Abstract

The theoretical framework for calculation of two-photon absorption cross sections for intermediate Hund’s cases (a) and (b) diatomic species is described in detail and applied toward the hydroxyl (OH) radical. Analytical expressions are derived for the 20 rotational branches that are present in the two-photon A Σ+2XΠ2 electronic transition. Calculation of the corresponding line strengths is necessary to permit accurate relative-concentration measurements obtained from the fluorescence induced by a broadband femtosecond excitation pulse. We demonstrate, in particular, that consideration of the temperature-dependent initial-state populations of OH is necessary to obtain accurate relative concentrations from observed two-photon-excitation based laser-induced-fluorescence measurements.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach, 1996).
  2. S. Kostka, S. Roy, P. J. Lakusta, T. R. Meyer, M. W. Renfro, J. R. Gord, and R. Branam, “Comparison of line-peak and line-scanning excitation in two-color laser-induced-fluorescence thermometry of OH,” Appl. Opt. 48, 6332–6343 (2009).
    [CrossRef] [PubMed]
  3. J. D. Miller, M. Slipchenko, T. R. Meyer, N. B. Jiang, W. R. Lempert, and J. R. Gord, “Ultrahigh-frame-rate OH fluorescence imaging in turbulent flames using a burst-mode optical parametric oscillator,” Opt. Lett. 34, 1309–1311 (2009).
    [CrossRef] [PubMed]
  4. I. Boxx, M. Stöhr, C. Carter, and W. Meier, “Temporally resolved planar measurements of transient phenomena in a partially pre-mixed swirl flame in a gas turbine model combustor,” Combust. Flame 157, 1510–1525 (2010).
    [CrossRef]
  5. C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
    [CrossRef]
  6. N. B. Jiang, R. A. Patton, W. R. Lempert, and J. A. Sutton, “Development of high-repetition rate CH PLIF imaging in turbulent non-premixed flames,” Proc. Combust. Inst. 33, 767–774(2011).
    [CrossRef]
  7. J. R. Gord, T. R. Meyer, and S. Roy, “Applications of ultrafast lasers for optical measurements in combusting flows,” Annu. Rev. Anal. Chem. 1, 663–687 (2008).
    [CrossRef]
  8. P. Beaud, P. P. Radi, D. Franzke, H. M. Frey, B. Mischler, A. P. Tzannis, and T. Gerber, “Picosecond investigation of the collisional deactivation of OH A∑+2 (v′=1, N′=4, 12) in an atmospheric-pressure flame,” Appl. Opt. 37, 3354–3367 (1998).
    [CrossRef]
  9. M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, “Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH,” Combust. Flame 123, 389–401 (2000).
    [CrossRef]
  10. M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
    [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, 5418–5426 (2001).
    [CrossRef]
  12. 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, 251112 (2006).
    [CrossRef]
  13. S. Roy, W. D. Kulatilaka, D. R. Richardson, R. P. Lucht, and J. R. Gord, “Gas-phase single-shot thermometry at 1 kHz using fs-CARS spectroscopy,” Opt. Lett. 34, 3857–3859 (2009).
    [CrossRef] [PubMed]
  14. S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
    [CrossRef]
  15. 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. Energy Combust. Sci. 36, 280–306 (2010).
    [CrossRef]
  16. 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, 2430–2432 (2010).
    [CrossRef] [PubMed]
  17. H. U. Stauffer, W. D. Kulatilaka, P. S. Hsu, J. R. Gord, and S. Roy, “Gas-phase thermometry using delayed-probe-pulse picosecond coherent anti-Stokes Raman scattering spectra of H2,” Appl. Opt. 50, A38–A48 (2011).
    [CrossRef] [PubMed]
  18. H. U. Stauffer, W. D. Kulatilaka, J. R. Gord, and S. Roy, “Laser-induced fluorescence detection of hydroxyl (OH) radical by femtosecond excitation,” Opt. Lett. 36, 1776–1778 (2011).
    [CrossRef] [PubMed]
  19. A. C. Eckbreth and T. J. Anderson, “Simultaneous rotational coherent anti-Stokes Raman-spectroscopy and coherent stokes Raman-spectroscopy with arbitrary pump Stokes spectral separation,” Opt. Lett. 11, 496–498 (1986).
    [CrossRef] [PubMed]
  20. Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
    [CrossRef]
  21. J. Kiefer, Z. S. Li, T. Seeger, A. Leipertz, and M. Aldén, “Planar laser-induced fluorescence of HCO for instantaneous flame front imaging in hydrocarbon flames,” Proc. Combust. Inst. 32, 921–928 (2009).
    [CrossRef]
  22. S. Roy, T. R. Meyer, and J. R. Gord, “Time-resolved dynamics of resonant and nonresonant broadband picosecond coherent anti-Stokes Raman scattering signals,” Appl. Phys. Lett. 87, 264103 (2005).
    [CrossRef]
  23. S. Roy, T. R. Meyer, and J. R. Gord, “Broadband coherent anti-Stokes Raman scattering spectroscopy of nitrogen using a picosecond modeless dye laser,” Opt. Lett. 30, 3222–3224 (2005).
    [CrossRef] [PubMed]
  24. 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, 1135–1140 (2007).
    [CrossRef] [PubMed]
  25. W. D. Kulatilaka, P. S. Hsu, H. U. Stauffer, J. R. Gord, and S. Roy, “Direct measurement of rotationally resolved H2Q-branch Raman coherence lifetimes using time-resolved picosecond coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 97, 081112 (2010).
    [CrossRef]
  26. N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
    [CrossRef] [PubMed]
  27. D. R. Crosley and G. P. Smith, “Two-photon spectroscopy of the A∑+2–X2Πi system of OH,” J. Chem. Phys. 79, 4764–4773(1983).
    [CrossRef]
  28. R. G. Bray and R. M. Hochstrasser, “Two-photon absorption by rotating diatomic molecules,” Mol. Phys. 31, 1199–1211(1976).
    [CrossRef]
  29. J. T. Hougen, The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules, NBS Monograph 115 (National Institute of Standards and Technology, 1970).
    [PubMed]
  30. R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner,” Combust. Flame 109, 323–331 (1997).
    [CrossRef]
  31. T. R. Meyer, S. Roy, T. N. Anderson, J. D. Miller, V. R. Katta, R. P. Lucht, and J. R. Gord, “Measurements of OH mole fraction and temperature up to 20 kHz by using a diode-laser-based UV absorption sensor,” Appl. Opt. 44, 6729–6740(2005).
    [CrossRef] [PubMed]
  32. R. N. Zare, Angular Momentum (Wiley, 1988).
  33. J. H. Van Vleck, “On σ-type doubling and electron spin in the spectra of diatomic molecules,” Phys. Rev. 33, 467–506 (1929).
    [CrossRef]
  34. R. S. Mulliken and A. Christy, “Λ-type doubling and electron configurations in diatomic molecules,” Phys. Rev. 38, 87–119(1931).
    [CrossRef]

