Abstract

Nonresonant third-order susceptibilities (χnr) of N2 and Ar gases by using an off-resonant coherent anti-Stokes Raman spectroscopy of the N2 Q branch, whose spectral profile is highly sensitive to the value of χnr, have been measured to demonstrate the possibility of the present method. The χnr of N2 and Ar using the off-resonant coherent anti-Stokes Raman spectroscopy were 8.4 ± 0.2 and 9.7 ± 0.8 (× 10−18 cm3/erg/amagat), respectively. These values are in good agreement with those of previous studies. The off-resonant spectra were theoretically calculated by using the Raman linewidth given by a modified exponential gap model, and they were compared with the experimental ones to determine χnr. The effects of uncertainties of the Raman linewidth of the N2 Q branch on the determination of χnr were investigated by changing the parameters in the modified exponential gap model. The determined χnr value changed by only 0.05% with 50% change of the Raman linewidth. The potential advantages of this method are no requirements of high spectral resolution measurements, no accurate Raman linewidth data for each experimental condition, and no optical delay between pump beams.

© 1993 Optical Society of America

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References

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  1. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Tunbridge Wells, UK, 1988), pp. 220–292.
  2. A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
    [Crossref] [PubMed]
  3. S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
    [Crossref]
  4. R. J. Hall, L. R. Boedeker, “CARS thermometry in fuel-rich combustion zones,” Appl. Opt. 23, 1340–1346 (1984).
    [Crossref] [PubMed]
  5. R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
    [Crossref]
  6. R. L. Farrow, R. P. Lucht, L. A. Rahn, “Measurements of the nonresonant third-order susceptibilities of gases using coherent anti-Stokes Raman spectroscopy,” J. Opt. Soc. Am. B 4, 1241–1246 (1987).
    [Crossref]
  7. R. L. Farrow, L. A. Rahn, “Interpreting coherent anti-Stokes Raman spectra measured with multimode Nd:YAG pump lasers,” J. Opt. Soc. Am. B 2, 903–907 (1985).
    [Crossref]
  8. K. Akihama, T. Asai, “Application of polarization S-branch CARS: studies of thermometry and nonresonant susceptibility measurement,” Trans. Jpn. Soc. Mech. Eng. 56(B), 200–205 (1990).
    [Crossref]
  9. K. Akihama, T. Asai, “Measurement of nonresonant third-order susceptibility using off-resonant CARS,” in Proceedings of the Twelfth International Conferenceon Raman Spectroscopy, J. R. Durig, J. F. Sullivan, eds. (Wiley, New York, 1990), pp. 216–217.
  10. R. L. Farrow, P. L. Mattern, L. A. Rahn, “Comparison between CARS and corrected thermocouple measurements in a diffusion flame,” Appl. Opt. 21, 3119–3125 (1982).
    [Crossref] [PubMed]
  11. H. Kataoka, S. Maeda, C. Hirose, “Effects of laser linewidth on the coherent anti-Stokes Raman spectroscopy spectral profile,” Appl. Spectrosc. 36, 565–569 (1982).
    [Crossref]
  12. R. E. Teets, “Accurate convolutions of coherent anti-Stokes Raman spectra,” Opt. Lett. 9, 226–228 (1984).
    [Crossref] [PubMed]
  13. K. Akihama, T. Asai, “S-branch CARS applicability to thermometry,” Appl. Opt. 29, 3143–3149 (1990).
    [Crossref] [PubMed]
  14. R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
    [Crossref]
  15. H. W. Schrötter, H. W. Klöcker, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, New York, 1979), pp. 123–201.
    [Crossref]
  16. L. A. Rahn, R. E. Palmer, “Studies of nitrogen self-broadening at high temperature with inverse Raman spectroscopy,” J. Opt. Soc. Am. B 3, 1164–1169 (1986).
    [Crossref]
  17. T. Lundeen, S.-Y. Hou, J.W. Nibler, “Nonresonant third order susceptibilities for various gases,” J. Chem. Phys. 79, 6301–6305 (1983), and references therein.
    [Crossref]
  18. W. G. Rado, “The nonlinear third order dielectric susceptibility coefficients of gases and optical third harmonic generation,” Appl. Phys. Lett. 11, 123–125 (1967).
    [Crossref]
  19. D. P. Shelton, A. D. Buckingham, “Optical second-harmonic generation in gases with a low-power laser,” Phys. Rev. A 26, 2787–2798 (1982).
    [Crossref]

