Abstract

Broadband and dual-broadband coherent anti-Stokes Raman scattering (CARS) are widely established tools for nonintrusive gas diagnostics. Up to now the investigations have been mainly performed for electronic nonresonant conditions of the gas species of interest. We report on the enhancement of the O2–N2 detection limit of dual-broadband pure rotational CARS by shifting the wavelength of the narrowband pump laser from the commonly used 532–266 nm. This enhancement is caused when the Schumann–Runge absorption band is approached near 176 nm. The principal concept of this experiment, i.e., covering the Raman resonance with a single- or dual-broadband combination of lasers in the visible range and moving only the narrowband probe laser near or directly into electronic resonant conditions in the UV range, should also be applicable to broadband CARS experiments to directly exploit electronic resonance effects for the purpose of single-shot concentration measurements of minority species. To quantify the enhancement in O2 sensitivity, comparative measurements at both a 266 and a 532 nm narrowband pump laser wavelength are presented, employing a 4-dicyanomethylene-2-methyl-6-(p-dimethylaminostyryl)-4H-pyram (DCM) dye laser as a broadband laser source at 635 nm. An increase of ≈ 13% in the ratio of the rotational CARS cross sections of O2 and N2 was obtained. The broad spectral width of the CARS excitation profile was approximately equal for both setups. Further enhancement should be achievable by shifting the narrowband pump laser closer toward 176 nm, for example, with a frequency-doubled optical parametric oscillator or an excimer laser. The principal concept of this experiment should also be applicable to broadband CARS experiments to directly exploit electronic resonance effects of the narrowband pump laser with electronic transitions of minority species for the purpose of single-shot concentration measurements of those species.

