Abstract

Light propagating through an optically anisotropic resonant medium excites coherent Raman fields that propagate together with the original wave; the interference between the two fields generates the well-known Raman beats. We solve the coupled-wave equations for finite optical path lengths and show how the coherent exchange of energy between the two fields leads to interference effects that distort the observed signal for different detection schemes. Theoretical analysis is compared with experimental results from the Na D1 transition.

© 1993 Optical Society of America

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References

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  1. R. W. Hellwarth, Phys. Rev. 130, 850 (1963).
    [CrossRef]
  2. J. A. Giordmaine, W. Kaiser, Phys. Rev. 144, 676 (1966).
    [CrossRef]
  3. J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
    [CrossRef]
  4. M. Mitsunaga, E. S. Kintzer, R. G. Brewer, Phys. Rev. B 31, 6947 (1984).
    [CrossRef]
  5. N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
    [CrossRef]
  6. K. Holliday, X. F. He, P. T. Fisk, N. B. Manson, Opt. Lett. 15, 983 (1990).
    [CrossRef] [PubMed]
  7. M. Bassini, F. Biraben, B. Cagnac, G. Grynberg, Opt. Commun. 21, 263 (1977).
    [CrossRef]
  8. R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
    [CrossRef]
  9. R. L. Shoemaker, R. G. Brewer, Phys. Rev. Lett. 28, 1430 (1972).
    [CrossRef]
  10. R. G. Brewer, E. L. Hahn, Phys. Rev. A 8, 464 (1973).
    [CrossRef]
  11. E. W. Van Stryland, R. L. Shoemaker, Phys. Rev. A 20, 1376 (1979).
    [CrossRef]
  12. N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
    [CrossRef]
  13. R. J. McLean, P. Hannaford, R. M. Lowe, Phys. Rev. A 42, 6616 (1990).
    [CrossRef] [PubMed]
  14. D. Suter, J. Mlynek, Adv. Magn. Opt. Reson. 16, 1 (1991).
  15. H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]

1991 (1)

D. Suter, J. Mlynek, Adv. Magn. Opt. Reson. 16, 1 (1991).

1990 (2)

1984 (1)

M. Mitsunaga, E. S. Kintzer, R. G. Brewer, Phys. Rev. B 31, 6947 (1984).
[CrossRef]

1983 (3)

J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
[CrossRef]

H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
[CrossRef] [PubMed]

N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
[CrossRef]

1979 (1)

E. W. Van Stryland, R. L. Shoemaker, Phys. Rev. A 20, 1376 (1979).
[CrossRef]

1977 (1)

M. Bassini, F. Biraben, B. Cagnac, G. Grynberg, Opt. Commun. 21, 263 (1977).
[CrossRef]

1976 (1)

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

1973 (1)

R. G. Brewer, E. L. Hahn, Phys. Rev. A 8, 464 (1973).
[CrossRef]

1972 (1)

R. L. Shoemaker, R. G. Brewer, Phys. Rev. Lett. 28, 1430 (1972).
[CrossRef]

1966 (1)

J. A. Giordmaine, W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

1963 (1)

R. W. Hellwarth, Phys. Rev. 130, 850 (1963).
[CrossRef]

1960 (1)

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

Bassini, M.

M. Bassini, F. Biraben, B. Cagnac, G. Grynberg, Opt. Commun. 21, 263 (1977).
[CrossRef]

Biraben, F.

M. Bassini, F. Biraben, B. Cagnac, G. Grynberg, Opt. Commun. 21, 263 (1977).
[CrossRef]

Bloembergen, N.

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

Brewer, R. G.

M. Mitsunaga, E. S. Kintzer, R. G. Brewer, Phys. Rev. B 31, 6947 (1984).
[CrossRef]

N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
[CrossRef]

J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
[CrossRef]

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

R. G. Brewer, E. L. Hahn, Phys. Rev. A 8, 464 (1973).
[CrossRef]

R. L. Shoemaker, R. G. Brewer, Phys. Rev. Lett. 28, 1430 (1972).
[CrossRef]

Cagnac, B.