1990 (2)

K. Akihama, T. Asai, “Application of polarization S-branch CARS: studies of thermometry and nonresonant susceptibility measurement,” Trans. Jpn. Soc. Mech. Eng. 56(B), 200–205 (1990).
[Crossref]

K. Akihama, T. Asai, “S-branch CARS applicability to thermometry,” Appl. Opt. 29, 3143–3149 (1990).
[Crossref] [PubMed]

1987 (2)

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[Crossref]

R. L. Farrow, R. P. Lucht, L. A. Rahn, “Measurements of the nonresonant third-order susceptibilities of gases using coherent anti-Stokes Raman spectroscopy,” J. Opt. Soc. Am. B 4, 1241–1246 (1987).
[Crossref]

1986 (1)

1985 (1)

1984 (3)

1983 (2)

S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
[Crossref]

T. Lundeen, S.-Y. Hou, J.W. Nibler, “Nonresonant third order susceptibilities for various gases,” J. Chem. Phys. 79, 6301–6305 (1983), and references therein.
[Crossref]

1982 (3)

1980 (1)

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[Crossref]

1967 (1)

W. G. Rado, “The nonlinear third order dielectric susceptibility coefficients of gases and optical third harmonic generation,” Appl. Phys. Lett. 11, 123–125 (1967).
[Crossref]

Akihama, K.

K. Akihama, T. Asai, “Application of polarization S-branch CARS: studies of thermometry and nonresonant susceptibility measurement,” Trans. Jpn. Soc. Mech. Eng. 56(B), 200–205 (1990).
[Crossref]

K. Akihama, T. Asai, “S-branch CARS applicability to thermometry,” Appl. Opt. 29, 3143–3149 (1990).
[Crossref] [PubMed]

S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
[Crossref]

K. Akihama, T. Asai, “Measurement of nonresonant third-order susceptibility using off-resonant CARS,” in Proceedings of the Twelfth International Conferenceon Raman Spectroscopy, J. R. Durig, J. F. Sullivan, eds. (Wiley, New York, 1990), pp. 216–217.

Asai, T.

K. Akihama, T. Asai, “Application of polarization S-branch CARS: studies of thermometry and nonresonant susceptibility measurement,” Trans. Jpn. Soc. Mech. Eng. 56(B), 200–205 (1990).
[Crossref]

K. Akihama, T. Asai, “S-branch CARS applicability to thermometry,” Appl. Opt. 29, 3143–3149 (1990).
[Crossref] [PubMed]

K. Akihama, T. Asai, “Measurement of nonresonant third-order susceptibility using off-resonant CARS,” in Proceedings of the Twelfth International Conferenceon Raman Spectroscopy, J. R. Durig, J. F. Sullivan, eds. (Wiley, New York, 1990), pp. 216–217.

Boedeker, L. R.

Buckingham, A. D.

D. P. Shelton, A. D. Buckingham, “Optical second-harmonic generation in gases with a low-power laser,” Phys. Rev. A 26, 2787–2798 (1982).
[Crossref]

Dobbs, G. M.

Eckbreth, A. C.

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
[Crossref] [PubMed]

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[Crossref]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Tunbridge Wells, UK, 1988), pp. 220–292.

Farrow, R. L.

Ferguson, C. R.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[Crossref]

Furuno, S.

S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
[Crossref]

Green, R. M.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[Crossref]

Hall, R. J.

R. J. Hall, L. R. Boedeker, “CARS thermometry in fuel-rich combustion zones,” Appl. Opt. 23, 1340–1346 (1984).
[Crossref] [PubMed]

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[Crossref]

Hanabusa, M.