© 2005 Optical Society of America

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  1. B. Attal-Tretout, P. Bouchardy, “Detection of the OH radical in flames by resonance CARS,” Rech. Aerosp. 5, 19–38 (1987).
  2. B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
    [CrossRef]
  3. B. Attal, D. Debarre, K. Mullerdethlefs, J. P. E. Taran, “Resonance-enhanced coherent anti-Stokes Raman-scattering in C2,” Rev. Phys. Appl. 18, 39–50 (1983).
    [CrossRef]
  4. T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
    [CrossRef]
  5. T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
    [CrossRef]
  6. S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
    [CrossRef]
  7. W. K. Bischel, G. Black, “Wavelength dependence of the Raman scattering cross sections from 200–600 nm,” in Excimer Lasers, K. Rhodes, H. Egger, H. Pummer, eds. (American Institute of Physics, 1983), pp. 181–187.
  8. G. W. Faris, R. A. Copeland, “Ratio of oxygen and nitrogen Raman cross sections in the ultraviolet,” Appl. Opt. 36, 2684–2685 (1997).
    [CrossRef] [PubMed]
  9. J. A. Wehrmeyer, T. S. Cheng, R. W. Pitz, “Raman scattering measurements in flames using a tunable KrF excimer laser,” Appl. Opt. 31, 1495–1504 (1992).
    [CrossRef] [PubMed]
  10. P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kroll, “Rotational CARS thermometry in sooting flames,” Comb. Sci. Technol. 81, 129–140 (1992).
    [CrossRef]
  11. R. J. Santoro, C. R. Shaddix, “Laser-induced incandescence,” in Applied Combustion Diagnostics, K. Kohse Höinghaus, J. Jeffries, eds. (Taylor & Francis, 2002), pp. 252–286.
  12. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon & Breach, 1996), Vol. 3.
  13. N. Bloembergen, H. Lotem, R. T. Lynch, “Lineshapes in coherent resonant Raman scattering,” Indian J. Pure Appl. Phys. 16, 151–158 (1978).
  14. S. A. J. Druet, B. Attal, T. K. Gustafson, J.-P. E. Taran, “Electronic resonance enhancement of coherent anti-Stokes Raman scattering,” Phys. Rev. A 18, 1529–1557 (1978).
    [CrossRef]
  15. S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
    [CrossRef]
  16. Y. Prior, “A complete expression for the third-order susceptibility (χ(3))—perturbative and diagrammatic approaches,” IEEE J. Quantum Electron. 20, 37–42 (1984).
    [CrossRef]
  17. M. Weissbluth, Photon-Atom Interactions (Academic, 1988).
  18. M. Schenk, Simultane Temperatur- und Konzentrationsmes-sung in binären und ternären Gemischen mittels Rotations-CARS-Spektroskopie, Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, 2000), Vol. 2000.2.
  19. J. W. Nibler, G. V. Knighten, “Coherent anti-Stokes Raman spectroscopy,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, 1979), Vol. 11, pp. 253–299.
    [CrossRef]
  20. A. Thumann, M. Schenk, J. Jonuscheit, T. Seeger, A. Leipertz, “Simultaneous temperature and relative nitrogen-oxygen concentration measurements in air with pure rotational coherent anti-Stokes-Raman scattering for temperatures to as high as 2050 K,” Appl. Opt. 36, 3500–3505 (1997).
    [CrossRef] [PubMed]
  21. A. C. Eckbreth, “BOXCARS: crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
    [CrossRef]
  22. E. Magens, Nutzung von Rotations-CARS zur Temperaturund Konzentrationsmessung in Flammen, Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, 1993), Vol. 93.2.
  23. D. A. Greenhalgh, “Quantitative CARS spectroscopy,” in Advances in Non-Linear Spectroscopy, R. J. H. Clark, R. E. Hester, eds. (Wiley, 1988), Vol. 15, pp. 193–251.
  24. A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
    [CrossRef]
  25. L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
    [CrossRef]
  26. G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
    [CrossRef]
  27. M. Bérard, P. Lallemand, J. P. Cebe, M. Giraud, “Experimental and theoretical analysis of the temperature dependence of rotational Raman linewidths of oxygen,” J. Chem. Phys. 78, 672–687 (1983).
    [CrossRef]
  28. A. Thumann, Temperaturbestimmung mittels der Kohärenten-Anti-Stokes-Raman-Streuung (CARS) unter Berücksichtigung des Druckeinflusses und nichteinheitlicher Temperaturverhältnisse im Meβvolumen, Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, 1997), Vol. 97.4.
  29. M. Woyde, “Temperaturbestimmung hoher genauigkeit mit CARS in hochdruckverbrennungssystemen,” Ph.D. dissertation (Universität Stuttgart, 1992).
  30. L. Martinsson, “Theoretical development of rotational CARS for combustion diagnostics,” Ph.D. dissertation (Lund Institute of Technology, 1994).
  31. V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
    [CrossRef]
  32. V. Alekeyev, I. Sobelman, “Influence of collisions on stimulated random scattering in gases,” Sov. Phys. JETP 28, 991–994 (1969).
  33. J. D. Drake, “Rotational Raman intensity-correction factors due to vibrational anharmonicity: their effect on temperature measurements,” Opt. Lett. 7, 440–441 (1982).
    [CrossRef] [PubMed]
  34. T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
    [CrossRef]
  35. M. Afzelius, P. E. Bengtsson, “Dual-broadband rotational CARS modelling of nitrogen at pressures up to 9 MPa. I. Interbranch interference effect,” Appl. Phys. B 75, 763–769 (2002).
    [CrossRef]
  36. T. Seeger, F. Beyrau, A. Bräuer, A. Leipertz, “High-pressure pure rotational CARS: comparison of temperature measurements with O2N2and synthetic air,” J. Raman Spectrosc. 34, 932–939 (2003).
    [CrossRef]
  37. M. Schenk, A. Thumann, T. Seeger, A. Leipertz, “Pure rotational coherent anti-Stokes Raman scattering: comparison of evaluation techniques for determining single-shot temperature and relative N2-O2concentration,” Appl. Opt. 37, 5659–5671 (1998).
    [CrossRef]

2003 (2)