2011

2010

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. Energy Combust. Sci. 36, 280–306 (2010).
[CrossRef]

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, 2430–2432 (2010).
[CrossRef] [PubMed]

I. Boxx, M. Stöhr, C. Carter, and W. Meier, “Temporally resolved planar measurements of transient phenomena in a partially pre-mixed swirl flame in a gas turbine model combustor,” Combust. Flame 157, 1510–1525 (2010).
[CrossRef]

C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
[CrossRef]

W. D. Kulatilaka, P. S. Hsu, H. U. Stauffer, J. R. Gord, and S. Roy, “Direct measurement of rotationally resolved H2Q-branch Raman coherence lifetimes using time-resolved picosecond coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 97, 081112 (2010).
[CrossRef]

2009

2008

J. R. Gord, T. R. Meyer, and S. Roy, “Applications of ultrafast lasers for optical measurements in combusting flows,” Annu. Rev. Anal. Chem. 1, 663–687 (2008).
[CrossRef]

2007

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

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, 1135–1140 (2007).
[CrossRef] [PubMed]

2006

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, 251112 (2006).
[CrossRef]

2005

2001

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

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, 5418–5426 (2001).
[CrossRef]

2000

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, “Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH,” Combust. Flame 123, 389–401 (2000).
[CrossRef]

1998

1997

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

1994

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
[CrossRef]

1986

1983

D. R. Crosley and G. P. Smith, “Two-photon spectroscopy of the A∑+2–X2Πi system of OH,” J. Chem. Phys. 79, 4764–4773(1983).
[CrossRef]

1976

R. G. Bray and R. M. Hochstrasser, “Two-photon absorption by rotating diatomic molecules,” Mol. Phys. 31, 1199–1211(1976).
[CrossRef]

1931

R. S. Mulliken and A. Christy, “Λ-type doubling and electron configurations in diatomic molecules,” Phys. Rev. 38, 87–119(1931).
[CrossRef]

1929

J. H. Van Vleck, “On σ-type doubling and electron spin in the spectra of diatomic molecules,” Phys. Rev. 33, 467–506 (1929).
[CrossRef]

Aldén, M.

J. Kiefer, Z. S. Li, T. Seeger, A. Leipertz, and M. Aldén, “Planar laser-induced fluorescence of HCO for instantaneous flame front imaging in hydrocarbon flames,” Proc. Combust. Inst. 32, 921–928 (2009).
[CrossRef]

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

Anderson, T. J.

Anderson, T. N.

Bai, X. S.

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

Beaud, P.

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, 5418–5426 (2001).
[CrossRef]

P. Beaud, P. P. Radi, D. Franzke, H. M. Frey, B. Mischler, A. P. Tzannis, and T. Gerber, “Picosecond investigation of the collisional deactivation of OH A∑+2 (v′=1, N′=4, 12) in an atmospheric-pressure flame,” Appl. Opt. 37, 3354–3367 (1998).
[CrossRef]

Bertagnolli, K. E.

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

Boxx, I.

I. Boxx, M. Stöhr, C. Carter, and W. Meier, “Temporally resolved planar measurements of transient phenomena in a partially pre-mixed swirl flame in a gas turbine model combustor,” Combust. Flame 157, 1510–1525 (2010).
[CrossRef]

Branam, R.

Bray, R. G.

R. G. Bray and R. M. Hochstrasser, “Two-photon absorption by rotating diatomic molecules,” Mol. Phys. 31, 1199–1211(1976).
[CrossRef]

Carter, C.

I. Boxx, M. Stöhr, C. Carter, and W. Meier, “Temporally resolved planar measurements of transient phenomena in a partially pre-mixed swirl flame in a gas turbine model combustor,” Combust. Flame 157, 1510–1525 (2010).
[CrossRef]

Christy, A.

R. S. Mulliken and A. Christy, “Λ-type doubling and electron configurations in diatomic molecules,” Phys. Rev. 38, 87–119(1931).
[CrossRef]

Crosley, D. R.

D. R. Crosley and G. P. Smith, “Two-photon spectroscopy of the A∑+2–X2Πi system of OH,” J. Chem. Phys. 79, 4764–4773(1983).
[CrossRef]

Dantus, M.

S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
[CrossRef]

Dayan, B.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Dreizler, A.

C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
[CrossRef]

Dudovich, N.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Eckbreth, A. C.

Faeder, S. M. G.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Franzke, D.

Frey, H. M.

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, 5418–5426 (2001).
[CrossRef]

P. Beaud, P. P. Radi, D. Franzke, H. M. Frey, B. Mischler, A. P. Tzannis, and T. Gerber, “Picosecond investigation of the collisional deactivation of OH A∑+2 (v′=1, N′=4, 12) in an atmospheric-pressure flame,” Appl. Opt. 37, 3354–3367 (1998).
[CrossRef]

Gerber, T.

Gord, J. R.

