Abstract

We present absolute intensities for rotational Raman scattering (RRS) from N2, O2, and CO2, excited at 488.0 and 647.1 nm. The absolute scattering intensity for N2 at 488.0 nm is characterized by its differential cross section for backscattering, summed over Stokes and anti-Stokes bands and over scattered-light polarizations, which we find to be 1.64 × 10−29 cm2/sr ±8%. The ratio of the cross section for O2 to that for N2 at 488.0 nm is 2.61 ± 5%, whereas the corresponding ratio for CO2 to N2 is 10.6 ± 10%. Our values for RRS cross sections relative to the N2 vibrational Raman cross section are in reasonable agreement with corresponding ratios reported recently by Fenner et al. On the other hand, our absolute cross sections are approximately twice as large as those obtained from the results of Fenner et al., but agree closely with values calculated from recent measurements of the depolarization of Rayleigh scattering. Detailed observations of relative rotational-Raman-line intensities at temperatures of 22, 75, and 125 °C are consistent with theoretical predictions.

© 1974 Optical Society of America

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References

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  1. J. Cooney, J. Appl. Meteorol. 9, 108 (1972).
    [Crossref]
  2. Jack A. Salzman, William J. Masica, and Thom A. Coney, Determination of Gas Temperatures from Laser-Raman Scattering, (National Technical Information Service, Springfield, Va., 1971); Jack A. Salzman and Thom A. Coney, Remote Measurement of Atmospheric Temperatures by Raman Lidar, (National Technical Information Service, Springfield, Va., 1973).
  3. R. S. Hickman and L. H. Liang, Rev. Sci. Instrum. 43, 796 (1972).
    [Crossref]
  4. R. L. Rowell, G. M. Aval, and J. J. Barrett, J. Chem. Phys. 54, 1960 (1971).
    [Crossref]
  5. N. J. Bridge and A. D. Buckingham, Proc. R. Soc. A 295, 334 (1966).
    [Crossref]
  6. W. R. Fenner, H. A. Hyatt, J. M. Kellam, and S. P. S. Porto, J. Opt. Soc. Am. 63, 73 (1973).
    [Crossref]
  7. Alfons Weber, in The Raman Effect, Vol. 2: Applications, edited by Anthony Anderson (Dekker, New York, 1973), Ch. 9.
  8. Gerhard Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules (Van Nostrand, Princeton, N. J., 1950).
  9. The O2 RRS spectrum departs slightly from that of an SLM because the ground electronic state is a spin triplet. In consequence, each RRS line is split into a triplet, having relatively weak satellite components separated by a few cm−1 from the central component. The satellite intensities decrease rapidly as the rotational quantum number increases. RRS cross sections reported in this work correspond to the sum of the three lines in each triplet. For a high-resolution spectrum of O2 RRS and its analysis, see for example, Daryl L. Renschler, James L. Hunt, T. K. McCubbin, and S. R. Polo, J. Mol. Spectrosc. 31, 173 (1969).
    [Crossref]
  10. The ground vibrational state of CO2 corresponds to an SLM, whereas the first vibrational excited state (containing about 7% of the molecules at standard temperature) is not linear, leading to characteristically different RRS. An analysis of the resulting RRS spectrum [J. J. Barrett and A. Weber, J. Opt. Soc. Am. 60, 70 (1970)] shows that the contribution from the excited state is small near standard temperature.
    [Crossref]
  11. C. M. Penney, J. Opt. Soc. Am. 59, 34 (1969).
    [Crossref]
  12. G. Placzek, in Handbuch der Radiologie, Vol. 6, edited by G. Marx (Akademische Verlagsgesellschaft, Leipzig, 1934), Part 2, p. 205. English translation by A. Werbin, U.C.R.L. Translation No. 526(L), Lawrence Radiation Laboratory (1959).
  13. C. M. Penney, L. M. Goldman, and M. Lapp, Nat. Phys. Sci. 235, 110 (1972).
    [Crossref]
  14. R. Stair, W. E. Schneider, and J. K. Jackson, Appl. Opt. 2, 1151 (1963).
    [Crossref]
  15. W. F. Murphy, W. Holzer, and H. J. Bernstein, Appl. Spectrosc. 23, 211 (1969).
    [Crossref]
  16. D. G. Fouche and R. K. Chang, Appl. Phys. Lett. 20, 256 (1972).
    [Crossref]

1973 (1)

1972 (4)

J. Cooney, J. Appl. Meteorol. 9, 108 (1972).
[Crossref]

R. S. Hickman and L. H. Liang, Rev. Sci. Instrum. 43, 796 (1972).
[Crossref]

C. M. Penney, L. M. Goldman, and M. Lapp, Nat. Phys. Sci. 235, 110 (1972).
[Crossref]

D. G. Fouche and R. K. Chang, Appl. Phys. Lett. 20, 256 (1972).
[Crossref]

1971 (1)