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

T. Seeger, F. Beyrau, A. Bräuer, A. Leipertz, “High-pressure pure rotational CARS: comparison of temperature measurements with O2N2and synthetic air,” J. Raman Spectrosc. 34, 932–939 (2003).
[CrossRef]

2002 (1)

M. Afzelius, P. E. Bengtsson, “Dual-broadband rotational CARS modelling of nitrogen at pressures up to 9 MPa. I. Interbranch interference effect,” Appl. Phys. B 75, 763–769 (2002).
[CrossRef]

1998 (1)

1997 (3)

1995 (1)

T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
[CrossRef]

1992 (3)

J. A. Wehrmeyer, T. S. Cheng, R. W. Pitz, “Raman scattering measurements in flames using a tunable KrF excimer laser,” Appl. Opt. 31, 1495–1504 (1992).
[CrossRef] [PubMed]

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kroll, “Rotational CARS thermometry in sooting flames,” Comb. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

1990 (1)

B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
[CrossRef]

1988 (1)

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

1987 (1)

B. Attal-Tretout, P. Bouchardy, “Detection of the OH radical in flames by resonance CARS,” Rech. Aerosp. 5, 19–38 (1987).

1984 (1)

Y. Prior, “A complete expression for the third-order susceptibility (χ(3))—perturbative and diagrammatic approaches,” IEEE J. Quantum Electron. 20, 37–42 (1984).
[CrossRef]

1983 (2)

M. Bérard, P. Lallemand, J. P. Cebe, M. Giraud, “Experimental and theoretical analysis of the temperature dependence of rotational Raman linewidths of oxygen,” J. Chem. Phys. 78, 672–687 (1983).
[CrossRef]

B. Attal, D. Debarre, K. Mullerdethlefs, J. P. E. Taran, “Resonance-enhanced coherent anti-Stokes Raman-scattering in C2,” Rev. Phys. Appl. 18, 39–50 (1983).
[CrossRef]

1982 (1)

1981 (1)

S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

1980 (1)

T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
[CrossRef]

1979 (1)

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

1978 (3)

A. C. Eckbreth, “BOXCARS: crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
[CrossRef]

N. Bloembergen, H. Lotem, R. T. Lynch, “Lineshapes in coherent resonant Raman scattering,” Indian J. Pure Appl. Phys. 16, 151–158 (1978).

S. A. J. Druet, B. Attal, T. K. Gustafson, J.-P. E. Taran, “Electronic resonance enhancement of coherent anti-Stokes Raman scattering,” Phys. Rev. A 18, 1529–1557 (1978).
[CrossRef]

1969 (1)

V. Alekeyev, I. Sobelman, “Influence of collisions on stimulated random scattering in gases,” Sov. Phys. JETP 28, 991–994 (1969).

1968 (1)

V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
[CrossRef]

Afzelius, M.

M. Afzelius, P. E. Bengtsson, “Dual-broadband rotational CARS modelling of nitrogen at pressures up to 9 MPa. I. Interbranch interference effect,” Appl. Phys. B 75, 763–769 (2002).
[CrossRef]

Alden, M.

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kroll, “Rotational CARS thermometry in sooting flames,” Comb. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

Alekeyev, V.

V. Alekeyev, I. Sobelman, “Influence of collisions on stimulated random scattering in gases,” Sov. Phys. JETP 28, 991–994 (1969).

V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
[CrossRef]

Arp, Z.

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

Attal, B.

B. Attal, D. Debarre, K. Mullerdethlefs, J. P. E. Taran, “Resonance-enhanced coherent anti-Stokes Raman-scattering in C2,” Rev. Phys. Appl. 18, 39–50 (1983).
[CrossRef]

S. A. J. Druet, B. Attal, T. K. Gustafson, J.-P. E. Taran, “Electronic resonance enhancement of coherent anti-Stokes Raman scattering,” Phys. Rev. A 18, 1529–1557 (1978).
[CrossRef]

Attal-Tretout, B.

B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
[CrossRef]

B. Attal-Tretout, P. Bouchardy, “Detection of the OH radical in flames by resonance CARS,” Rech. Aerosp. 5, 19–38 (1987).

