Abstract

The differential Raman cross sections of the main Raman-active vibrations have been measured in the gases N2, O2, H2, CO, NO, CO2, SO2, N2O, H2S, NH3, ND3, CH4, C2H6, and C6H6 using 488.0-nm laser light. The present results are compared with previous measurements made at other wavelengths. The Raman cross sections of the rotational lines in the diatomic gases were also measured, as were the vibrational-rotational lines of O2 and N2. Absolute measurement of the Raman cross sections were performed two ways: (i) by calibrating the Raman spectrometer, and (ii) by comparing the unknown against liquid benzene (for which the Raman cross section has been measured). Results of these measurements compare reasonably well with previous determinations for which corrections for the υ4 frequency dependence were made.

© 1973 Optical Society of America

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References

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  1. E. J. Stansbury, M. F. Crawford, and H. L. Welch, Can. J. Phys. 31, 954 (1953).
    [Crossref]
  2. W. F. Murphy, W. Holzer, and H. J. Bernstein, Appl. Spectrosc. 23, 211 (1969).
    [Crossref]
  3. D. G. Fouche and R. K. Chang, Appl. Phys. Letters 18, 579 (1971).
    [Crossref]
  4. D. G. Fouche and R. K. Chang, Appl. Phys. Letters 20, 256 (1972).
    [Crossref]
  5. C. M. Penney, L. M. Goldman, and M. Lapp, Nature Phys. Sci. 235, 110 (1972).
  6. The collection factor Fc is defined for the particular scattering geometry of laser Raman spectrometer, in which the spatial width of the object, i.e., the Raman scattered light from the scattering volume, is finite and small. When the entrance slits are wide compared to the spatial width of the object and the spectral bandwidth of the spectrometer is wider than the natural linewidth of the Raman scattered light, then Fc ≃ 1. When the slits are narrow, then Fc is the ratio of the integrated intensity of the measured Raman line to the integrated area of the same line measured with wide slits. Integrated intensity is used here as the measured area of the Raman line divided by the spectral slit width.
  7. W. Holzer, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys. 52, 399 (1970).
    [Crossref]
  8. K. Sakurai and H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
    [Crossref]
  9. G. Herzberg, Molecular Spectra and Molecular Structure, I. Spectra of Diatomic Molecules, 2nd ed.(Van Nostrand Reinhold, New York, 1950), p. 128.
  10. The differential Rayleigh cross section for incident polarized laser light and orthogonal scattering geometry was computed from the equations (dσ/dΩ)Ray= (3/8π)σtot, where σtot= 128π5α2/3λ4 and α= n2− 1/4πN≃n− 1/2πN. α is the polarizability, n the index of refraction, N the number density of gas molecules, λ the wavelength, and σtot the integrated (total) Rayleigh scattering cross section per molecule, assuming no depolarization. Corrections for finite depolarization are small.Explanation of Rayleigh scattering is given in the standard text: S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 35.
  11. Indices of refraction were computed from the dispersion relationships for each of the gases considered here.Sources for dispersion equations and indices are E. R. Peck and B. N. Khanna, J. Opt. Soc. Am. 56, 1059 (1966);C. W. Allen, Astrophysical Quantities (Athens Press, New York, 1963), p. 87;Landolt-Bornstein (Springer, Berlin, 1950), Table 1, p. 401;International Critical Tables (McGraw–Hill, New York, 1930), Vol. 7, pp. 1–11.
    [Crossref]
  12. Yoshiaki Kato and Hiroski Takuma, J. Opt. Soc. Am. 61, 347 (1971).
    [Crossref]

1972 (2)

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

C. M. Penney, L. M. Goldman, and M. Lapp, Nature Phys. Sci. 235, 110 (1972).

1971 (2)

D. G. Fouche and R. K. Chang, Appl. Phys. Letters 18, 579 (1971).
[Crossref]

Yoshiaki Kato and Hiroski Takuma, J. Opt. Soc. Am. 61, 347 (1971).
[Crossref]

1970 (1)

W. Holzer, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys. 52, 399 (1970).
[Crossref]

1969 (2)

1966 (1)

1953 (1)

E. J. Stansbury, M. F. Crawford, and H. L. Welch, Can. J. Phys. 31, 954 (1953).
[Crossref]

Bernstein, H. J.

W. Holzer, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys. 52, 399 (1970).
[Crossref]

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

Broida, H. P.

K. Sakurai and H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
[Crossref]

Chandrasekhar, S.

The differential Rayleigh cross section for incident polarized laser light and orthogonal scattering geometry was computed from the equations (dσ/dΩ)Ray= (3/8π)σtot, where σtot= 128π5α2/3λ4 and α= n2− 1/4πN≃n− 1/2πN. α is the polarizability, n the index of refraction, N the number density of gas molecules, λ the wavelength, and σtot the integrated (total) Rayleigh scattering cross section per molecule, assuming no depolarization. Corrections for finite depolarization are small.Explanation of Rayleigh scattering is given in the standard text: S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 35.

Chang, R. K.

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

D. G. Fouche and R. K. Chang, Appl. Phys. Letters 18, 579 (1971).
[Crossref]

Crawford, M. F.