H. U. Stauffer, W. D. Kulatilaka, P. S. Hsu, J. R. Gord, and S. Roy, “Gas-phase thermometry using delayed-probe-pulse picosecond coherent anti-Stokes Raman scattering spectra of H2,” Appl. Opt. 50, A38–A48 (2011).
[CrossRef] [PubMed]

H. U. Stauffer, W. D. Kulatilaka, J. R. Gord, and S. Roy, “Laser-induced fluorescence detection of hydroxyl (OH) radical by femtosecond excitation,” Opt. Lett. 36, 1776–1778 (2011).
[CrossRef] [PubMed]

W. D. Kulatilaka, P. S. Hsu, H. U. Stauffer, J. R. Gord, and S. Roy, “Direct measurement of rotationally resolved H2Q-branch Raman coherence lifetimes using time-resolved picosecond coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 97, 081112 (2010).
[CrossRef]

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. Energy Combust. Sci. 36, 280–306 (2010).
[CrossRef]

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, 2430–2432 (2010).
[CrossRef] [PubMed]

S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
[CrossRef]

S. Roy, W. D. Kulatilaka, D. R. Richardson, R. P. Lucht, and J. R. Gord, “Gas-phase single-shot thermometry at 1 kHz using fs-CARS spectroscopy,” Opt. Lett. 34, 3857–3859 (2009).
[CrossRef] [PubMed]

S. Kostka, S. Roy, P. J. Lakusta, T. R. Meyer, M. W. Renfro, J. R. Gord, and R. Branam, “Comparison of line-peak and line-scanning excitation in two-color laser-induced-fluorescence thermometry of OH,” Appl. Opt. 48, 6332–6343 (2009).
[CrossRef] [PubMed]

J. D. Miller, M. Slipchenko, T. R. Meyer, N. B. Jiang, W. R. Lempert, and J. R. Gord, “Ultrahigh-frame-rate OH fluorescence imaging in turbulent flames using a burst-mode optical parametric oscillator,” Opt. Lett. 34, 1309–1311 (2009).
[CrossRef] [PubMed]

J. R. Gord, T. R. Meyer, and S. Roy, “Applications of ultrafast lasers for optical measurements in combusting flows,” Annu. Rev. Anal. Chem. 1, 663–687 (2008).
[CrossRef]

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, 1135–1140 (2007).
[CrossRef] [PubMed]

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, 251112 (2006).
[CrossRef]

S. Roy, T. R. Meyer, and J. R. Gord, “Time-resolved dynamics of resonant and nonresonant broadband picosecond coherent anti-Stokes Raman scattering signals,” Appl. Phys. Lett. 87, 264103 (2005).
[CrossRef]

S. Roy, T. R. Meyer, and J. R. Gord, “Broadband coherent anti-Stokes Raman scattering spectroscopy of nitrogen using a picosecond modeless dye laser,” Opt. Lett. 30, 3222–3224 (2005).
[CrossRef] [PubMed]

T. R. Meyer, S. Roy, T. N. Anderson, J. D. Miller, V. R. Katta, R. P. Lucht, and J. R. Gord, “Measurements of OH mole fraction and temperature up to 20 kHz by using a diode-laser-based UV absorption sensor,” Appl. Opt. 44, 6729–6740(2005).
[CrossRef] [PubMed]

Gordon, R. L.

C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
[CrossRef]

Gunaratne, T.

S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
[CrossRef]

Guttenfelder, W. A.

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, “Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH,” Combust. Flame 123, 389–401 (2000).
[CrossRef]

Hancock, R. D.

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

Heeger, C.

C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
[CrossRef]

Hochstrasser, R. M.

R. G. Bray and R. M. Hochstrasser, “Two-photon absorption by rotating diatomic molecules,” Mol. Phys. 31, 1199–1211(1976).
[CrossRef]

Hougen, J. T.

J. T. Hougen, The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules, NBS Monograph 115 (National Institute of Standards and Technology, 1970).
[PubMed]

Hsu, P. S.

H. U. Stauffer, W. D. Kulatilaka, P. S. Hsu, J. R. Gord, and S. Roy, “Gas-phase thermometry using delayed-probe-pulse picosecond coherent anti-Stokes Raman scattering spectra of H2,” Appl. Opt. 50, A38–A48 (2011).
[CrossRef] [PubMed]

W. D. Kulatilaka, P. S. Hsu, H. U. Stauffer, J. R. Gord, and S. Roy, “Direct measurement of rotationally resolved H2Q-branch Raman coherence lifetimes using time-resolved picosecond coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 97, 081112 (2010).
[CrossRef]

Jiang, N. B.

N. B. Jiang, R. A. Patton, W. R. Lempert, and J. A. Sutton, “Development of high-repetition rate CH PLIF imaging in turbulent non-premixed flames,” Proc. Combust. Inst. 33, 767–774(2011).
[CrossRef]

J. D. Miller, M. Slipchenko, T. R. Meyer, N. B. Jiang, W. R. Lempert, and J. R. Gord, “Ultrahigh-frame-rate OH fluorescence imaging in turbulent flames using a burst-mode optical parametric oscillator,” Opt. Lett. 34, 1309–1311 (2009).
[CrossRef] [PubMed]

Katta, V. R.

Kiefer, J.

J. Kiefer, Z. S. Li, T. Seeger, A. Leipertz, and M. Aldén, “Planar laser-induced fluorescence of HCO for instantaneous flame front imaging in hydrocarbon flames,” Proc. Combust. Inst. 32, 921–928 (2009).
[CrossRef]

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

King, G. B.

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, “Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH,” Combust. Flame 123, 389–401 (2000).
[CrossRef]

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
[CrossRef]

Klassen, M. S.

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
[CrossRef]

Kostka, S.

Kulatilaka, W. D.

Lakusta, P. J.

Lang, T.

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, 5418–5426 (2001).
[CrossRef]

Laurendeau, N. M.

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, “Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH,” Combust. Flame 123, 389–401 (2000).
[CrossRef]

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
[CrossRef]

Leipertz, A.

J. Kiefer, Z. S. Li, T. Seeger, A. Leipertz, and M. Aldén, “Planar laser-induced fluorescence of HCO for instantaneous flame front imaging in hydrocarbon flames,” Proc. Combust. Inst. 32, 921–928 (2009).
[CrossRef]

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

Lempert, W. R.

