Abstract

The focused beam of an argon–ion laser was used as a light source for Raman-scattering experiments in gases. Photoelectric recording of rotation–vibration Raman spectra has been observed from about 1011 gas molecules in the focal region of the laser beam. The focusing geometry used to illuminate the gas samples is discussed and the important parameters of the optical system for collecting the Raman-scattered light from the small volumes are considered. The pulse-counting detection system is described and the new experimental results are presented.

© 1968 Optical Society of America

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References

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  1. A. Weber, S. P. S. Porto, L. E. Cheesman, and J. J. Barrett, J. Opt. Soc. Am. 57, 19 (1967).
    [Crossref]
  2. S. P. S. Porto and D. L. Wood, J. Opt. Soc. Am. 52, 251 (1962).
    [Crossref]
  3. H. Kogelnik and S. P. S. Porto, J. Opt. Soc. Am. 53, 1446 (1963).
    [Crossref]
  4. R. C. C. Leite and S. P. S. Porto, J. Opt. Soc. Am. 54, 981 (1964). S. P. S. Porto, Ann. N. Y. Acad. Sci. 122, 643 (1965).
    [Crossref] [PubMed]
  5. J. A. Koningstein and R. G. Smith, J. Opt. Soc. Am. 54, 1061 (1964).
    [Crossref]
  6. A. Weber and S. P. S. Porto, J. Opt. Soc. Am. 55, 1033 (1965)
  7. J. H. Callomon, Can. J. Phys. 34, 1046 (1956).
    [Crossref]
  8. H. L. Welsh, E. J. Stansbury, J. Romanko, and T. Feldman, J. Opt. Soc. Am. 45, 338 (1955).
    [Crossref]
  9. G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
    [Crossref]
  10. G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
    [Crossref]
  11. G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).
    [Crossref]
  12. J. G. Atwood, J. Opt. Soc. Am. 53, 1343 (1963).
  13. A. Maréchal, Traité d’Optique Instrumentale, Tome I. Imagerie-Géométrique Aberrations (Editions de la Revue d’Optique Théorique et Instrumentale, Paris, 1952), p. 14.
  14. K. Halbach, Am. J. Phys. 32, 90 (1964).
    [Crossref]
  15. J. D. Rigden, IEEE J. Quant. Elec. 1, 221 (1965).
    [Crossref]
  16. W. A. Baum in Astronomical Techniques, W. A. Hiltner, Ed. (University of Chicago Press, Chicago, 1962), Vol. II, p. 1.
  17. W. A. Baum, Sky and Telescope 14, 264 (1955); Sky and Telescope 14, 330 (1955).
  18. H. L. Johnson, Sky and Telescope 17, 558 (1958).
  19. H. L. Johnson, in Astronomical Techniques, W. A. Hiltner, Ed. (University of Chicago Press, Chicago, 1962), Vol. II, p. 157.
  20. T. Dunham in Vistas in Astronomy, A. Beer, Ed. (Pergamon Press, New York, 1956), Vol. II, p. 1268.
  21. W. Blitzstein, in Astronomical Photoelectric Photometry, F. B. Wood, Ed. (Washington: American Association for the Advancement of Science, 1953), p. 64.
  22. L. Colli, U. Facchini, and A. Rossi, Nuovo Cimento 11, 255 (1954).
    [Crossref]
  23. E. H. Eberhardt, IEEE Trans. Nuclear Science NS-11, 48 (1964).
    [Crossref]
  24. E. H. Eberhardt, Appl. Opt. 6, 161 (1967).
    [Crossref] [PubMed]
  25. S. P. S. Porto, Bull. Am. Phys. Soc. 11, 79 (1966).
  26. A. T. Young, Rev. Sci. Instr. 37, 1472 (1966).
    [Crossref]
  27. A. Weber and E. A. McGinnis, J. Mol. Spectry. 4, 195 (1960).
    [Crossref]
  28. B. P. Stoicheff, Can. J. Phys. 32, 630 (1954).
    [Crossref]
  29. B. P. Stoicheff, Can. J. Phys. 36, 218 (1958).
    [Crossref]
  30. B. P. Stoicheff in Advances in Spectroscopy, H. W. Thompson, Ed. (Interscience Publishers, John Wiley & Sons, Inc., New York, 1959), Vol. I., p. 91.
  31. B. P. Stoicheff in Methods of Experimental Physics, D. Williams, Ed. (Academic Press Inc., New York1962), Vol. III, p. 111.
  32. The previous photographic work was done with high-resolution low-aperture spectrographs (approximately f/50) whereas in our experiments the aperture ratio of the spectrometer was f/8. This fact should be taken into account when making a comparison of exposure times.
  33. G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Co., Inc., New York, 1950), 2nd ed., p. 133.

