Abstract

A method for determining the depolarization ratio in Raman spectroscopy as a function of the scattering frequency (to the resolution limit of the spectrometer) is described. The method is analyzed briefly and compared to current methods. Experimental results for four well-known Raman bands of liquids are reported.

© 1973 Optical Society of America

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References

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  1. G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, New York, 1945), pp. 248–249.
  2. S. P. S. Porto, J. Opt. Soc. Am. 56, 1585 (1966).
    [Crossref]
  3. G. Placzek, in Marx’s Handbook of Radiol, Vol. 6 (Akademische Verlagsgesellshaft VI, Leipzig, 1934), pp. 209–374.
  4. A summary of various methods for determining depolarization ratios is contained in C. Allemand, Appl. Spectrosc. 24, 348 (1970).See also Ref. 5.
    [Crossref]
  5. H. H. Claasen, H. Selig, and J. Shamir, Appl. Spectrosc. 23, 8 (1969).
    [Crossref]
  6. A commercially available system that measures depolarization ratios as functions of frequency uses a mechanically chopped beam to accomplish the purpose.
  7. At least three means exist. In Ref. 2, the spectrometer was calibrated for all polarization states so that a correction could be applied as data were being reduced. Optical devices, as a half-wave plate or polarization scrambler, can be placed between the spectrometer and the polarizing filter to eliminate the need for correction. See Ref. 4.
  8. A. Yariv, Quantum Electronics (Wiley, New York, 1967), pp. 310–314.
  9. Some authors use ρ = 2ID/(ID+IP), which gives a range of zero to 6/7. This is discussed in Ref. 3.
  10. Other authors have considered aperture error. See N. J. Bridge and A. D. Buckingham, Proc. Roy. Soc. (London) A295, 334 (1966);P. Dawson, Spectrochim. Acta 28A, 715 (1972);and Ref. 4.
  11. R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, New York, 1969), p. 243.
  12. Reference 1, pp. 215–218, 276–277.
  13. A. Langseth, J. O. Sorensen, and J. R. Nielson, J. Chem. Phys. 2, 402 (1934).
    [Crossref]

1970 (1)

1969 (1)

1966 (2)

Other authors have considered aperture error. See N. J. Bridge and A. D. Buckingham, Proc. Roy. Soc. (London) A295, 334 (1966);P. Dawson, Spectrochim. Acta 28A, 715 (1972);and Ref. 4.

S. P. S. Porto, J. Opt. Soc. Am. 56, 1585 (1966).
[Crossref]

1934 (1)

A. Langseth, J. O. Sorensen, and J. R. Nielson, J. Chem. Phys. 2, 402 (1934).
[Crossref]

Allemand, C.

Bridge, N. J.

Other authors have considered aperture error. See N. J. Bridge and A. D. Buckingham, Proc. Roy. Soc. (London) A295, 334 (1966);P. Dawson, Spectrochim. Acta 28A, 715 (1972);and Ref. 4.

Buckingham, A. D.

Other authors have considered aperture error. See N. J. Bridge and A. D. Buckingham, Proc. Roy. Soc. (London) A295, 334 (1966);P. Dawson, Spectrochim. Acta 28A, 715 (1972);and Ref. 4.

Claasen, H. H.

Herzberg, G.

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, New York, 1945), pp. 248–249.

Langseth, A.

A. Langseth, J. O. Sorensen, and J. R. Nielson, J. Chem. Phys. 2, 402 (1934).
[Crossref]

Nielson, J. R.

A. Langseth, J. O. Sorensen, and J. R. Nielson, J. Chem. Phys. 2, 402 (1934).
[Crossref]

Pantell, R. H.

R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, New York, 1969), p. 243.

Placzek, G.

G. Placzek, in Marx’s Handbook of Radiol, Vol. 6 (Akademische Verlagsgesellshaft VI, Leipzig, 1934), pp. 209–374.

Porto, S. P. S.

