Abstract

Expressions for the angular dependence of the intensity of Raman lines in fluids are obtained. A one-to-one relation between depolarization ratio and the angular dependence is shown. Angular dependence was measured for a large number of lines, showing that the easy-to-measure depolarization ratio of a Raman line suffices to determine its angular dependence.

© 1966 Optical Society of America

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References

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  1. H. Kogelnik and S. P. S. Porto, J. Opt. Soc. Am. 53, 1446 (1963); R. C. C. Leite and S. P. S. Porto, ibid. 54, 981 (1964); R. C. C. Leite, R. S. Moore, and S. P. S. Porto, J. Chem. Phys. 40, 3741 (1964).
    [Crossref]
  2. T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
    [Crossref]
  3. R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. E. Ripper, Phys. Rev. Letters 14, 7 (1965); R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964); G. B. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, ibid. 54, 1284 (1964).
    [Crossref]
  4. G. Placzek, Marx’s Handb. Radiol. 6, 209 (1934).
  5. L. A. Woodward and D. A. Long, Trans. Faraday Soc. 45, 1131 (1949).
    [Crossref]
  6. E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill Book Co., Inc., New York, 1955).
  7. For a complete table of symmetry characters of all vibrations in the 32-point groups, see Ref. 6 or G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand Company, Inc., New York, 1945).

1965 (2)

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. E. Ripper, Phys. Rev. Letters 14, 7 (1965); R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964); G. B. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, ibid. 54, 1284 (1964).
[Crossref]

1963 (1)

1949 (1)

L. A. Woodward and D. A. Long, Trans. Faraday Soc. 45, 1131 (1949).
[Crossref]

1934 (1)

G. Placzek, Marx’s Handb. Radiol. 6, 209 (1934).

Cross, P. C.

E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill Book Co., Inc., New York, 1955).

Damen, T. C.

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

Decius, J. C.

E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill Book Co., Inc., New York, 1955).

Herzberg, G.

For a complete table of symmetry characters of all vibrations in the 32-point groups, see Ref. 6 or G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand Company, Inc., New York, 1945).

Kogelnik, H.

Leite, R. C. C.

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. E. Ripper, Phys. Rev. Letters 14, 7 (1965); R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964); G. B. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, ibid. 54, 1284 (1964).
[Crossref]

Long, D. A.

L. A. Woodward and D. A. Long, Trans. Faraday Soc. 45, 1131 (1949).
[Crossref]

Moore, R. S.

R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. E. Ripper, Phys. Rev. Letters 14, 7 (1965); R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964); G. B. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, ibid. 54, 1284 (1964).
[Crossref]

Placzek, G.

G. Placzek, Marx’s Handb. Radiol. 6, 209 (1934).

Porto, S. P. S.

R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. E. Ripper, Phys. Rev. Letters 14, 7 (1965); R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964); G. B. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, ibid. 54, 1284 (1964).
[Crossref]

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

H. Kogelnik and S. P. S. Porto, J. Opt. Soc. Am. 53, 1446 (1963); R. C. C. Leite and S. P. S. Porto, ibid. 54, 981 (1964); R. C. C. Leite, R. S. Moore, and S. P. S. Porto, J. Chem. Phys. 40, 3741 (1964).
[Crossref]

Ripper, J. E.

R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. E. Ripper, Phys. Rev. Letters 14, 7 (1965); R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964); G. B. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, ibid. 54, 1284 (1964).
[Crossref]

Wilson, E. B.

E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill Book Co., Inc., New York, 1955).

Woodward, L. A.

L. A. Woodward and D. A. Long, Trans. Faraday Soc. 45, 1131 (1949).
[Crossref]

J. Opt. Soc. Am. (1)

Marx’s Handb. Radiol. (1)

G. Placzek, Marx’s Handb. Radiol. 6, 209 (1934).

Phys. Rev. Letters (2)

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. E. Ripper, Phys. Rev. Letters 14, 7 (1965); R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964); G. B. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, ibid. 54, 1284 (1964).
[Crossref]

Trans. Faraday Soc. (1)

L. A. Woodward and D. A. Long, Trans. Faraday Soc. 45, 1131 (1949).
[Crossref]

Other (2)

E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill Book Co., Inc., New York, 1955).

For a complete table of symmetry characters of all vibrations in the 32-point groups, see Ref. 6 or G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand Company, Inc., New York, 1945).

