Abstract

Theoretical and experimental results are presented for the line shape of Raman-induced Kerr effect resonances observed with elliptical pump polarization. The line shape is sensitive to the ratio of the Kerr constant to the Raman tensor. Comparison of these results to those obtained by three-wave mixing reveals that the electronic contribution to the Kerr constant of benzene is 12%.

© 1976 Optical Society of America

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References

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  1. G. Mayer and F. Gires, C. R. Acad. Sci. (Paris) 258, 2039 (1964).
  2. P. Maker and R. Terhune, Phys. Rev. 137, A801 (1964).
    [CrossRef]
  3. R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
    [CrossRef]
  4. D. Heiman, R. W. Hellwarth, M. D. Levenson, and Graham Martin, Phys. Rev. Lett. 36, 189 (1976).
    [CrossRef]
  5. M. D. Levenson and N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
    [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 26.
  7. M. C. Tobin, Laser Raman Spectroscopy (Wiley, New York, 1971), p. 12.
  8. R. T. Lynch (private communication).
  9. J. G. Skinner and W. G. Nilsen, J. Opt. Soc. Am. 58, 113 (1968).
    [CrossRef]
  10. Y. Kato and H. Takuma, J. Opt. Soc. Am. 61, 347 (1971); J. Chem. Phys. 54, 5598 (1971).
    [CrossRef]
  11. A. Owyoung, Opt. Commun. 16, 266 (1976).
    [CrossRef]

1976 (2)

D. Heiman, R. W. Hellwarth, M. D. Levenson, and Graham Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

A. Owyoung, Opt. Commun. 16, 266 (1976).
[CrossRef]

1974 (1)

M. D. Levenson and N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
[CrossRef]

1971 (2)

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

Y. Kato and H. Takuma, J. Opt. Soc. Am. 61, 347 (1971); J. Chem. Phys. 54, 5598 (1971).
[CrossRef]

1968 (1)

1964 (2)

G. Mayer and F. Gires, C. R. Acad. Sci. (Paris) 258, 2039 (1964).

P. Maker and R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Bloembergen, N.

M. D. Levenson and N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 26.

George, N.

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

Gires, F.

G. Mayer and F. Gires, C. R. Acad. Sci. (Paris) 258, 2039 (1964).

Heiman, D.

D. Heiman, R. W. Hellwarth, M. D. Levenson, and Graham Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Hellwarth, R. W.

D. Heiman, R. W. Hellwarth, M. D. Levenson, and Graham Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

Kato, Y.

Levenson, M. D.

D. Heiman, R. W. Hellwarth, M. D. Levenson, and Graham Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

M. D. Levenson and N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
[CrossRef]

Lynch, R. T.

R. T. Lynch (private communication).

Maker, P.

P. Maker and R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Martin, Graham

D. Heiman, R. W. Hellwarth, M. D. Levenson, and Graham Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Mayer, G.

G. Mayer and F. Gires, C. R. Acad. Sci. (Paris) 258, 2039 (1964).

Nilsen, W. G.

Owyoung, A.

A. Owyoung, Opt. Commun. 16, 266 (1976).
[CrossRef]

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

Skinner, J. G.

Takuma, H.

Terhune, R.

P. Maker and R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Tobin, M. C.

M. C. Tobin, Laser Raman Spectroscopy (Wiley, New York, 1971), p. 12.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 26.

C. R. Acad. Sci. (Paris) (1)

G. Mayer and F. Gires, C. R. Acad. Sci. (Paris) 258, 2039 (1964).

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

A. Owyoung, Opt. Commun. 16, 266 (1976).
[CrossRef]

Phys. Rev. (1)

P. Maker and R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Phys. Rev. A (1)

R. W. Hellwarth, A. Owyoung, and N. George, Phys. Rev. A 4, 2342 (1971).
[CrossRef]

Phys. Rev. B (1)

M. D. Levenson and N. Bloembergen, Phys. Rev. B 10, 4447 (1974).
[CrossRef]

Phys. Rev. Lett. (1)

D. Heiman, R. W. Hellwarth, M. D. Levenson, and Graham Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 26.

M. C. Tobin, Laser Raman Spectroscopy (Wiley, New York, 1971), p. 12.

R. T. Lynch (private communication).

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Figures (3)

FIG. 1
FIG. 1

Experimental apparatus for observing Raman-induced Kerr effect. The vertical pump beam (e2) becomes elliptically polarized by quarter-wave plate Q and overlaps with linearly polarized probe beam inside the sample cell.

FIG. 2
FIG. 2

The spectra of the Raman-induced Kerr effect for the 992 cm−1 mode of benzene for various ellipticities of the pump beam. ϕ = 0 is the case for linear pump polarization; ϕ = ± 45° gives circular polarization. Note vertical scale is logarithmic.

FIG. 3
FIG. 3

Plot of the observed intensity as a function of ϕ at fixed pump frequency, ω1ω2 = ωR + Δ. The solid line is the calculated curve for (1 − 3ρ)Δ/Γ = 1.8 (see Eq. 6) and normalized to fit the experimental value at ϕ = + 45°.

Tables (1)

Tables Icon

TABLE I Comparison of recent measurements of χ(3). The values of the estimated uncertainty in parentheses include the estimated errors in the reference values from the literature, while those without parentheses represent only the uncertainty in the present experiment.

Equations (8)

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P y ( ω 1 ) = 6 E x ( ω 1 ) [ χ 1212 ( 3 ) ( - ω 1 , ω 2 , - ω 2 , ω 1 ) E x ( ω 2 ) E y * ( ω 2 ) + χ 1122 ( 3 ) ( - ω 1 , ω 2 - ω 2 , ω 1 ) E x * ( ω 2 ) E y ( ω 2 ) ] ,
E x ( ω 2 ) = a cos θ - i b sin θ ( a 2 + b 2 ) 1 / 2 , E y ( ω 2 ) = a sin θ + i b cos θ ( a 2 + b 2 ) 1 / 2 ,
E x ( ω 2 ) E y * ( ω 2 ) = [ E x * ( ω 2 ) E y ( ω 2 ) ] * = 1 2 E 1 2 ( cos 2 2 ϕ + i sin 2 ϕ ) ,
χ 1212 ( 3 ) ( - ω 1 , ω 2 , - ω 2 , ω 1 ) = χ NR + ρ N ( α 11 R ) 2 / 24 h c ω R - ( ω 1 - ω 2 ) + i Γ χ 1122 ( 3 ) ( - ω 1 , ω 2 , - ω 2 , ω 1 ) = χ NR + ( 1 - 2 ρ ) N ( α 11 R ) 2 / 24 h c ω R - ( ω 1 - ω 2 ) + i Γ .
Δ = N ( α 11 R ) 2 / 48 h c χ NR ,
I 1 ( ω 1 ) I ( ω 1 ) I 2 ( ω 2 ) = 9 ( χ NR ) 2 [ ω R - ( ω 1 - ω 2 ) + Δ ( 1 - ρ ) ] 2 cos 4 2 ϕ + [ Γ cos 2 2 ϕ + Δ ( 1 - 3 ρ ) sin 2 ϕ ] 2 [ ω R - ( ω 1 - ω 2 ) ] 2 + Γ 2 .
ω 1 - ω 2 = ω R + Δ ( 1 - ρ ) ,             Δ ( 1 - 3 ρ ) sin 2 ϕ + Γ cos 2 2 ϕ = 0.
χ 1122 E χ 1122 NR = σ σ + B 0 = 12.1 ± 0.7 % .