Augustin, S. D.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Bengtsson, P. E.

M. Afzelius, P. E. Bengtsson, “Dual-broadband rotational CARS modelling of nitrogen at pressures up to 9 MPa. I. Interbranch interference effect,” Appl. Phys. B 75, 763–769 (2002).
[CrossRef]

Bengtsson, P.-E.

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kroll, “Rotational CARS thermometry in sooting flames,” Comb. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

Bérard, M.

M. Bérard, P. Lallemand, J. P. Cebe, M. Giraud, “Experimental and theoretical analysis of the temperature dependence of rotational Raman linewidths of oxygen,” J. Chem. Phys. 78, 672–687 (1983).
[CrossRef]

Berger, H.

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Beyrau, F.

T. Seeger, F. Beyrau, A. Bräuer, A. Leipertz, “High-pressure pure rotational CARS: comparison of temperature measurements with O2N2and synthetic air,” J. Raman Spectrosc. 34, 932–939 (2003).
[CrossRef]

Bischel, W. K.

W. K. Bischel, G. Black, “Wavelength dependence of the Raman scattering cross sections from 200–600 nm,” in Excimer Lasers, K. Rhodes, H. Egger, H. Pummer, eds. (American Institute of Physics, 1983), pp. 181–187.

Black, G.

W. K. Bischel, G. Black, “Wavelength dependence of the Raman scattering cross sections from 200–600 nm,” in Excimer Lasers, K. Rhodes, H. Egger, H. Pummer, eds. (American Institute of Physics, 1983), pp. 181–187.

Bloembergen, N.

N. Bloembergen, H. Lotem, R. T. Lynch, “Lineshapes in coherent resonant Raman scattering,” Indian J. Pure Appl. Phys. 16, 151–158 (1978).

Bonamy, J.

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Bonamy, L.

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Bouchardy, P.

B. Attal-Tretout, P. Bouchardy, “Detection of the OH radical in flames by resonance CARS,” Rech. Aerosp. 5, 19–38 (1987).

Bräuer, A.

T. Seeger, F. Beyrau, A. Bräuer, A. Leipertz, “High-pressure pure rotational CARS: comparison of temperature measurements with O2N2and synthetic air,” J. Raman Spectrosc. 34, 932–939 (2003).
[CrossRef]

Cebe, J. P.

M. Bérard, P. Lallemand, J. P. Cebe, M. Giraud, “Experimental and theoretical analysis of the temperature dependence of rotational Raman linewidths of oxygen,” J. Chem. Phys. 78, 672–687 (1983).
[CrossRef]

Chaux, R.

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Cheng, T. S.

Copeland, R. A.

Crete, E.

B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
[CrossRef]

Debarre, D.

B. Attal, D. Debarre, K. Mullerdethlefs, J. P. E. Taran, “Resonance-enhanced coherent anti-Stokes Raman-scattering in C2,” Rev. Phys. Appl. 18, 39–50 (1983).
[CrossRef]

DePristo, A. E.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Doerk, T.

T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
[CrossRef]

T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
[CrossRef]

Drake, J. D.

Druet, S. A. J.

S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

S. A. J. Druet, B. Attal, T. K. Gustafson, J.-P. E. Taran, “Electronic resonance enhancement of coherent anti-Stokes Raman scattering,” Phys. Rev. A 18, 1529–1557 (1978).
[CrossRef]

Dumas, P.

B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, “BOXCARS: crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
[CrossRef]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon & Breach, 1996), Vol. 3.

Faizulov, F.

V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
[CrossRef]

Faris, G. W.

Giraud, M.

M. Bérard, P. Lallemand, J. P. Cebe, M. Giraud, “Experimental and theoretical analysis of the temperature dependence of rotational Raman linewidths of oxygen,” J. Chem. Phys. 78, 672–687 (1983).
[CrossRef]

Grasiuk, A.

V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
[CrossRef]

Greenhalgh, D. A.