E. J. Stansbury, M. F. Crawford, and H. L. Welch, Can. J. Phys. 31, 954 (1953).
[Crossref]

Fouche, D. G.

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

D. G. Fouche and R. K. Chang, Appl. Phys. Letters 18, 579 (1971).
[Crossref]

Goldman, L. M.

C. M. Penney, L. M. Goldman, and M. Lapp, Nature Phys. Sci. 235, 110 (1972).

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure, I. Spectra of Diatomic Molecules, 2nd ed.(Van Nostrand Reinhold, New York, 1950), p. 128.

Holzer, W.

W. Holzer, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys. 52, 399 (1970).
[Crossref]

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

Kato, Yoshiaki

Khanna, B. N.

Lapp, M.

C. M. Penney, L. M. Goldman, and M. Lapp, Nature Phys. Sci. 235, 110 (1972).

Murphy, W. F.

W. Holzer, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys. 52, 399 (1970).
[Crossref]

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

Peck, E. R.

Penney, C. M.

C. M. Penney, L. M. Goldman, and M. Lapp, Nature Phys. Sci. 235, 110 (1972).

Sakurai, K.

K. Sakurai and H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
[Crossref]

Stansbury, E. J.

E. J. Stansbury, M. F. Crawford, and H. L. Welch, Can. J. Phys. 31, 954 (1953).
[Crossref]

Takuma, Hiroski

Welch, H. L.

E. J. Stansbury, M. F. Crawford, and H. L. Welch, Can. J. Phys. 31, 954 (1953).
[Crossref]

Appl. Phys. Letters (2)

D. G. Fouche and R. K. Chang, Appl. Phys. Letters 18, 579 (1971).
[Crossref]

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

Appl. Spectrosc. (1)

Can. J. Phys. (1)

E. J. Stansbury, M. F. Crawford, and H. L. Welch, Can. J. Phys. 31, 954 (1953).
[Crossref]

J. Chem. Phys. (2)

W. Holzer, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys. 52, 399 (1970).
[Crossref]

K. Sakurai and H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
[Crossref]

J. Opt. Soc. Am. (2)

Nature Phys. Sci. (1)

C. M. Penney, L. M. Goldman, and M. Lapp, Nature Phys. Sci. 235, 110 (1972).

Other (3)

The collection factor Fc is defined for the particular scattering geometry of laser Raman spectrometer, in which the spatial width of the object, i.e., the Raman scattered light from the scattering volume, is finite and small. When the entrance slits are wide compared to the spatial width of the object and the spectral bandwidth of the spectrometer is wider than the natural linewidth of the Raman scattered light, then Fc ≃ 1. When the slits are narrow, then Fc is the ratio of the integrated intensity of the measured Raman line to the integrated area of the same line measured with wide slits. Integrated intensity is used here as the measured area of the Raman line divided by the spectral slit width.

G. Herzberg, Molecular Spectra and Molecular Structure, I. Spectra of Diatomic Molecules, 2nd ed.(Van Nostrand Reinhold, New York, 1950), p. 128.

The differential Rayleigh cross section for incident polarized laser light and orthogonal scattering geometry was computed from the equations (dσ/dΩ)Ray= (3/8π)σtot, where σtot= 128π5α2/3λ4 and α= n2− 1/4πN≃n− 1/2πN. α is the polarizability, n the index of refraction, N the number density of gas molecules, λ the wavelength, and σtot the integrated (total) Rayleigh scattering cross section per molecule, assuming no depolarization. Corrections for finite depolarization are small.Explanation of Rayleigh scattering is given in the standard text: S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 35.

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Tables (4)

Tables Icon

Table I Pertinent properties of molecules studied.

Tables Icon

Table II Ratios of differential Raman cross sections of various vibrational lines to that of the υ1 vibration in N2 at 488.0 nm. Other workers’ results adjusted to 488.0 nm using an assumed frequency dependence of υR4.

Tables Icon

Table III Ratio of Raman cross sections of the rotational lines of certain molecules to that of the Q-branch of the υ1 vibration of the same molecule. The rotational cross section is the differential cross section for both polarizations at 90°. All lines refer to the sum of all Stokes and anti-Stokes rotational lines; peak refers to the strongest Stokes line. Data taken at 22 °C.

Tables Icon

Table IV Absolute differential Raman cross section of the vibrational line in N2 at 488.0 nm. Results of other authors were adjusted using a υR4 frequency dependence.

Equations (10)

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I s = [ Ω c ( d σ d Ω ) d Ω ] I 0 A n V ,
( d σ d Ω ) 0 1 Ω c Ω c ( d σ d Ω ) d Ω ,
( d σ d Ω ) 0 = I s Ω c n L I 0 .
N c = η F c I s ,
Ω c L = ( M 2 Ω m ) ( H / M ) = M Ω m H .
( d σ d Ω ) 0 = N c η F c M Ω m H n I 0 .
( d σ d Ω ) J = K C ( λ R ) υ R 4 S J exp { h c B J ( J + 1 ) / k T } ,
S J = 3 ( J + 1 ) ( J + 2 ) 2 ( 2 J + 3 ) for stokes lines , = 3 ( J 1 ) J 2 ( 2 J 1 ) for anti‐Stokes lines .
A 1 { ² 1 2 ² 1 2
{ a 1 a 1 g