S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
[Crossref]

Hirose, C.

Hou, S.-Y.

T. Lundeen, S.-Y. Hou, J.W. Nibler, “Nonresonant third order susceptibilities for various gases,” J. Chem. Phys. 79, 6301–6305 (1983), and references therein.
[Crossref]

Iguchi, S.

S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
[Crossref]

Inoue, T.

S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
[Crossref]

Kataoka, H.

Klöcker, H. W.

H. W. Schrötter, H. W. Klöcker, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, New York, 1979), pp. 123–201.
[Crossref]

Lucht, R. P.

R. L. Farrow, R. P. Lucht, L. A. Rahn, “Measurements of the nonresonant third-order susceptibilities of gases using coherent anti-Stokes Raman spectroscopy,” J. Opt. Soc. Am. B 4, 1241–1246 (1987).
[Crossref]

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[Crossref]

Lundeen, T.

T. Lundeen, S.-Y. Hou, J.W. Nibler, “Nonresonant third order susceptibilities for various gases,” J. Chem. Phys. 79, 6301–6305 (1983), and references therein.
[Crossref]

Maeda, S.

Mattern, P. L.

Nibler, J.W.

T. Lundeen, S.-Y. Hou, J.W. Nibler, “Nonresonant third order susceptibilities for various gases,” J. Chem. Phys. 79, 6301–6305 (1983), and references therein.
[Crossref]

Palmer, R. E.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[Crossref]

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

Rado, W. G.

W. G. Rado, “The nonlinear third order dielectric susceptibility coefficients of gases and optical third harmonic generation,” Appl. Phys. Lett. 11, 123–125 (1967).
[Crossref]

Rahn, L. A.

Schrötter, H. W.

H. W. Schrötter, H. W. Klöcker, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, New York, 1979), pp. 123–201.
[Crossref]

Shelton, D. P.

D. P. Shelton, A. D. Buckingham, “Optical second-harmonic generation in gases with a low-power laser,” Phys. Rev. A 26, 2787–2798 (1982).
[Crossref]

Stufflebeam, J. H.

Teets, R. E.

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[Crossref]

R. E. Teets, “Accurate convolutions of coherent anti-Stokes Raman spectra,” Opt. Lett. 9, 226–228 (1984).
[Crossref] [PubMed]

Tellex, P. A.

Verdieck, J. F.

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

W. G. Rado, “The nonlinear third order dielectric susceptibility coefficients of gases and optical third harmonic generation,” Appl. Phys. Lett. 11, 123–125 (1967).
[Crossref]

Appl. Spectrosc. (1)

Combust. Flame (1)

S. Furuno, K. Akihama, M. Hanabusa, S. Iguchi, T. Inoue, “Nitrogen CARS thermometry for a study of temperature profiles through flame fronts,” Combust. Flame 54, 149–154 (1983).
[Crossref]

Combust. Sci. Technol. (1)

R. P. Lucht, R. E. Teets, R. M. Green, R. E. Palmer, C. R. Ferguson, “Unburned gas temperatures in an internal combustion engine. I: CARS temperature measurements,” Combust. Sci. Technol. 55, 41–61 (1987).
[Crossref]

J. Chem. Phys. (1)

T. Lundeen, S.-Y. Hou, J.W. Nibler, “Nonresonant third order susceptibilities for various gases,” J. Chem. Phys. 79, 6301–6305 (1983), and references therein.
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

R. J. Hall, J. F. Verdieck, A. C. Eckbreth, “Pressure-induced narrowing of the CARS spectrum of N2,” Opt. Commun. 35, 69–75 (1980).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

D. P. Shelton, A. D. Buckingham, “Optical second-harmonic generation in gases with a low-power laser,” Phys. Rev. A 26, 2787–2798 (1982).
[Crossref]

Trans. Jpn. Soc. Mech. Eng. (1)

K. Akihama, T. Asai, “Application of polarization S-branch CARS: studies of thermometry and nonresonant susceptibility measurement,” Trans. Jpn. Soc. Mech. Eng. 56(B), 200–205 (1990).
[Crossref]

Other (3)

K. Akihama, T. Asai, “Measurement of nonresonant third-order susceptibility using off-resonant CARS,” in Proceedings of the Twelfth International Conferenceon Raman Spectroscopy, J. R. Durig, J. F. Sullivan, eds. (Wiley, New York, 1990), pp. 216–217.