R. L. Rowell, G. M. Aval, and J. J. Barrett, J. Chem. Phys. 54, 1960 (1971).
[Crossref]

1970 (1)

1969 (3)

C. M. Penney, J. Opt. Soc. Am. 59, 34 (1969).
[Crossref]

The O2 RRS spectrum departs slightly from that of an SLM because the ground electronic state is a spin triplet. In consequence, each RRS line is split into a triplet, having relatively weak satellite components separated by a few cm−1 from the central component. The satellite intensities decrease rapidly as the rotational quantum number increases. RRS cross sections reported in this work correspond to the sum of the three lines in each triplet. For a high-resolution spectrum of O2 RRS and its analysis, see for example, Daryl L. Renschler, James L. Hunt, T. K. McCubbin, and S. R. Polo, J. Mol. Spectrosc. 31, 173 (1969).
[Crossref]

W. F. Murphy, W. Holzer, and H. J. Bernstein, Appl. Spectrosc. 23, 211 (1969).
[Crossref]

1966 (1)

N. J. Bridge and A. D. Buckingham, Proc. R. Soc. A 295, 334 (1966).
[Crossref]

1963 (1)

Aval, G. M.

R. L. Rowell, G. M. Aval, and J. J. Barrett, J. Chem. Phys. 54, 1960 (1971).
[Crossref]

Barrett, J. J.

Bernstein, H. J.

Bridge, N. J.

N. J. Bridge and A. D. Buckingham, Proc. R. Soc. A 295, 334 (1966).
[Crossref]

Buckingham, A. D.

N. J. Bridge and A. D. Buckingham, Proc. R. Soc. A 295, 334 (1966).
[Crossref]

Chang, R. K.

D. G. Fouche and R. K. Chang, Appl. Phys. Lett. 20, 256 (1972).
[Crossref]

Coney, Thom A.

Jack A. Salzman, William J. Masica, and Thom A. Coney, Determination of Gas Temperatures from Laser-Raman Scattering, (National Technical Information Service, Springfield, Va., 1971); Jack A. Salzman and Thom A. Coney, Remote Measurement of Atmospheric Temperatures by Raman Lidar, (National Technical Information Service, Springfield, Va., 1973).

Cooney, J.

J. Cooney, J. Appl. Meteorol. 9, 108 (1972).
[Crossref]

Fenner, W. R.

Fouche, D. G.

D. G. Fouche and R. K. Chang, Appl. Phys. Lett. 20, 256 (1972).
[Crossref]

Goldman, L. M.

C. M. Penney, L. M. Goldman, and M. Lapp, Nat. Phys. Sci. 235, 110 (1972).
[Crossref]

Herzberg, Gerhard

Gerhard Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules (Van Nostrand, Princeton, N. J., 1950).

Hickman, R. S.

R. S. Hickman and L. H. Liang, Rev. Sci. Instrum. 43, 796 (1972).
[Crossref]

Holzer, W.

Hunt, James L.

The O2 RRS spectrum departs slightly from that of an SLM because the ground electronic state is a spin triplet. In consequence, each RRS line is split into a triplet, having relatively weak satellite components separated by a few cm−1 from the central component. The satellite intensities decrease rapidly as the rotational quantum number increases. RRS cross sections reported in this work correspond to the sum of the three lines in each triplet. For a high-resolution spectrum of O2 RRS and its analysis, see for example, Daryl L. Renschler, James L. Hunt, T. K. McCubbin, and S. R. Polo, J. Mol. Spectrosc. 31, 173 (1969).
[Crossref]

Hyatt, H. A.

Jackson, J. K.

Kellam, J. M.

Lapp, M.

C. M. Penney, L. M. Goldman, and M. Lapp, Nat. Phys. Sci. 235, 110 (1972).
[Crossref]

Liang, L. H.

R. S. Hickman and L. H. Liang, Rev. Sci. Instrum. 43, 796 (1972).
[Crossref]

Masica, William J.

Jack A. Salzman, William J. Masica, and Thom A. Coney, Determination of Gas Temperatures from Laser-Raman Scattering, (National Technical Information Service, Springfield, Va., 1971); Jack A. Salzman and Thom A. Coney, Remote Measurement of Atmospheric Temperatures by Raman Lidar, (National Technical Information Service, Springfield, Va., 1973).

McCubbin, T. K.

The O2 RRS spectrum departs slightly from that of an SLM because the ground electronic state is a spin triplet. In consequence, each RRS line is split into a triplet, having relatively weak satellite components separated by a few cm−1 from the central component. The satellite intensities decrease rapidly as the rotational quantum number increases. RRS cross sections reported in this work correspond to the sum of the three lines in each triplet. For a high-resolution spectrum of O2 RRS and its analysis, see for example, Daryl L. Renschler, James L. Hunt, T. K. McCubbin, and S. R. Polo, J. Mol. Spectrosc. 31, 173 (1969).
[Crossref]

Murphy, W. F.