N. B. Jiang, R. A. Patton, W. R. Lempert, and J. A. Sutton, “Development of high-repetition rate CH PLIF imaging in turbulent non-premixed flames,” Proc. Combust. Inst. 33, 767–774(2011).
[CrossRef]

J. D. Miller, M. Slipchenko, T. R. Meyer, N. B. Jiang, W. R. Lempert, and J. R. Gord, “Ultrahigh-frame-rate OH fluorescence imaging in turbulent flames using a burst-mode optical parametric oscillator,” Opt. Lett. 34, 1309–1311 (2009).
[CrossRef] [PubMed]

Li, Z. S.

J. Kiefer, Z. S. Li, T. Seeger, A. Leipertz, and M. Aldén, “Planar laser-induced fluorescence of HCO for instantaneous flame front imaging in hydrocarbon flames,” Proc. Combust. Inst. 32, 921–928 (2009).
[CrossRef]

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

Linvin, M.

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

Lucht, R. P.

S. Roy, W. D. Kulatilaka, D. R. Richardson, R. P. Lucht, and J. R. Gord, “Gas-phase single-shot thermometry at 1 kHz using fs-CARS spectroscopy,” Opt. Lett. 34, 3857–3859 (2009).
[CrossRef] [PubMed]

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, 251112 (2006).
[CrossRef]

T. R. Meyer, S. Roy, T. N. Anderson, J. D. Miller, V. R. Katta, R. P. Lucht, and J. R. Gord, “Measurements of OH mole fraction and temperature up to 20 kHz by using a diode-laser-based UV absorption sensor,” Appl. Opt. 44, 6729–6740(2005).
[CrossRef] [PubMed]

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

Meier, W.

I. Boxx, M. Stöhr, C. Carter, and W. Meier, “Temporally resolved planar measurements of transient phenomena in a partially pre-mixed swirl flame in a gas turbine model combustor,” Combust. Flame 157, 1510–1525 (2010).
[CrossRef]

Meyer, T. R.

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, 2430–2432 (2010).
[CrossRef] [PubMed]

S. Kostka, S. Roy, P. J. Lakusta, T. R. Meyer, M. W. Renfro, J. R. Gord, and R. Branam, “Comparison of line-peak and line-scanning excitation in two-color laser-induced-fluorescence thermometry of OH,” Appl. Opt. 48, 6332–6343 (2009).
[CrossRef] [PubMed]

J. D. Miller, M. Slipchenko, T. R. Meyer, N. B. Jiang, W. R. Lempert, and J. R. Gord, “Ultrahigh-frame-rate OH fluorescence imaging in turbulent flames using a burst-mode optical parametric oscillator,” Opt. Lett. 34, 1309–1311 (2009).
[CrossRef] [PubMed]

J. R. Gord, T. R. Meyer, and S. Roy, “Applications of ultrafast lasers for optical measurements in combusting flows,” Annu. Rev. Anal. Chem. 1, 663–687 (2008).
[CrossRef]

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, 1135–1140 (2007).
[CrossRef] [PubMed]

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, 251112 (2006).
[CrossRef]

S. Roy, T. R. Meyer, and J. R. Gord, “Time-resolved dynamics of resonant and nonresonant broadband picosecond coherent anti-Stokes Raman scattering signals,” Appl. Phys. Lett. 87, 264103 (2005).
[CrossRef]

T. R. Meyer, S. Roy, T. N. Anderson, J. D. Miller, V. R. Katta, R. P. Lucht, and J. R. Gord, “Measurements of OH mole fraction and temperature up to 20 kHz by using a diode-laser-based UV absorption sensor,” Appl. Opt. 44, 6729–6740(2005).
[CrossRef] [PubMed]

S. Roy, T. R. Meyer, and J. R. Gord, “Broadband coherent anti-Stokes Raman scattering spectroscopy of nitrogen using a picosecond modeless dye laser,” Opt. Lett. 30, 3222–3224 (2005).
[CrossRef] [PubMed]

Miller, J. D.

Mischler, B.

Motzkus, M.

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, 5418–5426 (2001).
[CrossRef]

Mulliken, R. S.

R. S. Mulliken and A. Christy, “Λ-type doubling and electron configurations in diatomic molecules,” Phys. Rev. 38, 87–119(1931).
[CrossRef]

Patnaik, A. K.

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. Energy Combust. Sci. 36, 280–306 (2010).
[CrossRef]

Patton, R. A.

N. B. Jiang, R. A. Patton, W. R. Lempert, and J. A. Sutton, “Development of high-repetition rate CH PLIF imaging in turbulent non-premixed flames,” Proc. Combust. Inst. 33, 767–774(2011).
[CrossRef]

Pestov, D.

S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
[CrossRef]

Radi, P. P.

Reichardt, T. A.

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
[CrossRef]

Renfro, M. W.

S. Kostka, S. Roy, P. J. Lakusta, T. R. Meyer, M. W. Renfro, J. R. Gord, and R. Branam, “Comparison of line-peak and line-scanning excitation in two-color laser-induced-fluorescence thermometry of OH,” Appl. Opt. 48, 6332–6343 (2009).
[CrossRef] [PubMed]

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, “Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH,” Combust. Flame 123, 389–401 (2000).
[CrossRef]

Richardson, D. R.

Roy, S.

