.

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Nonresonant background suppression is achieved by using a half-wave plate to rotate the polarization of the Stokes pulse to 60° from vertical while the pump and probe pulses are vertically polarized. A calcite polarizer oriented at −60° from vertical is inserted in the CARS signal path to reject the nonresonant background. Other polarization arrangements can also be used to suppress the nonresonant background and are presented in [32], the key being that the nonresonant background and resonant CARS signal be generated with different polarizations. A folded BOXCARS arrangement is used so that the CARS signal could be spatially filtered [32]. The CARS signal is detected using a CCD camera (iXon, Andor Technology) after passing through a spectrometer. To record single-laser-shot spectra at 5 kHz, the active region of the CCD camera is cropped to 1064 x 50 pixels (13-µm pixel size). Atomic emission lamps are used to calibrate the wavelength of the detection system.

3. Model

The theoretical model used to fit the experimental spectra is similar to that reported in [33]. The electric fields are modeled using the measured spectrum of each pulse, ${| E (ω) |}_{m e a s u r e d}^{2}$ , and assuming a polynomial spectral phase

E (ω) = \sqrt{{| E (ω) |}_{m e a s u r e d}^{2}} \times \exp [j (A {(ω - ω_{o})}^{2} + B {(ω - ω_{o})}^{3})],

where

ω_{o}

is the central frequency. The small deviations from the Fourier transform limit in the pump and Stokes pulses are modeled using quadratic spectral phase polynomials, while the chirped-probe pulse spectral phase is modeled as a cubic polynomial to account for deviations from linear chirp from the glass rod. In other words,

B

in Eq. (1) is nonzero only for the probe pulse. The polynomial coefficients

A_{p u m p}, A_{S t o k e s}, A_{p r o b e}

and

B_{p r o b e}

are varied to obtain agreement between experimental and theoretical spectra.

The nonresonant polarization induced by the pump and Stokes electric fields is modeled as being proportional to the instantaneous product of the pump and Stokes fields,

P_{n r e s} (t) = α E_{p} (t) E_{s} (t) .

The total resonant polarization (Raman coherence) is modeled as the sum of each Raman coherence,

i

, oscillating at its natural frequency

ω_{i}

,

P_{r e s} (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)} .

The Raman cross sections,

d σ / d Ω

, are calculated using the Raman tensor invariants, and the population differences are calculated using the Boltzmann distribution. The finite lifetime of each Raman coherence,

Γ_{i}

, is insignificant due to the short time scales of the laser pulses. The scaling parameters

α

and

β

are used to account for different ratios of nonresonant and resonant polarization contributing to the CARS signal. The ratio of these scaling parameters is a fitting parameter. The resonant polarization for all transitions is allowed to be phase shifted from the nonresonant polarization by

ϕ

. The CARS signal is calculated as the product of the probe pulse with the sum of the nonresonant and resonant polarizations,

E_{C A R S} (t) = E_{p r} (t) [P_{r e s} (t) + P_{n r e s} (t)] .

The squared amplitude of the CARS electric field spectrum is compared to experimental CPP fs CARS spectra.

Analysis of experimental CPP fs CARS spectra occurs in two stages. First, a spectrum recorded at a known temperature is fit to determine laser parameters such as the polynomial coefficients for the spectral phase, the Stokes and probe time delays, and the phase shift of the Raman coherence. These values are then held fixed while single-laser-shot CPP fs CARS spectra are fit by varying the temperature and the resonant-to-nonresonant ratio $β / α$ . A small vertical scale factor and horizontal shift which operate on the experimental spectra are also fitting parameters. This theoretical model can be used to fit experimental spectra recorded with and without nonresonant background suppression.

4. Results and discussion

Measurements are first performed in room air and steady, atmospheric pressure, near-adiabatic hydrogen-air flames to test the accuracy of the technique and the stability of the laser system. Spectra recorded at three temperatures and two probe time delays with and without nonresonant background suppressed are shown in Fig. 3 . The spectra in Fig. 3 have been shifted horizontally so that the oscillations seen in the high-frequency portion of the spectra occur at the same frequencies. This is necessary as the experimental Stokes and probe timing and spatial overlap were adjusted between recording data with and without the CARS analyzer. When data is recorded at different CARS analyzer orientations, and no other experimental adjustments are made, the spectral peaks in the high-frequency portion of the spectra occur at the same location because the CARS signal at this frequency is due primarily to the Raman coherence and not the nonresonant background. The spacing of the spectral peaks in the high-frequency portion of the spectra is the same for data recorded with and without the CARS analyzer.