Penney, C. M.

C. M. Penney, L. M. Goldman, and M. Lapp, Nat. Phys. Sci. 235, 110 (1972).
[Crossref]

C. M. Penney, J. Opt. Soc. Am. 59, 34 (1969).
[Crossref]

Placzek, G.

G. Placzek, in Handbuch der Radiologie, Vol. 6, edited by G. Marx (Akademische Verlagsgesellschaft, Leipzig, 1934), Part 2, p. 205. English translation by A. Werbin, U.C.R.L. Translation No. 526(L), Lawrence Radiation Laboratory (1959).

Polo, S. R.

The O2 RRS spectrum departs slightly from that of an SLM because the ground electronic state is a spin triplet. In consequence, each RRS line is split into a triplet, having relatively weak satellite components separated by a few cm−1 from the central component. The satellite intensities decrease rapidly as the rotational quantum number increases. RRS cross sections reported in this work correspond to the sum of the three lines in each triplet. For a high-resolution spectrum of O2 RRS and its analysis, see for example, Daryl L. Renschler, James L. Hunt, T. K. McCubbin, and S. R. Polo, J. Mol. Spectrosc. 31, 173 (1969).
[Crossref]

Porto, S. P. S.

Renschler, Daryl L.

The O2 RRS spectrum departs slightly from that of an SLM because the ground electronic state is a spin triplet. In consequence, each RRS line is split into a triplet, having relatively weak satellite components separated by a few cm−1 from the central component. The satellite intensities decrease rapidly as the rotational quantum number increases. RRS cross sections reported in this work correspond to the sum of the three lines in each triplet. For a high-resolution spectrum of O2 RRS and its analysis, see for example, Daryl L. Renschler, James L. Hunt, T. K. McCubbin, and S. R. Polo, J. Mol. Spectrosc. 31, 173 (1969).
[Crossref]

Rowell, R. L.

R. L. Rowell, G. M. Aval, and J. J. Barrett, J. Chem. Phys. 54, 1960 (1971).
[Crossref]

Salzman, Jack A.

Jack A. Salzman, William J. Masica, and Thom A. Coney, Determination of Gas Temperatures from Laser-Raman Scattering, (National Technical Information Service, Springfield, Va., 1971); Jack A. Salzman and Thom A. Coney, Remote Measurement of Atmospheric Temperatures by Raman Lidar, (National Technical Information Service, Springfield, Va., 1973).

Schneider, W. E.

Stair, R.

Weber, A.

Weber, Alfons

Alfons Weber, in The Raman Effect, Vol. 2: Applications, edited by Anthony Anderson (Dekker, New York, 1973), Ch. 9.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. G. Fouche and R. K. Chang, Appl. Phys. Lett. 20, 256 (1972).
[Crossref]

Appl. Spectrosc. (1)

J. Appl. Meteorol. (1)

J. Cooney, J. Appl. Meteorol. 9, 108 (1972).
[Crossref]

J. Chem. Phys. (1)

R. L. Rowell, G. M. Aval, and J. J. Barrett, J. Chem. Phys. 54, 1960 (1971).
[Crossref]

J. Mol. Spectrosc. (1)

The O2 RRS spectrum departs slightly from that of an SLM because the ground electronic state is a spin triplet. In consequence, each RRS line is split into a triplet, having relatively weak satellite components separated by a few cm−1 from the central component. The satellite intensities decrease rapidly as the rotational quantum number increases. RRS cross sections reported in this work correspond to the sum of the three lines in each triplet. For a high-resolution spectrum of O2 RRS and its analysis, see for example, Daryl L. Renschler, James L. Hunt, T. K. McCubbin, and S. R. Polo, J. Mol. Spectrosc. 31, 173 (1969).
[Crossref]

J. Opt. Soc. Am. (3)

Nat. Phys. Sci. (1)

C. M. Penney, L. M. Goldman, and M. Lapp, Nat. Phys. Sci. 235, 110 (1972).
[Crossref]

Proc. R. Soc. A (1)

N. J. Bridge and A. D. Buckingham, Proc. R. Soc. A 295, 334 (1966).
[Crossref]

Rev. Sci. Instrum. (1)

R. S. Hickman and L. H. Liang, Rev. Sci. Instrum. 43, 796 (1972).
[Crossref]

Other (4)

Alfons Weber, in The Raman Effect, Vol. 2: Applications, edited by Anthony Anderson (Dekker, New York, 1973), Ch. 9.

Gerhard Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules (Van Nostrand, Princeton, N. J., 1950).