D. A. Greenhalgh, “Quantitative CARS spectroscopy,” in Advances in Non-Linear Spectroscopy, R. J. H. Clark, R. E. Hester, eds. (Wiley, 1988), Vol. 15, pp. 193–251.

Gustafson, T. K.

S. A. J. Druet, B. Attal, T. K. Gustafson, J.-P. E. Taran, “Electronic resonance enhancement of coherent anti-Stokes Raman scattering,” Phys. Rev. A 18, 1529–1557 (1978).
[CrossRef]

Hadrich, S.

T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
[CrossRef]

T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
[CrossRef]

Hanna, S. F.

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

Hertl, M.

T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
[CrossRef]

Jauernik, P.

T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
[CrossRef]

T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
[CrossRef]

Jonuscheit, J.

Knighten, G. V.

J. W. Nibler, G. V. Knighten, “Coherent anti-Stokes Raman spectroscopy,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, 1979), Vol. 11, pp. 253–299.
[CrossRef]

Kroll, S.

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kroll, “Rotational CARS thermometry in sooting flames,” Comb. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

Kuehner, J. P.

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

Kulatilaka, W. D.

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

Lallemand, P.

M. Bérard, P. Lallemand, J. P. Cebe, M. Giraud, “Experimental and theoretical analysis of the temperature dependence of rotational Raman linewidths of oxygen,” J. Chem. Phys. 78, 672–687 (1983).
[CrossRef]

Lasser, T.

T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
[CrossRef]

Lavorel, B.

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Leipertz, A.

Lotem, H.

N. Bloembergen, H. Lotem, R. T. Lynch, “Lineshapes in coherent resonant Raman scattering,” Indian J. Pure Appl. Phys. 16, 151–158 (1978).

Lucht, R. P.

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

Lynch, R. T.

N. Bloembergen, H. Lotem, R. T. Lynch, “Lineshapes in coherent resonant Raman scattering,” Indian J. Pure Appl. Phys. 16, 151–158 (1978).

Magens, E.

E. Magens, Nutzung von Rotations-CARS zur Temperaturund Konzentrationsmessung in Flammen, Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, 1993), Vol. 93.2.

Martinsson, L.

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kroll, “Rotational CARS thermometry in sooting flames,” Comb. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

L. Martinsson, “Theoretical development of rotational CARS for combustion diagnostics,” Ph.D. dissertation (Lund Institute of Technology, 1994).

Millot, G.

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

Mullerdethlefs, K.

B. Attal, D. Debarre, K. Mullerdethlefs, J. P. E. Taran, “Resonance-enhanced coherent anti-Stokes Raman-scattering in C2,” Rev. Phys. Appl. 18, 39–50 (1983).
[CrossRef]

Nibler, J. W.

J. W. Nibler, G. V. Knighten, “Coherent anti-Stokes Raman spectroscopy,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, 1979), Vol. 11, pp. 253–299.
[CrossRef]

Opatrny, T.

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

Pfelzer, B.

T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
[CrossRef]

T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
[CrossRef]

Pitz, R. W.

Prior, Y.

Y. Prior, “A complete expression for the third-order susceptibility (χ(3))—perturbative and diagrammatic approaches,” IEEE J. Quantum Electron. 20, 37–42 (1984).
[CrossRef]

Rabitz, H.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Ragulsky, V.

V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
[CrossRef]

Ramaswany, R.

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

Robert, D.

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Saint-Loup, R.

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Santoro, R. J.

R. J. Santoro, C. R. Shaddix, “Laser-induced incandescence,” in Applied Combustion Diagnostics, K. Kohse Höinghaus, J. Jeffries, eds. (Taylor & Francis, 2002), pp. 252–286.

Santos, J.

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

Schenk, M.

Schmidt, S. C.

B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
[CrossRef]

Scully, M. O.

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

Seeger, T.

Shaddix, C. R.

R. J. Santoro, C. R. Shaddix, “Laser-induced incandescence,” in Applied Combustion Diagnostics, K. Kohse Höinghaus, J. Jeffries, eds. (Taylor & Francis, 2002), pp. 252–286.