Fig. 3 The effect of nonresonant background suppression is shown by these single-laser-shot experimental CPP fs CARS spectra. The data shown with black solid lines and symbols were recorded while suppressing the nonresonant background, while the data shown with blue dashed lines and symbols was recorded with the CARS analyzer removed and all laser polarizations vertical. The temperatures and probe time delays are noted in the figure.

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The modulations seen in CPP fs CARS spectra result from interference between different frequency components of the CARS signal and the nonresonant background. The CARS signal frequency depends on the Raman transition as well as the frequency of the CPP which varies in time. In some situations, it may be advantageous to purposefully transmit some of the nonresonant background as the interference between the nonresonant background and the resonant signal can greatly increase the signal strength. For spectra recorded at the two lower temperatures shown in Fig. 3, the nonresonant background suppressed CARS spectral peaks are phase shifted compared to the normal CARS spectra in the middle portion of the spectra. However, in the high-frequency portion of the spectrum, the spectral peak spacing is the same. The phase shift is due to varying amounts of the nonresonant background and the associated interference with the CARS signal. In the high-frequency portion of the spectra, little nonresonant background is present, and so the modulations occur at the same frequency regardless of the analyzer orientation. The first prominent spectral feature at low frequency disappears when the nonresonant background is suppressed as this feature is largely due to the nonresonant background. For all temperatures, the nonresonant polarization exists only while the pump and Stokes pulses are present. For spectra recorded at 2382 K, the resonant polarization decays very quickly—on time scale of the pump and Stokes pulses due to the many Raman transitions with significant population. The CARS signals recorded at 2382 K look very similar for all analyzer orientations.

At room temperature and 0.0 ps probe time delay the modulation depth of the CARS spectra is greatest when the nonresonant background is suppressed. However, at 1189 K, the modulation depth is greatest when the CARS analyzer is removed. For spectra recorded at 2382 K, the orientation of the CARS analyzer did not affect the modulation depth.

The signal-to-noise ratio of the single-laser-shot CPP fs CARS spectra decreases with increasing probe time delay and temperature. The noise in the experimental spectra was steady with a value of approximately five counts for all experimental conditions. The noise in the spectra was calculated as the standard deviation of 100 pixels at a location without any CARS signal. The calculated signal–to–noise values are shown in Table 1 . The maximum signal levels before normalization for the spectra shown in Fig. 3 are proportional to the values shown in Table 1. The relative signal strengths of the spectra recorded with and without nonresonant background suppression cannot be directly compared in this table as the temporal and spatial overlap of the pump, Stokes and probe pulses was adjusted between recording the different data sets. For the data recorded at 298 and 1189 K, the signal-to-noise ratio is sufficiently large to not affect single-laser-shot fits. For the data recorded at 2382 K, the spectra recorded without nonresonant background suppression had significantly higher signal levels

Table 1. The calculated signal-to-noise ratios for the data shown in Fig. 3 recorded with nonresonant background suppression/without any suppression.

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The CARS signal strength decreases because of the following reasons. The nitrogen density decreases linearly as the temperature increases. Also, at higher temperatures the Raman coherence decays more quickly as there are more Raman transitions with significant population which contribute to the resonant polarization—each at a slightly different frequency. This is the phenomenon of frequency-spread dephasing. As the probe time delay is increased from zero, less of the probe pulse is scattered from the nonresonant polarization which exists only when the driving fields are present. At higher probe time delays the magnitude of the resonant polarization (Raman coherence) also decreases as the different Raman transitions dephase, leading to a decrease in the CARS signal amplitude.

Single-laser-shot spectra recorded with nonresonant background suppression in room air and steady near-adiabatic hydrogen-air flames are shown in Fig. 4 with the corresponding best-fit theoretical spectra. Single-laser-shot experimental spectra recorded with the CARS analyzer removed are also shown for comparison and have been horizontally shifted so that the oscillations in the high-frequency portion of the spectrum are well matched to the nonresonant background suppressed data.

Fig. 4 Single-laser-shot experimental spectra recorded while suppressing the nonresonant background (black solid line and symbols) and best-fit theoretical spectra (red solid line) are shown for four temperatures at a probe time delay of 0.6ps. Single-laser-shot experimental spectra recorded with the CARS analyzer removed (blue dashed line and symbols) are shown for comparison. The nominal experimental temperature and best-fit theoretical temperature are shown in each plot.