H. U. Stauffer, W. D. Kulatilaka, P. S. Hsu, J. R. Gord, and S. Roy, “Gas-phase thermometry using delayed-probe-pulse picosecond coherent anti-Stokes Raman scattering spectra of H2,” Appl. Opt. 50, A38–A48 (2011).
[CrossRef] [PubMed]

H. U. Stauffer, W. D. Kulatilaka, J. R. Gord, and S. Roy, “Laser-induced fluorescence detection of hydroxyl (OH) radical by femtosecond excitation,” Opt. Lett. 36, 1776–1778 (2011).
[CrossRef] [PubMed]

W. D. Kulatilaka, P. S. Hsu, H. U. Stauffer, J. R. Gord, and S. Roy, “Direct measurement of rotationally resolved H2Q-branch Raman coherence lifetimes using time-resolved picosecond coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 97, 081112 (2010).
[CrossRef]

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. Energy Combust. Sci. 36, 280–306 (2010).
[CrossRef]

S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
[CrossRef]

S. Roy, W. D. Kulatilaka, D. R. Richardson, R. P. Lucht, and J. R. Gord, “Gas-phase single-shot thermometry at 1 kHz using fs-CARS spectroscopy,” Opt. Lett. 34, 3857–3859 (2009).
[CrossRef] [PubMed]

S. Kostka, S. Roy, P. J. Lakusta, T. R. Meyer, M. W. Renfro, J. R. Gord, and R. Branam, “Comparison of line-peak and line-scanning excitation in two-color laser-induced-fluorescence thermometry of OH,” Appl. Opt. 48, 6332–6343 (2009).
[CrossRef] [PubMed]

J. R. Gord, T. R. Meyer, and S. Roy, “Applications of ultrafast lasers for optical measurements in combusting flows,” Annu. Rev. Anal. Chem. 1, 663–687 (2008).
[CrossRef]

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, 1135–1140 (2007).
[CrossRef] [PubMed]

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, 251112 (2006).
[CrossRef]

S. Roy, T. R. Meyer, and J. R. Gord, “Broadband coherent anti-Stokes Raman scattering spectroscopy of nitrogen using a picosecond modeless dye laser,” Opt. Lett. 30, 3222–3224 (2005).
[CrossRef] [PubMed]

S. Roy, T. R. Meyer, and J. R. Gord, “Time-resolved dynamics of resonant and nonresonant broadband picosecond coherent anti-Stokes Raman scattering signals,” Appl. Phys. Lett. 87, 264103 (2005).
[CrossRef]

T. R. Meyer, S. Roy, T. N. Anderson, J. D. Miller, V. R. Katta, R. P. Lucht, and J. R. Gord, “Measurements of OH mole fraction and temperature up to 20 kHz by using a diode-laser-based UV absorption sensor,” Appl. Opt. 44, 6729–6740(2005).
[CrossRef] [PubMed]

Sattelmayer, T.

C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
[CrossRef]

Seeger, T.

J. Kiefer, Z. S. Li, T. Seeger, A. Leipertz, and M. Aldén, “Planar laser-induced fluorescence of HCO for instantaneous flame front imaging in hydrocarbon flames,” Proc. Combust. Inst. 32, 921–928 (2009).
[CrossRef]

Silberberg, Y.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Slipchenko, M.

Slipchenko, M. N.

Smith, G. P.

D. R. Crosley and G. P. Smith, “Two-photon spectroscopy of the A∑+2–X2Πi system of OH,” J. Chem. Phys. 79, 4764–4773(1983).
[CrossRef]

Stauffer, H. U.

Stöhr, M.

I. Boxx, M. Stöhr, C. Carter, and W. Meier, “Temporally resolved planar measurements of transient phenomena in a partially pre-mixed swirl flame in a gas turbine model combustor,” Combust. Flame 157, 1510–1525 (2010).
[CrossRef]

Sutton, J. A.

N. B. Jiang, R. A. Patton, W. R. Lempert, and J. A. Sutton, “Development of high-repetition rate CH PLIF imaging in turbulent non-premixed flames,” Proc. Combust. Inst. 33, 767–774(2011).
[CrossRef]

Thompson, B. D.

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
[CrossRef]

Tummers, M. J.

C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
[CrossRef]

Tzannis, A. P.

Van Vleck, J. H.

J. H. Van Vleck, “On σ-type doubling and electron spin in the spectra of diatomic molecules,” Phys. Rev. 33, 467–506 (1929).
[CrossRef]

Wrzesinski, P.

S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
[CrossRef]

Zare, R. N.

R. N. Zare, Angular Momentum (Wiley, 1988).

Zetterberg, J.

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

Annu. Rev. Anal. Chem.

J. R. Gord, T. R. Meyer, and S. Roy, “Applications of ultrafast lasers for optical measurements in combusting flows,” Annu. Rev. Anal. Chem. 1, 663–687 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. Roy, T. R. Meyer, and J. R. Gord, “Time-resolved dynamics of resonant and nonresonant broadband picosecond coherent anti-Stokes Raman scattering signals,” Appl. Phys. Lett. 87, 264103 (2005).
[CrossRef]

W. D. Kulatilaka, P. S. Hsu, H. U. Stauffer, J. R. Gord, and S. Roy, “Direct measurement of rotationally resolved H2Q-branch Raman coherence lifetimes using time-resolved picosecond coherent anti-Stokes Raman scattering,” Appl. Phys. Lett. 97, 081112 (2010).
[CrossRef]

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, 251112 (2006).
[CrossRef]

S. Roy, P. Wrzesinski, D. Pestov, T. Gunaratne, M. Dantus, and J. R. Gord, “Single-beam coherent anti-Stokes Raman scattering spectroscopy of N2 using a shaped 7 fs laser pulse,” Appl. Phys. Lett. 95, 074102 (2009).
[CrossRef]

Appl. Spectrosc.

Combust. Flame

R. D. Hancock, K. E. Bertagnolli, and R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner,” Combust. Flame 109, 323–331 (1997).
[CrossRef]

I. Boxx, M. Stöhr, C. Carter, and W. Meier, “Temporally resolved planar measurements of transient phenomena in a partially pre-mixed swirl flame in a gas turbine model combustor,” Combust. Flame 157, 1510–1525 (2010).
[CrossRef]

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, “Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH,” Combust. Flame 123, 389–401 (2000).
[CrossRef]

Combust. Sci. Technol.

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, “Flame concentration measurements using picosecond time-resolved laser-induced fluorescence,” Combust. Sci. Technol. 97, 391–403 (1994).
[CrossRef]

Exp. Fluids

C. Heeger, R. L. Gordon, M. J. Tummers, T. Sattelmayer, and A. Dreizler, “Experimental analysis of flashback in lean premixed swirling flames: upstream flame propagation,” Exp. Fluids 49, 853–863 (2010).
[CrossRef]

J. Chem. Phys.

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, 5418–5426 (2001).
[CrossRef]

D. R. Crosley and G. P. Smith, “Two-photon spectroscopy of the A∑+2–X2Πi system of OH,” J. Chem. Phys. 79, 4764–4773(1983).
[CrossRef]

Mol. Phys.