H. W. Schrötter, H. W. Klöcker, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, ed. (Springer-Verlag, New York, 1979), pp. 123–201.
[Crossref]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Tunbridge Wells, UK, 1988), pp. 220–292.

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Figures (6)

Fig. 1
Fig. 1

Change of off-resonant spectra of the N2 Q branch calculated at 295 K and 2 atm for pure N2 by using (a) χnr,N2 = 7.7 × 10−1, (b) χnr,N2 8.5 × 10−18, and (c) χnr,N2 9.4 × 10−18 (cm3/erg/amagat) in Eq. (2) with χnr,sys = 0.0 and χnr,Ar = 0.0.

Fig. 2
Fig. 2

Schematic illustration of off-resonant CARS experimental arrangement: BS, beam splitter; DM, dichroic mirror; GP, Glan–Taylor prism; PR, polarization rotator; L, lens; A, aperture; 1, double monochromator; 2, photomultiplier; 3, amplifier; 4, boxcar averages; 5, digitizer; 6, recorder; 7, gas cell A; 8, gas cell B; 9, power meter.

Fig. 3
Fig. 3

Typical dual-channel spectra. Spectra of Ch.A and Ch.B are the off-resonant spectra of the N2 Q branch with and without the N2 S-branch suppression, respectively.

Fig. 4
Fig. 4

Off-resonant spectra of pure N2 (solid curve) and fit (dashed curve) at 295 K and at various pressures. The best-fitted χnr,obs in Eq. (1) were (a) χnr,obs = 16.17 × 10−18 cm3/erg, (b) χnr,obs = 38.80 × 10−18 cm3/erg, and (c) χnr,obs = 78.16 × 10−18 cm3/erg, respectively.

Fig. 5
Fig. 5

N2 gas density dependence of χnr,obs. Graphs on the right-hand side indicate the detailed graphs at each point (a to d) in the graph on the left-hand side. Open circles and solid lines represent experimental results and regression lines for all data, respectively.

Fig. 6
Fig. 6

Spectra of off-resonant CARS obtained from (a) a gas mixture of 14.3% Ar in N2 at 295 K and 2 atm, and (b) pure N2 at 295 K and 2 atm. Solid and dashed curves represent measurement and fit, respectively. Fits were calculated using (a) χnr,obs = 16.67 × 10−18 cm3/erg and (b) χnr,obs = 16.17 × 10−18 cm3/erg in Eq. (1).

Tables (2)

Tables Icon

Table 1 Effects of Uncertainties of the Raman Linewidth for the Determination of χnr

Tables Icon

Table 2 Comparison of χnr,Arnr,N2 Between Several Methods

Equations (7)

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I ( ω d ) D ( 1 - C Ar ) 3 χ 1111 Q ( ω d ) Φ ( ρ Q ) + χ nr , obs Φ ( ρ nr ) 2 ,
χ nr , obs = D [ ( 1 - C Ar ) χ nr , N 2 + C Ar χ nr , Ar ] + χ nr , sys ,
Φ ( ρ ) = cos θ cos ϕ + ρ sin θ sin ϕ ,
3 χ 1111 Q ( ω d ) = A v j { p v j ( v + 1 ) [ ( α ) 2 + 4 45 b j j ( γ ) 2 ] × [ ( ω v j - ω d ) - i Γ j 2 ] - 1 } ,
A = N ( 2 π c 2 ) ( 2 m 0 ω 0 ) .
Γ j 2 = i j γ i j ,
γ i j = P α ( T 0 / T ) n [ ( 1 + 1.5 E j / k T δ ) / ( 1 + 1.5 E j / k T ) ] 2 × exp ( - β Δ E j i / k T ) .

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