Sobelman, I.

V. Alekeyev, I. Sobelman, “Influence of collisions on stimulated random scattering in gases,” Sov. Phys. JETP 28, 991–994 (1969).

V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
[CrossRef]

Taran, J. P. E.

B. Attal, D. Debarre, K. Mullerdethlefs, J. P. E. Taran, “Resonance-enhanced coherent anti-Stokes Raman-scattering in C2,” Rev. Phys. Appl. 18, 39–50 (1983).
[CrossRef]

Taran, J.-P. E.

B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
[CrossRef]

S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

S. A. J. Druet, B. Attal, T. K. Gustafson, J.-P. E. Taran, “Electronic resonance enhancement of coherent anti-Stokes Raman scattering,” Phys. Rev. A 18, 1529–1557 (1978).
[CrossRef]

Thumann, A.

Uhlenbusch, J.

T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
[CrossRef]

T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
[CrossRef]

Wehrmeyer, J. A.

Weissbluth, M.

M. Weissbluth, Photon-Atom Interactions (Academic, 1988).

Woyde, M.

M. Woyde, “Temperaturbestimmung hoher genauigkeit mit CARS in hochdruckverbrennungssystemen,” Ph.D. dissertation (Universität Stuttgart, 1992).

Appl. Opt. (4)

Appl. Phys. B (2)

M. Afzelius, P. E. Bengtsson, “Dual-broadband rotational CARS modelling of nitrogen at pressures up to 9 MPa. I. Interbranch interference effect,” Appl. Phys. B 75, 763–769 (2002).
[CrossRef]

T. Doerk, M. Hertl, B. Pfelzer, S. Hadrich, P. Jauernik, J. Uhlenbusch, “Resonance-enhanced coherent anti-Stokes-Raman scattering and laser-induced fluorescence applied to CH radicals—a comparative study,” Appl. Phys. B 64, 111–118 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

S. F. Hanna, W. D. Kulatilaka, Z. Arp, T. Opatrny, M. O. Scully, J. P. Kuehner, R. P. Lucht, “Electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy of nitric oxide,” Appl. Phys. Lett. 83, 1887–1889 (2003).
[CrossRef]

A. C. Eckbreth, “BOXCARS: crossed-beam phase-matched CARS generation in gases,” Appl. Phys. Lett. 32, 421–423 (1978).
[CrossRef]

Comb. Sci. Technol. (1)

P.-E. Bengtsson, L. Martinsson, M. Alden, S. Kroll, “Rotational CARS thermometry in sooting flames,” Comb. Sci. Technol. 81, 129–140 (1992).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Prior, “A complete expression for the third-order susceptibility (χ(3))—perturbative and diagrammatic approaches,” IEEE J. Quantum Electron. 20, 37–42 (1984).
[CrossRef]

V. Alekeyev, A. Grasiuk, V. Ragulsky, I. Sobelman, F. Faizulov, “S-6-stimulated Raman scattering in gases and gain pressure dependence,” IEEE J. Quantum Electron. QE-4, 654–656 (1968).
[CrossRef]

Indian J. Pure Appl. Phys. (1)

N. Bloembergen, H. Lotem, R. T. Lynch, “Lineshapes in coherent resonant Raman scattering,” Indian J. Pure Appl. Phys. 16, 151–158 (1978).

J. Chem. Phys. (4)

A. E. DePristo, S. D. Augustin, R. Ramaswany, H. Rabitz, “Quantum number and energy scaling for nonreactive collisions,” J. Chem. Phys. 71, 850–865 (1979).
[CrossRef]

L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, “Rotationally inelastic rates for N2-N2system from a scaling theoretical analysis of stimulated Raman Q branch,” J. Chem. Phys. 89, 5568–5577 (1988).
[CrossRef]

G. Millot, R. Saint-Loup, J. Santos, R. Chaux, H. Berger, J. Bonamy, “Collisional effects in the stimulated Raman Q branch of O2and O2-N2,” J. Chem. Phys. 96, 961–971 (1992).
[CrossRef]