R. G. Bray and R. M. Hochstrasser, “Two-photon absorption by rotating diatomic molecules,” Mol. Phys. 31, 1199–1211(1976).
[CrossRef]

Opt. Lett.

Phys. Rev.

J. H. Van Vleck, “On σ-type doubling and electron spin in the spectra of diatomic molecules,” Phys. Rev. 33, 467–506 (1929).
[CrossRef]

R. S. Mulliken and A. Christy, “Λ-type doubling and electron configurations in diatomic molecules,” Phys. Rev. 38, 87–119(1931).
[CrossRef]

Phys. Rev. Lett.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Proc. Combust. Inst.

Z. S. Li, J. Kiefer, J. Zetterberg, M. Linvin, A. Leipertz, X. S. Bai, and M. Aldén, “Development of improved PLIF CH detection using an Alexandrite laser for single-shot investigation of turbulent and lean flames,” Proc. Combust. Inst. 31, 727–735 (2007).
[CrossRef]

J. Kiefer, Z. S. Li, T. Seeger, A. Leipertz, and M. Aldén, “Planar laser-induced fluorescence of HCO for instantaneous flame front imaging in hydrocarbon flames,” Proc. Combust. Inst. 32, 921–928 (2009).
[CrossRef]

N. B. Jiang, R. A. Patton, W. R. Lempert, and J. A. Sutton, “Development of high-repetition rate CH PLIF imaging in turbulent non-premixed flames,” Proc. Combust. Inst. 33, 767–774(2011).
[CrossRef]

Prog. Energy Combust. Sci.

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. Energy Combust. Sci. 36, 280–306 (2010).
[CrossRef]

Other

J. T. Hougen, The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules, NBS Monograph 115 (National Institute of Standards and Technology, 1970).
[PubMed]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Gordon and Breach, 1996).

R. N. Zare, Angular Momentum (Wiley, 1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Potential energy curves for ground ( X Π 2 ) and first excited state ( A Σ + 2 ) OH. A degenerate NR two-photon excitation pathway for LIF excitation is shown for the 0–0 vibronic branch.

Fig. 2
Fig. 2

Broadband spectral contributions to two-photon transitions. Within the broadband-excitation pulse, multiple pairs of frequencies that are detuned by ± Δ relative to half of the two-photon transition frequency contribute to a given two-photon- allowed transition [such as the Q 1 (1) transition in the A Σ + 2 X 2 Π manifold of OH depicted here]. The relative contribution of this specific pair of detuned frequencies depends on the relative amplitudes and phases of the excitation-pulse electric field at these two frequencies.

Fig. 3
Fig. 3

Energy diagram depicting splitting of Λ doublets in the ground Π 2 state of OH. Calculated Δ ν has been exaggerated 50-fold for the purpose of clarity.

Fig. 4
Fig. 4

Calculated TPA stick spectrum over the 15,600 to 16,500 cm 1 spectral range for two-photon transitions of OH radical thermalized at 2400 K . A typical broadband spectrum (curve) associated with an fs-duration excitation pulse is shown for comparison purposes.

Fig. 5
Fig. 5

Changes in simulated TPA spectrum of OH with temperature. Simulated TPA spectra are shown in (b) for thermalized distributions at 1800 K and 2400 K ; these spectra have been convolved with a 0.35 cm 1 Lorentzian profile to mimic experimental linewidths that are expected under these conditions. A representative broadband-excitation pulse spectrum is also shown in (b). The difference between these two spectra is shown in (a) to emphasize the change in this excitation spectrum as the temperature decreases.

Fig. 6
Fig. 6

a) Adiabatic temperature, T ad , calculated for a C 2 H 4 –air flame as a function of the equivalence ratio, Φ. (b) Calculated probabilities for TPA of OH thermalized at T ad , integrated over the experimental broadband-pulse spectrum and normalized to the excitation probability at T = 2400 K . (c) Measured fluorescence intensity [corrected for the relative temperature-dependent sensitivities shown in panel (b)] for a C 2 H 4 –air flame as a function of Φ. Errors bars represent 2 standard deviations calculated from three replicate measurements. OH PLIF results (similar C 2 H 4 –air flame conditions) from Meyer et al.[31] are included for comparison purposes.

Fig. 7
Fig. 7

Schematic diagrammatic representation of allowed pathways for Σ + 2 Π 2 two-photon excitation in OH based on consecutive application of the one-photon selection rules discussed in Section 6. (a) TPA pathways for transitions into an F 1 Σ + 2 rovibrational manifold; this diagram depicts two-photon pathways associated with the branches labeled O 1 , P 1 , Q 1 , R 1 , and S 1 (corresponding to Δ J = 2 , 1 , 0, + 1 , + 2 ) and the satellite branches labeled O 12 N , P 12 O , Q 12 P , R 12 Q , and S 12 R (with the same Δ J correspondence). (b) TPA pathways for transitions into an F 2 Σ + 2 rovibrational manifold; this diagram depicts two-photon pathways associated with the branches labeled O 2 , P 2 , Q 2 , R 2 , and S 2 (corresponding to Δ J = 2 , 1 , 0, + 1 , + 2 ) and the satellite branches labeled O 21 P , P 21 Q , Q 21 R , R 21 S , and S 21 T (with the same Δ J correspondence). The two pathways contributing to the P 21 Q branch manifold, discussed explicitly in Appendix A, have been emphasized in this diagram.

Fig. 8
Fig. 8

Comparison of experimental and calculated line strengths for the R 2 rotational branch of OH as a function of ground-state total angular momentum quantum number, J . Experimental results are taken from Fig. 3 of Ref. [27]. Computational line strengths are calculated using the corresponding expression in Table 3 and scaled to match the line strength scaling depicted in Figs. 2 and 3 of Ref. [27].