1967 (2)

1966 (3)

S. P. S. Porto, Bull. Am. Phys. Soc. 11, 79 (1966).

A. T. Young, Rev. Sci. Instr. 37, 1472 (1966).
[Crossref]

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

1965 (2)

A. Weber and S. P. S. Porto, J. Opt. Soc. Am. 55, 1033 (1965)

J. D. Rigden, IEEE J. Quant. Elec. 1, 221 (1965).
[Crossref]

1964 (4)

1963 (2)

1962 (2)

G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).
[Crossref]

S. P. S. Porto and D. L. Wood, J. Opt. Soc. Am. 52, 251 (1962).
[Crossref]

1961 (1)

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

1960 (1)

A. Weber and E. A. McGinnis, J. Mol. Spectry. 4, 195 (1960).
[Crossref]

1958 (2)

B. P. Stoicheff, Can. J. Phys. 36, 218 (1958).
[Crossref]

H. L. Johnson, Sky and Telescope 17, 558 (1958).

1956 (1)

J. H. Callomon, Can. J. Phys. 34, 1046 (1956).
[Crossref]

1955 (2)

H. L. Welsh, E. J. Stansbury, J. Romanko, and T. Feldman, J. Opt. Soc. Am. 45, 338 (1955).
[Crossref]

W. A. Baum, Sky and Telescope 14, 264 (1955); Sky and Telescope 14, 330 (1955).

1954 (2)

L. Colli, U. Facchini, and A. Rossi, Nuovo Cimento 11, 255 (1954).
[Crossref]

B. P. Stoicheff, Can. J. Phys. 32, 630 (1954).
[Crossref]

Atwood, J. G.

J. G. Atwood, J. Opt. Soc. Am. 53, 1343 (1963).

Barrett, J. J.

Baum, W. A.

W. A. Baum, Sky and Telescope 14, 264 (1955); Sky and Telescope 14, 330 (1955).

W. A. Baum in Astronomical Techniques, W. A. Hiltner, Ed. (University of Chicago Press, Chicago, 1962), Vol. II, p. 1.

Benedek, G. B.

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

Blitzstein, W.

W. Blitzstein, in Astronomical Photoelectric Photometry, F. B. Wood, Ed. (Washington: American Association for the Advancement of Science, 1953), p. 64.

Boyd, G. D.

G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).
[Crossref]

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

Callomon, J. H.

J. H. Callomon, Can. J. Phys. 34, 1046 (1956).
[Crossref]

Cheesman, L. E.

Colli, L.

L. Colli, U. Facchini, and A. Rossi, Nuovo Cimento 11, 255 (1954).
[Crossref]

Dunham, T.

T. Dunham in Vistas in Astronomy, A. Beer, Ed. (Pergamon Press, New York, 1956), Vol. II, p. 1268.

Eberhardt, E. H.

E. H. Eberhardt, Appl. Opt. 6, 161 (1967).
[Crossref] [PubMed]

E. H. Eberhardt, IEEE Trans. Nuclear Science NS-11, 48 (1964).
[Crossref]

Facchini, U.

L. Colli, U. Facchini, and A. Rossi, Nuovo Cimento 11, 255 (1954).
[Crossref]

Feldman, T.

Fritsch, K.

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

Gordon, J. P.

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

Halbach, K.

K. Halbach, Am. J. Phys. 32, 90 (1964).
[Crossref]

Herzberg, G.

G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Co., Inc., New York, 1950), 2nd ed., p. 133.