M. Bérard, P. Lallemand, J. P. Cebe, M. Giraud, “Experimental and theoretical analysis of the temperature dependence of rotational Raman linewidths of oxygen,” J. Chem. Phys. 78, 672–687 (1983).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

B. Attal-Tretout, S. C. Schmidt, E. Crete, P. Dumas, J.-P. E. Taran, “Resonance CARS of OH in high-pressure flames,” J. Quant. Spectrosc. Radiat. Transfer 43, 351–364 (1990).
[CrossRef]

J. Raman Spectrosc. (1)

T. Seeger, F. Beyrau, A. Bräuer, A. Leipertz, “High-pressure pure rotational CARS: comparison of temperature measurements with O2N2and synthetic air,” J. Raman Spectrosc. 34, 932–939 (2003).
[CrossRef]

Opt. Commun. (2)

T. Lasser, “An alternative method for CARS-spectra calculation,” Opt. Commun. 35, 447–450 (1980).
[CrossRef]

T. Doerk, P. Jauernik, S. Hadrich, B. Pfelzer, J. Uhlenbusch, “Resonance-enhanced CARS applied to the CH radical,” Opt. Commun. 118, 637–647 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

S. A. J. Druet, B. Attal, T. K. Gustafson, J.-P. E. Taran, “Electronic resonance enhancement of coherent anti-Stokes Raman scattering,” Phys. Rev. A 18, 1529–1557 (1978).
[CrossRef]

Prog. Quantum Electron. (1)

S. A. J. Druet, J.-P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
[CrossRef]

Rech. Aerosp. (1)

B. Attal-Tretout, P. Bouchardy, “Detection of the OH radical in flames by resonance CARS,” Rech. Aerosp. 5, 19–38 (1987).

Rev. Phys. Appl. (1)

B. Attal, D. Debarre, K. Mullerdethlefs, J. P. E. Taran, “Resonance-enhanced coherent anti-Stokes Raman-scattering in C2,” Rev. Phys. Appl. 18, 39–50 (1983).
[CrossRef]

Sov. Phys. JETP (1)

V. Alekeyev, I. Sobelman, “Influence of collisions on stimulated random scattering in gases,” Sov. Phys. JETP 28, 991–994 (1969).

Other (11)

A. Thumann, Temperaturbestimmung mittels der Kohärenten-Anti-Stokes-Raman-Streuung (CARS) unter Berücksichtigung des Druckeinflusses und nichteinheitlicher Temperaturverhältnisse im Meβvolumen, Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, 1997), Vol. 97.4.

M. Woyde, “Temperaturbestimmung hoher genauigkeit mit CARS in hochdruckverbrennungssystemen,” Ph.D. dissertation (Universität Stuttgart, 1992).

L. Martinsson, “Theoretical development of rotational CARS for combustion diagnostics,” Ph.D. dissertation (Lund Institute of Technology, 1994).

E. Magens, Nutzung von Rotations-CARS zur Temperaturund Konzentrationsmessung in Flammen, Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, 1993), Vol. 93.2.

D. A. Greenhalgh, “Quantitative CARS spectroscopy,” in Advances in Non-Linear Spectroscopy, R. J. H. Clark, R. E. Hester, eds. (Wiley, 1988), Vol. 15, pp. 193–251.

R. J. Santoro, C. R. Shaddix, “Laser-induced incandescence,” in Applied Combustion Diagnostics, K. Kohse Höinghaus, J. Jeffries, eds. (Taylor & Francis, 2002), pp. 252–286.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon & Breach, 1996), Vol. 3.

W. K. Bischel, G. Black, “Wavelength dependence of the Raman scattering cross sections from 200–600 nm,” in Excimer Lasers, K. Rhodes, H. Egger, H. Pummer, eds. (American Institute of Physics, 1983), pp. 181–187.

