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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 5003–5010
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Interference-free gas-phase thermometry at elevated pressure using hybrid femtosecond/picosecond rotational coherent anti-Stokes Raman scattering

Joseph D. Miller, Chloe E. Dedic, Sukesh Roy, James R. Gord, and Terrence R. Meyer  »View Author Affiliations


Optics Express, Vol. 20, Issue 5, pp. 5003-5010 (2012)
http://dx.doi.org/10.1364/OE.20.005003


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Abstract

Rotational-level-dependent dephasing rates and nonresonant background can lead to significant uncertainties in coherent anti-Stokes Raman scattering (CARS) thermometry under high-pressure, low-temperature conditions if the gas composition is unknown. Hybrid femtosecond/picosecond rotational CARS is employed to minimize or eliminate the influence of collisions and nonresonant background for accurate, frequency-domain thermometry at elevated pressure. The ability to ignore these interferences and achieve thermometric errors of <5% is demonstrated for N2 and O2 at pressures up to 15 atm. Beyond 15 atm, the effects of collisions cannot be ignored but can be minimized using a short probe delay (~6.5 ps) after Raman excitation, thereby improving thermometric accuracy with a time- and frequency-resolved theoretical model.

© 2012 OSA

1. Introduction

As an alternative to time-domain detection, it is of interest to determine if measurements that are free of collisions and nonresonant-background can be achieved using frequency-domain thermometry at high pressure. Recently, the authors demonstrated a hybrid fs/ps CARS technique that employed 100-fs pump and Stokes pulses to induce coherent vibrational or pure rotational Raman oscillations in N2 while probing the molecular response using a frequency-narrowed, time-delayed 1–10 ps probe pulse [17

17. J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express 19(16), 15627–15640 (2011). [CrossRef] [PubMed]

20

20. J. D. Miller, S. Roy, J. R. Gord, and T. R. Meyer, “Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond∕picosecond coherent anti-Stokes Raman scattering,” J. Chem. Phys. 135(20), 201104 (2011). [CrossRef] [PubMed]

]. In this approach, a short (0.3–10 ps) probe-pulse delay was sufficient to avoid overlap with the pump and Stokes pulses to eliminate nonresonant background, while the transform-limited ps pulse allowed for single-shot frequency-domain detection of individual N2 rotational [17

17. J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express 19(16), 15627–15640 (2011). [CrossRef] [PubMed]

] or vibrational transitions [18

18. J. D. Miller, M. N. Slipchenko, T. R. Meyer, H. U. Stauffer, and J. R. Gord, “Hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering for high-speed gas-phase thermometry,” Opt. Lett. 35(14), 2430–2432 (2010). [CrossRef] [PubMed]

]. In the current work, we investigate the ability of hybrid fs/ps rotational coherent anti-Stokes Raman scattering (RCARS) to avoid the effects of collisions and nonresonant background for accurate, interference-free thermometry at high pressure. The ability to avoid collisional effects at high pressure is of particular interest for frequency-domain thermometry, which typically carries inherent sensitivity to rotational-level-dependent linewidths in the case of ns or ps CARS. The ability of the current approach to isolate individual rotational transitions enables detailed analysis of the effects of rotational-level-dependent dephasing rates on thermometric accuracy. Expanding the technique to include fs/ps RCARS thermometry of O2, we use a phenomenological model to compare the relative effects of collisions on N2 and O2 spectra for probe delays of 6.5 to 150 ps at elevated pressure. For conditions in which collisions cannot be avoided (beyond 15 atm), we evaluate the feasibility of improving temperature accuracy by minimizing the effects of collisions with short probe delays and including the collisional linewidth in a time- and frequency-resolved theoretical model.