Tables (3)

Tables Icon

Table 1 Important Symbols/Notation Introduced in the Text

Tables Icon

Table 2 Factors a Comprising the Nonvanishing Direction Cosine Matrix Elements for Diatomic Species, α β γ , Where β = X , Y , Z (Lab-Fixed Components) and γ = x , y , z (Molecule-Fixed Components)

Tables Icon

Table 3 Far-from-Resonance Two-Photon Relative Line Strengths for Σ + 2 Π 2 Transitions [Intermediate Hund’s Coupling Case (a)/(b) Molecule]

Equations (66)

Equations on this page are rendered with MathJax. Learn more.

P fi σ fi | E ˜ ( ω fi 2 + Δ ) · E ˜ ( ω fi 2 Δ ) · d Δ | 2 .
σ fi , β β = | n φ f | μ β | φ n φ n | μ β | φ i ( ω n i ω ) + i ( Γ n / 2 ) | 2 ,
σ fi , β β | n φ f | μ β | φ n φ n | μ β | φ i | 2 .
| Λ S Σ ; Ω J M = | Λ S Σ | Ω J M ,
H nr = H nr ° + A L · S ,
H r = B [ ( J x L x S x ) 2 + ( J y L y S y ) 2 ] = B [ ( J 2 J z 2 ) + ( S 2 S z 2 ) + ( L 2 L z 2 ) ] + B [ ( L + S + L S + ) ( J + L + J L + ) ( J + S + J S + ) ] ,
θ 2 | Λ S Σ ; Ω J M = 2 θ ( θ + 1 ) | Λ S Σ ; Ω J M ,
θ z | Λ S Σ ; Ω J M = ρ | Λ S Σ ; Ω J M ,
S ± | S Σ = [ ( S Σ ) ( S ± Σ + 1 ) ] 1 / 2 | S ( Σ ± 1 ) ;
J ± | Ω J = [ ( J ± Ω ) ( J Ω + 1 ) ] 1 / 2 | ( Ω 1 ) J .
H nr | Λ S Σ = ( E Λ S Σ ° + A 2 Λ S ) | Λ S Σ ,
ψ 0 , 1 2 ( J , M ) = | 0 1 2 1 2 | 1 2 J M ;
ψ 0 , 1 2 ( J , M ) = | 0 1 2 1 2 | 1 2 J M .
H nr = [ E Σ ° 0 0 E Σ ° ] ;
H r = 2 [ B Σ { ( J ) ( J + 1 ) + 1 4 + L , Σ 2 } B Σ ( J + 1 2 ) B Σ ( J + 1 2 ) B Σ { ( J ) ( J + 1 ) + 1 4 + L , Σ 2 } ] ,
φ 1 , Σ ( J , M ) = 2 1 / 2 { ψ 0 , 1 2 ( J , M ) + ψ 0 , 1 2 ( J , M ) } ;
φ 2 , Σ ( J , M ) = 2 1 / 2 { ψ 0 , 1 2 ( J , M ) ψ 0 , 1 2 ( J , M ) } ,
ε 1 , Σ ( J ) = E Σ ° + B Σ 2 L , Σ 2 + B Σ 2 [ ( J 1 2 ) ( J + 1 2 ) ] ;
ε 2 , Σ ( J ) = E Σ ° + B Σ 2 L , Σ 2 + B Σ 2 [ ( J + 1 2 ) ( J + 3 2 ) ] .
ε i , Σ ( N ) = E Σ + B Σ 2 [ ( N ) ( N + 1 ) ] ,
| ψ 1 , 3 2 ( J , M ) = | 1 1 2 1 2 | 3 2 J M ;
| ψ 1 , 1 2 ( J , M ) = | 1 1 2 1 2 | 1 2 J M ;
| ψ 1 , 3 2 ( J , M ) = | 1 1 2 1 2 | 3 2 J M ;
| ψ 1 , 1 2 ( J , M ) = | 1 1 2 1 2 | 1 2 J M .
H nr = [ [ M nr ] 0 0 [ M nr ] ] ;
H r = [ [ M r ] 0 0 [ M r ] ] ,
M nr = [ E Π ° + 1 2 A 2 0 0 E Π ° 1 2 A 2 ] ;
M r = 2 [ B Π { ( J ) ( J + 1 ) 7 4 + L , Π 2 } B Π [ ( J 1 2 ) ( J + 3 2 ) ] 1 / 2 B Π [ ( J 1 2 ) ( J + 3 2 ) ] 1 / 2 B Π { ( J ) ( J + 1 ) + 1 4 + L , Π 2 } ] .
ε 1 , Π ( J ) = E Π + B Π 2 { [ ( J + 1 2 ) 2 1 ] 1 2 U } ;
ε 2 , Π ( J ) = E Π + B Π 2 { [ ( J + 1 2 ) 2 1 ] + 1 2 U } ,
U = [ λ ( λ 4 ) + ( 2 J + 1 ) 2 ] 1 / 2 ,
φ 1 , Λ , Π ( J , M ) = 1 C 1 [ 2 [ ( J + 1 2 ) 2 1 ] 1 / 2 λ 2 + U ] Λ ;
φ 2 , Λ , Π ( J , M ) = 1 C 2 [ 2 [ ( J + 1 2 ) 2 1 ] 1 / 2 λ 2 U ] Λ ,
C k = { 2 U [ U + ( 1 ) ( k 1 ) ( λ 2 ) ] } 1 / 2 ; k = 1 , 2.
σ ^ x y | L Λ S Σ ; Ω J M = ± ( 1 ) ( L Λ + S Σ + J Ω ) | L Λ S Σ ; Ω J M ,
σ ^ x y | φ 1 , Σ + = ( 1 ) ( J 1 / 2 ) | φ 1 , Σ + = ( 1 ) N | φ 1 , Σ + ;