M. Weissbluth, Photon-Atom Interactions (Academic, 1988).

M. Schenk, Simultane Temperatur- und Konzentrationsmes-sung in binären und ternären Gemischen mittels Rotations-CARS-Spektroskopie, Berichte zur Energie- und Verfahrenstechnik (ESYTEC Energie und Systemtechnik GmbH, 2000), Vol. 2000.2.

J. W. Nibler, G. V. Knighten, “Coherent anti-Stokes Raman spectroscopy,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, 1979), Vol. 11, pp. 253–299.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Relative Raman-scattering cross section of the oxygen Q branch with respect to the nitrogen Q branch. Both interpolated values according to Bischel and Black7 (solid curve) and experimental results by Faris and Copeland8 (circles) are depicted.

Fig. 2
Fig. 2

Schematic energy-level diagram of a resonant CARS process, with a and b representing rovibrational energy levels of the electronic ground state and n and n′ of an excited electronic state. For the electronic off-resonant case, n and n′ represent so-called virtual energy levels.

Fig. 3
Fig. 3

Scheme of the experimental UV–visible setup as described in detail in Ref. 18. SHG, second-harmonic generation.

Fig. 4
Fig. 4

Comparison of accumulated spectra of air (300 K; 1 bar; 200 single-shot spectra accumulated, solid curve) recorded at a 532 nm (bottom) and a 266 nm (top) wavelength of the pump beam with the best fitting theoretical spectrum (dashed curve). The difference between the particular spectra is depicted as well. In the case of 266 nm, we recognize a significantly higher evaluated value of the oxygen concentration and therefore a relative cross-sectional enhancement with respect to nitrogen. Two oxygen lines are marked by arrows.

Fig. 5
Fig. 5

Ratios between mean values of the relative O2–N2 concentration determined experimentally and the particular reference values for spectra obtained from both natural air (experiments 1-8) and synthetic air (experiments 9 and 10; 20% O2, 80% N2). Depicted are the results of the LSF weighted either constantly or mainly inversely with respect to the normalized signal. The results of ten independent experiments at 266 and 532 nm each are depicted. The spectral resolution was comparable in both experiments.

Equations (9)

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σ Ω ν S 4 | n μ a n μ n b ν n ν p + μ a n μ n b ν n ν S | 2 .
σ Ω ν S 4 | n ν n μ a n μ n b ν n 2 ν P 2 | 2 .
σ Ω = A ν S 4 ν i 2 ν P 2 .
χ δ α β γ a b ( ω , ω 1 , ω 3 , ω 2 ) 1 [ ω b a ( ω 1 ω 2 ) i Γ b a ] × n { μ a n δ μ n b β [ ω n a ( ω 1 + ω 3 ω 2 ) i Γ n a ] + μ a n β μ n b δ [ ω n b + ( ω 1 + ω 3 ω 2 ) + i Γ n b ] } × n { [ μ b n α μ n a γ ( ω n a + ω 2 i Γ n a ) + μ b n γ μ n a α ( ω n a ω 1 i Γ n a ) ] ρ | a a | ( 0 ) [ μ b n γ μ n a α ( ω n b ω 2 i Γ n b ) + μ b n α μ n a γ ( ω n b + ω 1 i Γ n b ) ] ρ | a a | ( 0 ) } .
χ CARS = i { χ n r i + a , b 8 π 2 n ( ω 1 ) ε 0 c 4 n ( ω 2 ) ω 2 4 × N i [ i ρ | a a | 0 i ρ | b b | 0 ] [ ω b a i ( ω 1 ω 2 ) i Γ b a i ] ( d σ b a CARS d Ω ) i } .
( d σ b a d Ω ) b J J + 2 γ ν 2 .
d pump laser = f pump laser * { [ ( f broadband laser d broadband laser ) 2 + 1 ] × ( λ broadband laser d pump laser ) 1 } 1 / 2 ,
k g k | i e k i t k ( T , c ) | 2 = min ( T , c i ) .
g k = 1 c 0 + c 1 i e k + c 2 ( i e k ) 2 .

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