2. Theory and experiment

A detailed theoretical treatment of hybrid fs/ps CARS and experimental description can be found elsewhere [17

17. J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express 19(16), 15627–15640 (2011). [CrossRef] [PubMed]

, 21

21. B. D. Prince, A. Chakraborty, B. M. Prince, and H. U. Stauffer, “Development of simultaneous frequency- and time-resolved coherent anti-Stokes Raman scattering for ultrafast detection of molecular Raman spectra,” J. Chem. Phys. 125(4), 044502 (2006). [CrossRef] [PubMed]

]. For pure S-branch transitions (Δv = 0, ΔJ = + 2), the molecular response from the pump (ωpump) and Stokes (ωStokes) pulses is treated phenomenologically as a function of time, t, in Eq. (1),
R(t)=IJ+2,J(T)eiωJ+2,JtΓJ+2,Jt
(1)
where each transition is assigned an intensity, IJ + 2,J, a frequency (s−1), ωJ + 2,J, and linewidth (s−1), ΓJ + 2,J [17

17. J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express 19(16), 15627–15640 (2011). [CrossRef] [PubMed]

, 21

21. B. D. Prince, A. Chakraborty, B. M. Prince, and H. U. Stauffer, “Development of simultaneous frequency- and time-resolved coherent anti-Stokes Raman scattering for ultrafast detection of molecular Raman spectra,” J. Chem. Phys. 125(4), 044502 (2006). [CrossRef] [PubMed]

]. The transition intensity IJ + 2,J is not a function of time, but is highly dependent on temperature, T. The response decays exponentially with a time constant τJ + 2,J = ΓJ + 2,J−1. The linewidth is highly temperature and pressure dependent, displaying a linear dependence on pressure and more complex inverse relationship with temperature [22

22. L. A. Rahn and R. E. Palmer, “Studies of nitrogen self-broadening at high-temperature with inverse Raman-spectroscopy,” J. Opt. Soc. Am. B 3(9), 1164–1169 (1986). [CrossRef]

]. Because low rotational states decay more rapidly than high rotational states, the spectral and temporal features of the CARS signal begin to mimic higher temperatures at long delay times [8

8. T. Seeger, J. Kiefer, A. Leipertz, B. D. Patterson, C. J. Kliewer, and T. B. Settersten, “Picosecond time-resolved pure-rotational coherent anti-Stokes Raman spectroscopy for N(2) thermometry,” Opt. Lett. 34(23), 3755–3757 (2009). [CrossRef] [PubMed]

, 17

17. J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express 19(16), 15627–15640 (2011). [CrossRef] [PubMed]

, 23

23. B. Lavorel, H. Tran, E. Hertz, O. Faucher, P. Joubert, M. Motzkus, T. Buckup, T. Lang, H. Skenderovi, G. Knopp, P. Beaud, and H. M. Frey, “Femtosecond Raman time-resolved molecular spectroscopy,” C. R. Phys. 5, 215–229 (2004). [CrossRef]

]. The resulting thermometric error is more pronounced at low temperature where the difference between linewidths of low and high rotational states is largest [8

8. T. Seeger, J. Kiefer, A. Leipertz, B. D. Patterson, C. J. Kliewer, and T. B. Settersten, “Picosecond time-resolved pure-rotational coherent anti-Stokes Raman spectroscopy for N(2) thermometry,” Opt. Lett. 34(23), 3755–3757 (2009). [CrossRef] [PubMed]

, 17

17. J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express 19(16), 15627–15640 (2011). [CrossRef] [PubMed]

]. At higher pressure, rapid collisional dephasing can also significantly enhance rotational energy transfer and require detection at short delay times for accurate interference-free thermometry.

N2 and O2 CARS spectra were recorded at 298 and 295 K, respectively, from 1 to 20 atm. The pure gases were pressurized in a cylindrical stainless-steel vessel, and the temperature was measured with a 1/16-inch diameter K-type thermocouple and pressure with a digital pressure gauge (0–500 ± 1.25 psi). The frequency-dispersed RCARS signal is detected using a 0.303-m spectrometer (1200 line/mm) with sufficient resolution for distinguishing individual rotational transitions. The signal can be numerically integrated over the entire S-branch (~10–200 cm−1) as given in Fig. 1
Fig. 1 Spectrally integrated hybrid fs/ps RCARS signals from 1 to 20 atm for N2–N2 collisions at 298 K, and O2–O2 collisions at 295 K. The solid lines are theoretical simulations and the data are normalized to the nonresonant background.
for N2 and O2 at pressures of 1, 2.5, 5, 10, 15, and 20 atm, or numerically integrated over a single transition.