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A series of at least 1000 nonresonant background suppressed single-laser-shot spectra are fit to produce the histograms of best-fit temperatures shown in Fig. 5 . All flame data shown in Figs. 4 and 5 are fit using a single set of laser parameters obtained from fitting an average spectrum recorded at 2013 K. The room air data shown in Figs. 4 and 5 are fit using a set of laser parameters obtained from fitting an average spectra recorded in room air. For measurements performed in the flames, the deviation of the average measured temperature from the adiabatic flame temperature is less than 2.5% of the adiabatic flame temperature. This accuracy is very similar to that reported for fs CARS measurements performed without nonresonant background suppression. The precision of the nonresonant background suppressed temperature measurements is typically less than 3% of the mean temperature, which is slightly worse than fs CARS measurements reported without nonresonant background suppression [33]. This may be due to increased shot noise when the nonresonant background is suppressed.

Fig. 5 Histograms of best-fit temperatures for series of nonresonant background suppressed single-laser-shot spectra at a variety of temperatures. The nominal experimental temperature (adiabatic flame temperature for flames) and statics for each set of data are shown in the plots.

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Nonresonant background suppressed measurements are also performed in an unsteady hydrogen jet diffusion flame. The nozzle diameter for the hydrogen jet is 5 mm, and the velocity at the jet exit is approximately 2 m/s. Measurements are performed 3 mm above the nozzle exit at different radial locations. Fluctuations in CARS signal amplitude are seen as the unsteady flame front moved through the probe volume. Beam steering by the unsteady flame does not significantly inhibit the ability to record single-laser-shot spectra with high signal-to-noise ratios. Different from the single-laser-shot ultrafast CARS measurements reported in [5,21], the probe time delay used for these measurements is 0.0 ps (temporally overlapped with the pump and Stokes pulses) as the maximum resonant signal occurs at a probe time delay of 0.0 ps. Sufficient nonresonant background suppression is achieved using the CARS analyzer so that the large amount of nonresonant background present near zero probe time delay was not a hindrance.

Best-fit temperatures for a series of more than 1000 consecutive single-laser-shot spectra are shown in Fig. 6 . Nonresonant background suppressed single-laser-shot experimental CARS spectra recorded in the jet diffusion flame and the best-fit theoretical spectra are shown in Fig. 7 . The best-fit temperature varies continuously from 500 to 1800 K. Data shown in Figs. 6 and 7 are fit using a set of laser parameters obtained from fitting an average spectra recorded at 1210 K using a near-adiabatic hydrogen-air flame.

Fig. 6 Best-fit temperature for a series of nonresonant background suppressed single-laser-shot CPP fs CARS spectra recorded in a hydrogen jet diffusion flame.

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Fig. 7 Nonresonant background suppressed single-laser-shot experimental spectra (black) with the best-fit theoretical spectra (red) recorded at four different times. The best-fit theoretical temperature is shown for each spectrum.

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5. Conclusion

In conclusion, polarization suppression of the nonresonant background was used with CPP fs CARS to perform flame thermometry at 5 kHz. The single-laser-shot experimental spectra are compared to a theoretical model to determine temperature. The evolution of the Raman coherence after excitation by the broadband pump and Stokes pulses is more clearly apparent in these spectra due to suppression of the nonresonant background. Understanding the dependence of the Raman coherence on pump and Stokes pulse timing and temperature is important to the further development of a high-fidelity CPP fs CARS model. The high data rate of the measurement technique and ability to track large temperature fluctuations makes this technique a power tool for future studies of practical combustion devices where the turbulent frequencies are on the order of a few kHz or higher.

Acknowledgments

Funding for this research was provided by the U.S. Department of Energy, Division of Chemical Sciences, Geosciences, and Biosciences under Grant No. DE=FG02-03ER15391. Funding for the purchase of the ultrafast laser system was provided by the Air Force Office of Scientific Research under DURIP Grant No. FA9550-09-1-0387.

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	Temperature
Probe time delay	298 K	1189 K	2382 K
0.0ps	1000/990	72/66	30/71
0.6ps	1200/300	63/72	12/37

Polarization suppression of the nonresonant background in femtosecond coherent anti-Stokes Raman scattering for flame thermometry at 5 kHz

Abstract

1. Introduction

2. Experimental system

3. Model

4. Results and discussion

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (4)

Optics Express