σ ^ x y | φ 2 , Σ + = ( 1 ) ( J + 1 / 2 ) | φ 2 , Σ + = ( 1 ) N | φ 2 , Σ +
| φ k , Π ± = 2 1 / 2 ( | φ k , + 1 , Π ± | φ k , 1 , Π ) .
σ ^ x y | φ k , Π ± = ± ( 1 ) ( J + 1 / 2 ) | φ k , Π ± .
σ ^ x y μ β = μ β ; β = X , Y , Z .
μ β = γ α β γ μ γ ; β = X , Y , Z ; γ = x , y , z ,
Ω J M | α β γ | Ω J M = f ( J ; J ) g γ ( J Ω ; J Ω ) h β ( J M ; J M ) .
μ Z = α Z z μ z + 1 2 ( α Z x α Z y ) ( μ x + i μ y ) + 1 2 ( α Z x + α Z y ) ( μ x i μ y ) .
σ ( J ) = M = J J σ ( J , M ) .
Δ ν = ( J + 1 2 ) [ ( p 2 + q ) ( ± 1 + 2 λ U ) + 2 q ( J 1 2 ) ( J + 3 2 ) U ] ,
p = p 0 [ 1 2 u ( N ( N 1 ) ) ] ;
q = q 0 [ 1 4 u ( N ( N 1 ) ) ] .
φ 2 , Σ + ( J , M ) | μ Z | φ 1 , Π ( J , M ) = 1 2 { ψ 0 , 1 2 ( J , M ) | ψ 0 , 1 2 ( J , M ) | } μ Z { | φ 1 , + 1 , Π ( J , M ) | φ 1 , 1 , Π ( J , M ) } ,
φ 2 , Σ + ( J , M ) | μ Z | φ 1 , Π ( J , M ) = 1 C 1 { 2 [ ( J + 1 2 ) 2 1 ] 1 / 2 I a + ( λ 2 + U ) I b } ,
I a = 1 2 × { ψ 0 , 1 2 ( J , M ) | ψ 0 , 1 2 ( J , M ) | } μ Z { | ψ 1 , 3 2 ( J , M ) | ψ 1 , 3 2 ( J , M ) } ;
I b = 1 2 × { ψ 0 , 1 2 ( J , M ) | ψ 0 , 1 2 ( J , M ) | } μ Z { | ψ 1 , 1 2 ( J , M ) | ψ 1 , 1 2 ( J , M ) } ,
T 1 = 1 2 ψ 0 , 1 2 ( J , M ) | μ Z | ψ 1 , 3 2 ( J , M ) ;
T 2 = 1 2 ψ 0 , 1 2 ( J , M ) | μ Z | ψ 1 , 3 2 ( J , M ) ;
T 3 = 1 2 ψ 0 , 1 2 ( J , M ) | μ Z | ψ 1 , 3 2 ( J , M ) ;
T 4 = 1 2 ψ 0 , 1 2 ( J , M ) | μ Z | ψ 1 , 3 2 ( J , M ) .
T 1 = 1 2 0 1 2 1 2 | ( μ x i μ y ) | 1 1 2 1 2 1 2 J M | ( α Z x + i α Z y ) | 3 2 J M = μ · ( 2 M ) [ ( J + 3 2 ) ( J 1 2 ) ] 1 / 2 4 J ( J + 1 ) δ M , M ,
T 4 = 1 2 0 1 2 1 2 | ( μ x + i μ y ) | 1 1 2 1 2 1 2 J M | ( α Z x i α Z y ) | 3 2 J M = μ · ( 2 M ) [ ( J + 3 2 ) ( J 1 2 ) ] 1 / 2 4 J ( J + 1 ) δ M , M ,
I a = μ · ( M ) [ ( J + 3 2 ) ( J 1 2 ) ] 1 / 2 J ( J + 1 ) δ M , M .
I b = μ · ( M ) [ ( J + 1 2 ) ( J + 1 2 ) ] 1 / 2 J ( J + 1 ) δ M , M .
φ 2 , Σ + ( J 1 , M ) | μ Z | φ 2 , Σ + ( J , M ) = 1 2 { ψ 0 , 1 2 ( J 1 , M ) | ψ 0 , 1 2 ( J 1 , M ) | } μ Z { | ψ 0 , 1 2 ( J , M ) | ψ 0 , 1 2 ( J , M ) } .
φ 2 , Σ + ( J 1 , M ) | μ Z | φ 2 , Σ + ( J , M ) = μ | | · [ ( J + M ) ( J M ) ] 1 / 2 2 J δ M , M .
φ 2 , Σ + ( J 1 , M ) | μ Z | φ 2 , Σ + ( J , M ) φ 2 , Σ + ( J , M ) | μ Z | φ 1 , Π ( J , M ) = μ μ | | · [ ( J + M ) ( J M ) ] 1 / 2 M 4 C 1 ( J ) 2 ( J + 1 ) { ( 2 J + 3 ) ( 2 J 1 ) ( λ 2 + U ) ( 2 J + 1 ) } δ M , M .
φ 2 , Σ + ( J 1 , M ) | μ Z | φ 1 , Σ + ( J 1 , M ) φ 1 , Σ + ( J 1 , M ) | μ Z | φ 1 , Π ( J , M ) = μ μ | | · [ ( J + M ) ( J M ) ] 1 2 M 4 C 1 ( J ) 2 ( J 1 ) { ( 2 J + 3 ) + ( λ 2 + U ) } δ M , M .
σ P 21 Q , Z Z ( J , M ) | n φ 2 , Σ + ( J 1 , M ) | μ Z | φ n φ n | μ Z | φ 1 , Π ( J , M ) | 2 M 2 ( J 2 M 2 ) 4 C 1 2 J 2 ( J 2 1 ) 2 { ( J 2 ) ( 2 J + 3 ) J ( λ 2 + U ) } 2 .
σ P 21 Q , Z Z ( J ) = M = ( J 1 ) J 1 σ P 21 Q , Z Z ( J , M ) .
S P 21 Q , Z Z ( J ) = ( 2 J 1 ) 60 ( J 1 ) J ( J + 1 ) × [ ( J 2 ) ( 2 J + 3 ) J ( λ 2 + U ) ] 2 C 1 2 .

Metrics