3. Results and discussion

As noted earlier avoiding the effects of collisions is important when the gas composition is not known a priori, but at elevated pressure this requires that the probe pulse be shorter than and arrive sooner than 25 ps. To evaluate the potential for interference-free measurements from 1 to 20 atm, the thermometric error was investigated from a minimum probe delay of 6.5 ps (to avoid nonresonant background) to a maximum of 150 ps (typical of ps CARS with probe pulses of ~80 ps or higher). This investigation was performed by fitting the time-dependent spectra using a spectral database where the linewidth was set to zero in the molecular response function (Eq. (1)) for all rotational transitions. Best-fit temperatures are plotted as a function of probe delay in Figs. 3(a)
Fig. 3 (a) Best-fit temperatures from experimental spectra of N2 (at 298 K) neglecting collisional linewidths at pressures from 1 to 20 atm. Solid curve fits are based on Eq. (2) and dashed lines represent errors of ± 5%. (b) Corrected temperatures using MEG linewidths.
and 4(a)
Fig. 4 (a) Best-fit temperatures from experimental spectra of O2 (at 295 K) neglecting collisional linewidths at pressures from 1 to 20 atm. Solid curve fits are based on Eq. (2) and dashed lines represent errors of ± 5%. (b) Corrected temperatures using MEG linewidths.
. The constant solid line represents the actual temperature, and the constant dashed lines represent ± 5% error.

Near room temperature, the interference-free assumption is limited even for probe delays as short as 6.5 ps where the error increases to 9% at 20 atm, thus requiring corrections for the effects of collisions. In cases for which corrections are necessary, however, the current data indicate that the use of short probe delays significantly reduces the impact of collisions and minimizes the corresponding corrections for rotational-level-dependent dephasing with the time- and frequency-resolved theoretical model. As shown in Figs. 3(b) and 4(b), the theoretical simulation with linewidths from the MEG model predicts temperatures that are within 5% of the known temperatures for all pressures and probe delays. At shorter probe delays (<100 ps), the accuracy is improved to 2.5% for all pressures, and at the shortest probe delay (6.5 ps), the accuracy improves to 1% for all pressures. The fact that the theoretical fit is improved at shorter probe delays is indicative of reduced interference from collisional effects, which could be critical in environments with unknown species compositions. Since the composition is known in this case, the increase in thermometric error at 150 ps may be partially attributed to uncertainties in linewidths derived from the MEG model, as well as uncertainties due to the Q-branch approximation. By minimizing the necessary corrections, the fs/ps hybrid RCARS approach reduces the effects of errors associated with uncertainties in linewidth.

To characterize further the sensitivity to collisional dephasing and predict thermometric errors for arbitrary pressures and probe delays, we utilized a phenomenological model, Eq. (2), that captures the increase in thermometric error with pressure and time (as indicated by the solid lines in Figs. 3 and 4),
TApp(τ23,P)=(1a1P)Toexp[(a2P2+a3P)τ23]
(2)
where TApp is the apparent temperature with the collision-free assumption (K), τ23 is the probe delay (ps), To is the reference temperature (K), P is the pressure (atm), and ai are fit parameters. The coefficients have been determined with a fair degree of consistency from 1 to 20 atm and at room temperature for N2 (a1 = 7.36 × 10−3 atm−1, a2 = 4.257 × 10−5 atm−2ps−1, and a3 = 1.016 × 10−3 atm−1ps−1) and for O2 (a1 = 1.405 × 10−3 atm−1, a2 = 1.563 × 10−5 atm−2ps−1, and a3 = 4.77 × 10−4 atm−1ps−1). The reduced sensitivity of O2 to collisional effects at elevated pressure is quantified by the lower values of a2 and a3 in the exponential term in Eq. (2). This is due to greater uniformity in linewidth across the rotational energy levels of O2. This simple model can also be used to estimate the probe delay, τ23, and the associated minimum probe pulse width necessary for avoiding the effects of collisions at even higher pressures with frequency-domain ps or fs/ps CARS thermometry. At 20 atm, for example, the temperature shift is as high as 14.5 K/ps for N2 and 5.7 K/ps for O2. Without this knowledge, the use of longer probe delays or slight jitter between the preparation and probe pulses can cause significant variations in the apparent temperature (as high as 5% per ps).