Puthoff, H. E.

R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, New York, 1969), p. 243.

Selig, H.

Shamir, J.

Sorensen, J. O.

A. Langseth, J. O. Sorensen, and J. R. Nielson, J. Chem. Phys. 2, 402 (1934).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1967), pp. 310–314.

Appl. Spectrosc. (2)

J. Chem. Phys. (1)

A. Langseth, J. O. Sorensen, and J. R. Nielson, J. Chem. Phys. 2, 402 (1934).
[Crossref]

J. Opt. Soc. Am. (1)

Proc. Roy. Soc. (London) (1)

Other authors have considered aperture error. See N. J. Bridge and A. D. Buckingham, Proc. Roy. Soc. (London) A295, 334 (1966);P. Dawson, Spectrochim. Acta 28A, 715 (1972);and Ref. 4.

Other (8)

R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, New York, 1969), p. 243.

Reference 1, pp. 215–218, 276–277.

G. Placzek, in Marx’s Handbook of Radiol, Vol. 6 (Akademische Verlagsgesellshaft VI, Leipzig, 1934), pp. 209–374.

A commercially available system that measures depolarization ratios as functions of frequency uses a mechanically chopped beam to accomplish the purpose.

At least three means exist. In Ref. 2, the spectrometer was calibrated for all polarization states so that a correction could be applied as data were being reduced. Optical devices, as a half-wave plate or polarization scrambler, can be placed between the spectrometer and the polarizing filter to eliminate the need for correction. See Ref. 4.

A. Yariv, Quantum Electronics (Wiley, New York, 1967), pp. 310–314.

Some authors use ρ = 2ID/(ID+IP), which gives a range of zero to 6/7. This is discussed in Ref. 3.

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, New York, 1945), pp. 248–249.

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Figures (6)

F. 1
F. 1

Geometries for depolarization-ratio experiments. The sample is at the origin, the laser beam is z directed, and scattering is observed in the x direction. Iyy is the only polarized component and may be compared with either Izy or Iyx for the two methods discussed in the text. Angles θ and φ are rotations about the y and z axes, respectively, and measure deviations from the x direction.

F. 2
F. 2

Schematic of a depolarization-ratio experiment using a Pockell’s cell. The modulator must be oriented precisely for proper operation. The vertical slit is for reducing error due to aperture effects, and the prism is required only if depth of polarization is poor in the laser beam.

F. 3
F. 3

Spectrum of the benzene doublet, 3045–3062 cm−1. The polarized spectrum is normalized to unit peak height, the depolarized spectrum (multiplied by the indicated gain) relative to it. The depolarization ratio is plotted on a zero-to-one scale.

F. 4
F. 4

Spectrum of the benzene line, 992 cm−1. The plot is on the same scale as Fig. 3.

F. 5
F. 5

Spectrum of the carbon disulfide ν1 band, 657 cm−1. The plot is on the same scale as Fig. 3.

F. 6
F. 6

Spectrum of the carbon disulfide 2ν2 band, 796 cm−1. The plot is on the same scale as Fig. 3.

Equations (3)

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α x x 2 = α y y 2 = α z z 2 α P 2 = α 2 + 4 β 2 / 15 , α x y 2 = α y x 2 = α y z 2 = α z y 2 = α z x 2 = α x z 2 α D 2 = β 2 / 15 ,
ρ I D I P = I y x I y y = α y x 2 α y y 2 = α D 2 α P 2 = 3 β 2 4 β 2 + 45 α 2 ,
ρ meas = ρ + ρ F ( Θ ) 1 + ρ F ( Θ ) ( method 1 ) , ρ meas = ρ + F ( Θ ) 1 + ρ F ( Θ ) ( method 2 ) , F ( Θ ) = 2 3 cos ( Θ ) + cos 3 ( Θ ) 4 3 cos ( Θ ) cos 3 ( Θ ) ,