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Figures (7)

Fig. 1
Fig. 1

Geometries used to specify the depolarization ratio and angular dependence of the Raman effect. The sample is at origin 0; the laser beam is incident in the Y direction and the scattered light is measured in the XY plane. At the left the laser light is polarized perpendicular to the XY plane; at the right the laser is polarized in the XY plane.

Fig. 2
Fig. 2

Angular dependence of the 318-cm−1 line of CCl4. The depolarization ratio of this line is 0.75 and the solid curve is the theoretical curve obtained from Eq. (7) in text.

Fig. 3
Fig. 3

Angular dependence of the 1585–1606 cm−1 unresolved benzene doublet. Both lines have a symmetry character E2g. The depolarization ratio is 0.75; the solid line corresponds to the theoretical curve.

Fig. 4
Fig. 4

Angular dependence of the totally symmetric A1g-character symmetry line of CCl4 at 458 cm−1. The depolarization ratio is 0.005.

Fig. 5
Fig. 5

Angular dependence of the 992-cm−1A1g line of benzene, where the depolarization ratio is 0.065.

Fig. 6
Fig. 6

Angular dependence of the symmetric A vibration in nitrobenzene at 1347 cm−1; the depolarization ratio is 0.17.

Fig. 7
Fig. 7

Angular dependence of the 3045–62 cm−1 doublet in benzene. One of the lines has an A1g character while the other is Eg. The depolarization ratio measured for the doublet was P = 0.19.

Equations (21)

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I a b ( ρ ) = 2 π 2 ( ν 0 ν a b ) 4 h N μ c 4 ν a b [ 1 exp ( h ν a b / K T ) ] ( α σ ρ ) a b 2 I 0 ( σ ) .
ρ I Z Y / I Z Z = α Z Y 2 / α zz 2 .
α Ω Σ = ρ , σ α σ ρ cos ( σ , Σ ) cos ( ρ , Ω ) .
α Ω Σ = i α i cos ( i , Σ ) cos ( i , Ω ) .
cos ( i , Σ ) cos ( j , Ω ) cos ( i , Ω ) cos ( j , Σ ) av = 1 / 5 , if i = j and Σ = Ω = 1 / 15 , if i = j and Σ Ω or i j and Σ = Ω = 1 / 30 , if i j , Σ Ω
ρ = 3 β 2 / ( 45 α 2 + 4 β 2 ) ,
β 2 = 1 2 [ ( α 1 α 2 ) 2 + ( α 2 α 3 ) 2 + ( α 3 α 1 ) 2 ]
α = 1 3 ( α 1 + α 2 + α 3 ) ;
I ( θ ) = 2 π 2 ν 4 h c 4 N a μ ν a b 1 1 exp ( h ν a b / K T ) × I 0 [ α Z Z 2 + α Z X 2 cos 2 θ + α Z Y 2 sin 2 θ ] I ( θ ) = 2 π 2 ν 4 h c 4 N a μ ν a b 1 1 exp ( h ν a b / K T ) × I 0 [ α X Z 2 + α X Y 2 sin 2 θ + α X X 2 cos 2 θ ] ,
I ( θ ) = 2 π 2 ν 4 h c 4 N a μ ν a b 1 1 exp ( h ν a b / K T ) I 0 45 × [ 45 α 2 + 7 β 2 ] I ( θ ) = 2 π 2 ν 4 h c 4 N a μ ν a b 1 1 exp ( h ν a b / K T ) I 0 45 × [ 6 β 2 + ( 45 α 2 + β 2 ) cos 2 θ ] ,
α = 0 , so ρ = 0.75 , I = 7 k s , I = k s ( 6 + cos 2 θ ) ;
α x x = α y y = α z z so β = 0 ;
ρ = 0 , I = k ( 0 ) , I = k ( 0 ) cos 2 θ ;
α 0 , β 0 so 0 ρ 0.75 since α 1 = α 2 α 3 ;
α 2 = β 2 [ ( 3 4 ρ ) / 45 ρ ] .
I = k β 2 [ ( 3 + 3 ρ ) / ρ ] I = k β 2 { 6 + [ ( 3 3 ρ ) / ρ ] cos 2 θ } .
I = 7 k s , I = k s ( 6 + cos 2 θ ) .
I k I k cos 2 θ .
I = k I = k ( 0.12 + 0.88 cos 2 θ ) .
I = k I = k ( 0.3 + 0.7 cos 2 θ ) .
I = k I = k ( 0.34 + 0.66 cos 2 θ ) .