4. Conclusions

In summary, we have quantified the effects of pressure on hybrid fs/ps CARS thermometric errors for both N2 and O2 up to 20 atm. Utilizing fs pump and Stokes pulses and a probe-pulse delay of 6.5 ps, it is possible to avoid the effects of collisions for pressures up to 15 atm and minimize corrections for collisional effects at even higher pressures. This can be achieved while avoiding nonresonant background and isolating individual rotational transitions for accurate frequency-domain thermometry. Future work will focus on testing the interference-free assumption at higher temperatures and pressures.

Acknowledgments

Funding was provided, in part, by the National Science Foundation (CBET-1056006, Dr. A. Atreya, Program Official) and Air Force Office of Scientific Research (Drs. T. Curcic and M. Birkan, Program Managers). J. Miller was supported by the National Science Foundation Graduate Fellowship Program. The authors also thank M. Johnson and B. Halls of Iowa State University and Drs. S. Danczyk and D. Talley of the Air Force Research Laboratory.

References and links

1.

S. Roy, J. R. Gord, and A. K. Patnaik, “Recent advances in coherent anti-Stokes Raman scattering spectroscopy: Fundamental developments and applications in reacting flows,” Prog. Energ. Combust. Sci. 36(2), 280–306 (2010). [CrossRef]

2.

T. Seeger, F. Beyrau, A. Brauer, and A. Leipertz, “High-pressure pure rotational CARS: comparison of temperature measurements with O2, N2 and synthetic air,” J. Raman Spectrosc. 34, 932–939 (2003). [CrossRef]

3.

F. Vestin, M. Afzelius, and P. E. Bengtsson, “Development of rotational CARS for combustion diagnostics using a polarization approach,” Proc. Combust. Inst. 31(1), 833–840 (2007). [CrossRef]

4.

F. M. Kamga and M. G. Sceats, “Pulse-sequenced coherent anti-Stokes Raman scattering: Method for suppression of the non-resonant background,” Opt. Lett. 5(3), 126–128 (1980). [CrossRef] [PubMed]

5.

H. M. Frey, P. Beaud, T. Gerber, B. Mischler, P. Radi, and A. P. Tzannis, “Femtosecond nonresonant degenerate four-wave mixing at atmospheric pressure and in a free jet,” Appl. Phys. B 68(4), 735–739 (1999). [CrossRef]

6.

P. Beaud, H. M. Frey, T. Lang, and M. Motzkus, “Flame thermometry by femtosecond CARS,” Chem. Phys. Lett. 344(3-4), 407–412 (2001). [CrossRef]

7.

T. R. Meyer, S. Roy, and J. R. Gord, “Improving signal-to-interference ratio in rich hydrocarbon-air flames using picosecond coherent anti-Stokes Raman scattering,” Appl. Spectrosc. 61(11), 1135–1140 (2007). [CrossRef] [PubMed]

8.

T. Seeger, J. Kiefer, A. Leipertz, B. D. Patterson, C. J. Kliewer, and T. B. Settersten, “Picosecond time-resolved pure-rotational coherent anti-Stokes Raman spectroscopy for N(2) thermometry,” Opt. Lett. 34(23), 3755–3757 (2009). [CrossRef] [PubMed]

9.

G. Knopp, P. Beaud, P. Radi, M. Tulej, B. Bougie, D. Cannavo, and T. Gerber, “Pressure-dependent N2 Q-branch fs-CARS measurements,” J. Raman Spectrosc. 33(11-12), 861–865 (2002). [CrossRef]

10.