Johnson, H. L.

H. L. Johnson, Sky and Telescope 17, 558 (1958).

H. L. Johnson, in Astronomical Techniques, W. A. Hiltner, Ed. (University of Chicago Press, Chicago, 1962), Vol. II, p. 157.

Kogelnik, H.

H. Kogelnik and S. P. S. Porto, J. Opt. Soc. Am. 53, 1446 (1963).
[Crossref]

G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).
[Crossref]

Koningstein, J. A.

Leite, R. C. C.

Maréchal, A.

A. Maréchal, Traité d’Optique Instrumentale, Tome I. Imagerie-Géométrique Aberrations (Editions de la Revue d’Optique Théorique et Instrumentale, Paris, 1952), p. 14.

McGinnis, E. A.

A. Weber and E. A. McGinnis, J. Mol. Spectry. 4, 195 (1960).
[Crossref]

Porto, S. P. S.

Rigden, J. D.

J. D. Rigden, IEEE J. Quant. Elec. 1, 221 (1965).
[Crossref]

Romanko, J.

Rossi, A.

L. Colli, U. Facchini, and A. Rossi, Nuovo Cimento 11, 255 (1954).
[Crossref]

Smith, R. G.

Stansbury, E. J.

Stoicheff, B. P.

B. P. Stoicheff, Can. J. Phys. 36, 218 (1958).
[Crossref]

B. P. Stoicheff, Can. J. Phys. 32, 630 (1954).
[Crossref]

B. P. Stoicheff in Advances in Spectroscopy, H. W. Thompson, Ed. (Interscience Publishers, John Wiley & Sons, Inc., New York, 1959), Vol. I., p. 91.

B. P. Stoicheff in Methods of Experimental Physics, D. Williams, Ed. (Academic Press Inc., New York1962), Vol. III, p. 111.

Weber, A.

Welsh, H. L.

Wood, D. L.

Young, A. T.

A. T. Young, Rev. Sci. Instr. 37, 1472 (1966).
[Crossref]

Am. J. Phys. (1)

K. Halbach, Am. J. Phys. 32, 90 (1964).
[Crossref]

Appl. Opt. (1)

Bell System Tech. J. (2)

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).
[Crossref]

Bull. Am. Phys. Soc. (1)

S. P. S. Porto, Bull. Am. Phys. Soc. 11, 79 (1966).

Can. J. Phys. (3)

B. P. Stoicheff, Can. J. Phys. 32, 630 (1954).
[Crossref]

B. P. Stoicheff, Can. J. Phys. 36, 218 (1958).
[Crossref]

J. H. Callomon, Can. J. Phys. 34, 1046 (1956).
[Crossref]

IEEE J. Quant. Elec. (1)

J. D. Rigden, IEEE J. Quant. Elec. 1, 221 (1965).
[Crossref]

IEEE Trans. Nuclear Science (1)

E. H. Eberhardt, IEEE Trans. Nuclear Science NS-11, 48 (1964).
[Crossref]

J. Mol. Spectry. (1)

A. Weber and E. A. McGinnis, J. Mol. Spectry. 4, 195 (1960).
[Crossref]

J. Opt. Soc. Am. (8)

Nuovo Cimento (1)

L. Colli, U. Facchini, and A. Rossi, Nuovo Cimento 11, 255 (1954).
[Crossref]

Phys. Rev. (1)

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

Rev. Sci. Instr. (1)

A. T. Young, Rev. Sci. Instr. 37, 1472 (1966).
[Crossref]

Sky and Telescope (2)

W. A. Baum, Sky and Telescope 14, 264 (1955); Sky and Telescope 14, 330 (1955).

H. L. Johnson, Sky and Telescope 17, 558 (1958).

Other (9)

H. L. Johnson, in Astronomical Techniques, W. A. Hiltner, Ed. (University of Chicago Press, Chicago, 1962), Vol. II, p. 157.

T. Dunham in Vistas in Astronomy, A. Beer, Ed. (Pergamon Press, New York, 1956), Vol. II, p. 1268.

W. Blitzstein, in Astronomical Photoelectric Photometry, F. B. Wood, Ed. (Washington: American Association for the Advancement of Science, 1953), p. 64.