Jack A. Salzman, William J. Masica, and Thom A. Coney, Determination of Gas Temperatures from Laser-Raman Scattering, (National Technical Information Service, Springfield, Va., 1971); Jack A. Salzman and Thom A. Coney, Remote Measurement of Atmospheric Temperatures by Raman Lidar, (National Technical Information Service, Springfield, Va., 1973).

G. Placzek, in Handbuch der Radiologie, Vol. 6, edited by G. Marx (Akademische Verlagsgesellschaft, Leipzig, 1934), Part 2, p. 205. English translation by A. Werbin, U.C.R.L. Translation No. 526(L), Lawrence Radiation Laboratory (1959).

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Figures (1)

Fig. 1
Fig. 1

Relationship between polarization angle ψ and scattering angles θ, ϕ, and ξ. The unit vectors k ˆ 1 and k ˆ 2 denote the directions of the incident beam, and the observed scattered beam, respectively. Likewise, ˆ 1 and ˆ 2 denote the directions of the electric field polarization of the incident and scattered beam. The line OA is perpendicular to k ˆ 2 and in the plane defined by ˆ 1 and k ˆ 2. The quantity cos2ψ in Eq. (5) is equal to cos2ξ (1 − sin2θ cos2ϕ).

Tables (4)

Tables Icon

Table I Values of the statistical weight factor gJ, nuclear spin I, and rotational constant B0. The rotational constant values are taken from a compilation of results from Raman-scattering data in Ref. 7.

Tables Icon

Table II Representative values of the sums S2, S−2, S0, and S.

Tables Icon

Table III Results for γ2 for N2, O2, and CO2. Values in the last column are calculated from Eq. (12) using measured depolarization ratios for the band comprising unshifted Rayleigh scattering plus RRS wings at 488.0 nm (Ref. 4) and 632.8 nm (Ref. 5). The expected percent errors refer to the absolute values presented here. However, the ratios of γ2 for O2 and CO2 to γ2 for N2 have smaller expected errors of ±5% and ±10%, respectively, because the basic data for these gases were obtained relative to data from N2.

Tables Icon

Table IV Values for RRS-line cross sections (σzz)JJ for incident light at 488.0 nm. Also shown are corresponding rotational line to Q-branch vibrational-band intensity ratios RJJ, as defined by Fenner et al.6 and by Eq. (15) in this paper. The ratios are calculated for a temperature of 22°C, and involve lines summed over polarization for the right-angle-scattering configuration described in the text. The ratios for CO2 are calculated with respect to its ν1 (1388 cm−1) vibrational band.

Equations (19)

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I J J = P N L F J σ J J ,
F J = Q - 1 g J ( 2 J + 1 ) exp ( - E J / k T ) .
J = 0 F J = 1.
Q ( 2 I + 1 ) 2 k T / 2 h c B 0 ,
σ J J ( θ , ϕ , ξ ) = ( σ z z ) J J [ ( 1 - ρ ) cos 2 ψ + ρ ] .
( σ z z ) J J = 64 π 4 45 b J J ( ω 0 + Δ ω J J ) 4 γ 2 ,
b J J + 2 = 3 ( J + 1 ) ( J + 2 ) 2 ( 2 J + 1 ) ( 2 J + 3 ) , b J J - 2 = 3 J ( J - 1 ) 2 ( 2 J + 1 ) ( 2 J - 1 ) , b J J = J ( J + 1 ) ( 2 J - 1 ) ( 2 J + 3 ) .
σ T = ( 8 π 3 ) σ z z ( 1 + 2 ρ ) .
polarized Rayleigh scattering C t ( n ) + C q ( γ ) ,
depolarized Rayleigh scattering 3 4 C q ( γ ) .
S Δ J J 0 F J b J J + Δ J ( ω 0 + Δ ω J J + Δ J ω 0 ) 4 ,
S S 0 + S 2 + S - 2 .
ρ L = 3 4 ( 64 π 4 45 S 0 γ 2 ω 0 4 ) / ( σ t + 64 π 4 45 S 0 γ 2 ω 0 4 ) ,
ρ B = 3 4 ( 64 π 4 45 S γ 2 ω 0 4 ) / ( σ t + 64 π 4 45 S γ 2 ω 0 4 ) .
σ t = 4 π 2 ω 0 4 ( n - 1 N ) 2 ,
( σ z z ) Ray = 4 π 2 ω 0 4 ( n - 1 N ) 2 ( 3 3 - 4 ρ Ray ) ,
R J J = ( 7 / 4 ) F J ( σ z z ) J J / σ vib .
σ back = 112 π 4 45 ω 0 4 γ 2 ( S 2 + S - 2 ) .
σ back = 1.64 × 10 - 29 cm 2 / sr ± 8 % .