T. Lang and M. Motzkus, “Determination of line shift coefficients with femtosecond time resolved CARS,” J. Raman Spectrosc. 31(1-2), 65–70 (2000). [CrossRef]

11.

T. Lang, M. Motzkus, H. M. Frey, and P. Beaud, “High resolution femtosecond coherent anti-Stokes Raman scattering: Determination of rotational constants, molecular anharmonicity, collisional line shifts, and temperature,” J. Chem. Phys. 115(12), 5418–5426 (2001). [CrossRef]

12.

P. Beaud and G. Knopp, “Scaling rotationally inelastic collisions with an effective angular momentum parameter,” Chem. Phys. Lett. 371(1-2), 194–201 (2003). [CrossRef]

13.

P. Beaud, T. Gerber, P. Radi, M. Tulej, and G. Knopp, “Rotationally inelastic collisions between N2 and rare gases: An extension of the angular momentum scaling law,” Chem. Phys. Lett. 373(3-4), 251–257 (2003). [CrossRef]

14.

G. Knopp, P. Radi, M. Tulej, T. Gerber, and P. Beaud, “Collision induced rotational energy transfer probed by time-resolved coherent anti-Stokes Raman scattering,” J. Chem. Phys. 118(18), 8223–8233 (2003). [CrossRef]

15.

T. Lang and M. Motzkus, “Single-shot femtosecond coherent anti-Stokes Raman scattering thermometry,” J. Opt. Soc. Am. B 19(2), 340–344 (2002). [CrossRef]

16.

R. P. Lucht, S. Roy, T. R. Meyer, and J. R. Gord, “Femtosecond coherent anti-Stokes Raman scattering measurement of gas temperatures from frequency-spread dephasing of the Raman coherence,” Appl. Phys. Lett. 89(25), 251112 (2006). [CrossRef]

17.

J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express 19(16), 15627–15640 (2011). [CrossRef] [PubMed]

18.

J. D. Miller, M. N. Slipchenko, T. R. Meyer, H. U. Stauffer, and J. R. Gord, “Hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering for high-speed gas-phase thermometry,” Opt. Lett. 35(14), 2430–2432 (2010). [CrossRef] [PubMed]

19.

J. D. Miller, M. N. Slipchenko, and T. R. Meyer, “Probe-pulse optimization for nonresonant suppression in hybrid fs/ps coherent anti-Stokes Raman scattering at high temperature,” Opt. Express 19(14), 13326–13333 (2011). [CrossRef] [PubMed]

20.

J. D. Miller, S. Roy, J. R. Gord, and T. R. Meyer, “Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond∕picosecond coherent anti-Stokes Raman scattering,” J. Chem. Phys. 135(20), 201104 (2011). [CrossRef] [PubMed]

21.

B. D. Prince, A. Chakraborty, B. M. Prince, and H. U. Stauffer, “Development of simultaneous frequency- and time-resolved coherent anti-Stokes Raman scattering for ultrafast detection of molecular Raman spectra,” J. Chem. Phys. 125(4), 044502 (2006). [CrossRef] [PubMed]

22.

L. A. Rahn and R. E. Palmer, “Studies of nitrogen self-broadening at high-temperature with inverse Raman-spectroscopy,” J. Opt. Soc. Am. B 3(9), 1164–1169 (1986). [CrossRef]

23.

B. Lavorel, H. Tran, E. Hertz, O. Faucher, P. Joubert, M. Motzkus, T. Buckup, T. Lang, H. Skenderovi, G. Knopp, P. Beaud, and H. M. Frey, “Femtosecond Raman time-resolved molecular spectroscopy,” C. R. Phys. 5, 215–229 (2004). [CrossRef]

24.

L. Martinsson, P. E. Bengtsson, M. Alden, S. Kroll, and J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes-Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys. 99(4), 2466–2477 (1993). [CrossRef]

25.