W. A. Baum in Astronomical Techniques, W. A. Hiltner, Ed. (University of Chicago Press, Chicago, 1962), Vol. II, p. 1.

A. Maréchal, Traité d’Optique Instrumentale, Tome I. Imagerie-Géométrique Aberrations (Editions de la Revue d’Optique Théorique et Instrumentale, Paris, 1952), p. 14.

B. P. Stoicheff in Advances in Spectroscopy, H. W. Thompson, Ed. (Interscience Publishers, John Wiley & Sons, Inc., New York, 1959), Vol. I., p. 91.

B. P. Stoicheff in Methods of Experimental Physics, D. Williams, Ed. (Academic Press Inc., New York1962), Vol. III, p. 111.

The previous photographic work was done with high-resolution low-aperture spectrographs (approximately f/50) whereas in our experiments the aperture ratio of the spectrometer was f/8. This fact should be taken into account when making a comparison of exposure times.

G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Co., Inc., New York, 1950), 2nd ed., p. 133.

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Figures (8)

Fig. 1
Fig. 1

Geometry of the focal region of the laser beam. The diagram is cylindrically symmetric about the z axis. The effective volume of the Raman sample was taken to be the volume of a cylinder of diameter 2w0 and length 2b.

Fig. 2
Fig. 2

Experimental arrangement for determining the dependence of the detected Raman signal on the focusing angle α.

Fig. 3
Fig. 3

Relative intensity of the Stokes-shifted, J=7 pure rotation. Raman line of oxygen versus the focusing angle α of the illuminating laser beam. The points shown are experimental. The solid curve is sketched through the points to emphasize that the Raman intensity at α=0.10 is substantially less than would be consistent with a linear extrapolation from small values of α. The curve as drawn conforms to the theoretical expectation that the Raman intensity goes to zero linearly as α goes to zero.

Fig. 4
Fig. 4

A logarithmic plot of the values of the fractional Raman flux F and the total Raman flux R as calculated for our experimental conditions (see Table II), versus the focusing angle α of the illuminating laser beam.

Fig. 5
Fig. 5

General experimental arrangement. The polarization vector of the laser beam lies in the plane of the figure and the Raman-scattered light is observed in a direction parallel to the polarization vector. The lens L2, which has an aperture ratio of f/0.95 and a focal length of 5.0 cm, was used to collect the Raman-scattered light over a large solid angle.

Fig. 6
Fig. 6

Rotation–vibration Raman band of O2 at a gas pressure of one atmosphere. The Ar+ 4880 Å laser line was used to obtain the spectrum. The lower scale gives the Stokes frequency shift (in cm−1) from the exciting line. This spectrum corresponds to scattering from about 1011 molecules in a volume of about 10−8 cm3. The irregular intensity distribution of the rotational lines is due to the statistical fluctuations of the numbers of photons detected by the photomultiplier tube and intensity fluctuations of the laser.

Fig. 7
Fig. 7

Rotation–vibration Raman band in N2. The spectrum clearly shows the alternation of intensities for the rotational lines. The total number of photomultiplier pulses for a typical rotational line [e.g., O (8)] would be approximately 200–300.

Fig. 8
Fig. 8

Rotation–vibration bands of CO2 showing the Fermi diad ν1, 2ν2. The rotational structure is not completely resolved, owing to the monochromator being slightly out of focus.

Tables (2)

Tables Icon

Table I Focusing Parameters.

Tables Icon

Table II Calculated Raman fluxes for the three focusing regions.a

Equations (7)

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α = d / f ,
b = 8 λ / ( π α 2 ) .
b = w 0 2 k ,
w 0 = ( b λ / 2 π ) 1 2 = 2 λ / π α .
w ( z ) = w 0 [ 1 + ( 2 z / b ) 2 ] 1 2 .
L = L s / M ; W = W s / M ; Ω = Ω s M 2 ,
α W = 4 λ / π W = 4 λ M / π W s α L = ( 16 λ / π L ) 1 2 = ( 16 λ M / π L s ) 1 2 .