M. Afzelius, P. E. Bengtsson, J. Bood, J. Bonamy, F. Chaussard, H. Berger, and T. Dreier, “Dual-broadband rotational CARS modelling of nitrogen at pressures up to 9 MPa II. Rotaitonal Raman linewidths,” Appl. Phys. B 75(6-7), 771–778 (2002). [CrossRef]

OCIS Codes
(280.1740) Remote sensing and sensors : Combustion diagnostics
(300.6230) Spectroscopy : Spectroscopy, coherent anti-Stokes Raman scattering
(300.6530) Spectroscopy : Spectroscopy, ultrafast
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.5390) Ultrafast optics : Picosecond phenomena

ToC Category:
Sensors

History
Original Manuscript: November 7, 2011
Revised Manuscript: December 20, 2011
Manuscript Accepted: December 23, 2011
Published: February 13, 2012

Citation
Joseph D. Miller, Chloe E. Dedic, Sukesh Roy, James R. Gord, and Terrence R. Meyer, "Interference-free gas-phase thermometry at elevated pressure using hybrid femtosecond/picosecond rotational coherent anti-Stokes Raman scattering," Opt. Express 20, 5003-5010 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5003


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References

  1. S. Roy, J. R. Gord, and A. K. Patnaik, “Recent advances in coherent anti-Stokes Raman scattering spectroscopy: Fundamental developments and applications in reacting flows,” Prog. Energ. Combust. Sci.36(2), 280–306 (2010). [CrossRef]
  2. T. Seeger, F. Beyrau, A. Brauer, and A. Leipertz, “High-pressure pure rotational CARS: comparison of temperature measurements with O2, N2 and synthetic air,” J. Raman Spectrosc.34, 932–939 (2003). [CrossRef]
  3. F. Vestin, M. Afzelius, and P. E. Bengtsson, “Development of rotational CARS for combustion diagnostics using a polarization approach,” Proc. Combust. Inst.31(1), 833–840 (2007). [CrossRef]
  4. F. M. Kamga and M. G. Sceats, “Pulse-sequenced coherent anti-Stokes Raman scattering: Method for suppression of the non-resonant background,” Opt. Lett.5(3), 126–128 (1980). [CrossRef] [PubMed]
  5. H. M. Frey, P. Beaud, T. Gerber, B. Mischler, P. Radi, and A. P. Tzannis, “Femtosecond nonresonant degenerate four-wave mixing at atmospheric pressure and in a free jet,” Appl. Phys. B68(4), 735–739 (1999). [CrossRef]
  6. P. Beaud, H. M. Frey, T. Lang, and M. Motzkus, “Flame thermometry by femtosecond CARS,” Chem. Phys. Lett.344(3-4), 407–412 (2001). [CrossRef]
  7. T. R. Meyer, S. Roy, and J. R. Gord, “Improving signal-to-interference ratio in rich hydrocarbon-air flames using picosecond coherent anti-Stokes Raman scattering,” Appl. Spectrosc.61(11), 1135–1140 (2007). [CrossRef] [PubMed]
  8. T. Seeger, J. Kiefer, A. Leipertz, B. D. Patterson, C. J. Kliewer, and T. B. Settersten, “Picosecond time-resolved pure-rotational coherent anti-Stokes Raman spectroscopy for N(2) thermometry,” Opt. Lett.34(23), 3755–3757 (2009). [CrossRef] [PubMed]
  9. G. Knopp, P. Beaud, P. Radi, M. Tulej, B. Bougie, D. Cannavo, and T. Gerber, “Pressure-dependent N2 Q-branch fs-CARS measurements,” J. Raman Spectrosc.33(11-12), 861–865 (2002). [CrossRef]
  10. T. Lang and M. Motzkus, “Determination of line shift coefficients with femtosecond time resolved CARS,” J. Raman Spectrosc.31(1-2), 65–70 (2000). [CrossRef]
  11. T. Lang, M. Motzkus, H. M. Frey, and P. Beaud, “High resolution femtosecond coherent anti-Stokes Raman scattering: Determination of rotational constants, molecular anharmonicity, collisional line shifts, and temperature,” J. Chem. Phys.115(12), 5418–5426 (2001). [CrossRef]
  12. P. Beaud and G. Knopp, “Scaling rotationally inelastic collisions with an effective angular momentum parameter,” Chem. Phys. Lett.371(1-2), 194–201 (2003). [CrossRef]
  13. P. Beaud, T. Gerber, P. Radi, M. Tulej, and G. Knopp, “Rotationally inelastic collisions between N2 and rare gases: An extension of the angular momentum scaling law,” Chem. Phys. Lett.373(3-4), 251–257 (2003). [CrossRef]
  14. G. Knopp, P. Radi, M. Tulej, T. Gerber, and P. Beaud, “Collision induced rotational energy transfer probed by time-resolved coherent anti-Stokes Raman scattering,” J. Chem. Phys.118(18), 8223–8233 (2003). [CrossRef]
  15. T. Lang and M. Motzkus, “Single-shot femtosecond coherent anti-Stokes Raman scattering thermometry,” J. Opt. Soc. Am. B19(2), 340–344 (2002). [CrossRef]
  16. R. P. Lucht, S. Roy, T. R. Meyer, and J. R. Gord, “Femtosecond coherent anti-Stokes Raman scattering measurement of gas temperatures from frequency-spread dephasing of the Raman coherence,” Appl. Phys. Lett.89(25), 251112 (2006). [CrossRef]
  17. J. D. Miller, S. Roy, M. N. Slipchenko, J. R. Gord, and T. R. Meyer, “Single-shot gas-phase thermometry using pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering,” Opt. Express19(16), 15627–15640 (2011). [CrossRef] [PubMed]
  18. J. D. Miller, M. N. Slipchenko, T. R. Meyer, H. U. Stauffer, and J. R. Gord, “Hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering for high-speed gas-phase thermometry,” Opt. Lett.35(14), 2430–2432 (2010). [CrossRef] [PubMed]
  19. J. D. Miller, M. N. Slipchenko, and T. R. Meyer, “Probe-pulse optimization for nonresonant suppression in hybrid fs/ps coherent anti-Stokes Raman scattering at high temperature,” Opt. Express19(14), 13326–13333 (2011). [CrossRef] [PubMed]
  20. J. D. Miller, S. Roy, J. R. Gord, and T. R. Meyer, “Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond∕picosecond coherent anti-Stokes Raman scattering,” J. Chem. Phys.135(20), 201104 (2011). [CrossRef] [PubMed]
  21. B. D. Prince, A. Chakraborty, B. M. Prince, and H. U. Stauffer, “Development of simultaneous frequency- and time-resolved coherent anti-Stokes Raman scattering for ultrafast detection of molecular Raman spectra,” J. Chem. Phys.125(4), 044502 (2006). [CrossRef] [PubMed]
  22. L. A. Rahn and R. E. Palmer, “Studies of nitrogen self-broadening at high-temperature with inverse Raman-spectroscopy,” J. Opt. Soc. Am. B3(9), 1164–1169 (1986). [CrossRef]
  23. B. Lavorel, H. Tran, E. Hertz, O. Faucher, P. Joubert, M. Motzkus, T. Buckup, T. Lang, H. Skenderovi, G. Knopp, P. Beaud, and H. M. Frey, “Femtosecond Raman time-resolved molecular spectroscopy,” C. R. Phys.5, 215–229 (2004). [CrossRef]
  24. L. Martinsson, P. E. Bengtsson, M. Alden, S. Kroll, and J. Bonamy, “A test of different rotational Raman linewidth models: accuracy of rotational coherent anti-Stokes-Raman scattering thermometry in nitrogen from 295 to 1850 K,” J. Chem. Phys.99(4), 2466–2477 (1993). [CrossRef]
  25. M. Afzelius, P. E. Bengtsson, J. Bood, J. Bonamy, F. Chaussard, H. Berger, and T. Dreier, “Dual-broadband rotational CARS modelling of nitrogen at pressures up to 9 MPa II. Rotaitonal Raman linewidths,” Appl. Phys. B75(6-7), 771–778 (2002). [CrossRef]

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