M. Bassini, F. Biraben, B. Cagnac, G. Grynberg, Opt. Commun. 21, 263 (1977).
[CrossRef]

Chan, V. W. S.

DeVoe, R. G.

J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
[CrossRef]

N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
[CrossRef]

Fisk, P. T.

Genack, A. Z.

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

Grynberg, G.

M. Bassini, F. Biraben, B. Cagnac, G. Grynberg, Opt. Commun. 21, 263 (1977).
[CrossRef]

Hahn, E. L.

R. G. Brewer, E. L. Hahn, Phys. Rev. A 8, 464 (1973).
[CrossRef]

Hannaford, P.

R. J. McLean, P. Hannaford, R. M. Lowe, Phys. Rev. A 42, 6616 (1990).
[CrossRef] [PubMed]

He, X. F.

Hellwarth, R. W.

R. W. Hellwarth, Phys. Rev. 130, 850 (1963).
[CrossRef]

Holliday, K.

Kaiser, W.

J. A. Giordmaine, W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

Kintzer, E. S.

M. Mitsunaga, E. S. Kintzer, R. G. Brewer, Phys. Rev. B 31, 6947 (1984).
[CrossRef]

J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
[CrossRef]

N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
[CrossRef]

Lowe, R. M.

R. J. McLean, P. Hannaford, R. M. Lowe, Phys. Rev. A 42, 6616 (1990).
[CrossRef] [PubMed]

Manson, N. B.

McLean, R. J.

R. J. McLean, P. Hannaford, R. M. Lowe, Phys. Rev. A 42, 6616 (1990).
[CrossRef] [PubMed]

Mitsunaga, M.

M. Mitsunaga, E. S. Kintzer, R. G. Brewer, Phys. Rev. B 31, 6947 (1984).
[CrossRef]

Mlynek, J.

D. Suter, J. Mlynek, Adv. Magn. Opt. Reson. 16, 1 (1991).

N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
[CrossRef]

J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
[CrossRef]

Pershan, P. S.

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

Shoemaker, R. L.

E. W. Van Stryland, R. L. Shoemaker, Phys. Rev. A 20, 1376 (1979).
[CrossRef]

R. L. Shoemaker, R. G. Brewer, Phys. Rev. Lett. 28, 1430 (1972).
[CrossRef]

Suter, D.

D. Suter, J. Mlynek, Adv. Magn. Opt. Reson. 16, 1 (1991).

Van Stryland, E. W.

E. W. Van Stryland, R. L. Shoemaker, Phys. Rev. A 20, 1376 (1979).
[CrossRef]

Wilcox, L. R.

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

Wong, N. C.

J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
[CrossRef]

N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
[CrossRef]

Yuen, H. P.

Adv. Magn. Opt. Reson. (1)

D. Suter, J. Mlynek, Adv. Magn. Opt. Reson. 16, 1 (1991).

Opt. Commun. (1)

M. Bassini, F. Biraben, B. Cagnac, G. Grynberg, Opt. Commun. 21, 263 (1977).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (3)

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

R. W. Hellwarth, Phys. Rev. 130, 850 (1963).
[CrossRef]

J. A. Giordmaine, W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

Phys. Rev. A (3)

R. G. Brewer, E. L. Hahn, Phys. Rev. A 8, 464 (1973).
[CrossRef]

E. W. Van Stryland, R. L. Shoemaker, Phys. Rev. A 20, 1376 (1979).
[CrossRef]

R. J. McLean, P. Hannaford, R. M. Lowe, Phys. Rev. A 42, 6616 (1990).
[CrossRef] [PubMed]

Phys. Rev. B (2)

M. Mitsunaga, E. S. Kintzer, R. G. Brewer, Phys. Rev. B 31, 6947 (1984).
[CrossRef]

N. C. Wong, E. S. Kintzer, J. Mlynek, R. G. DeVoe, R. G. Brewer, Phys. Rev. B 28, 4993 (1983).
[CrossRef]

Phys. Rev. Lett. (3)

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

R. L. Shoemaker, R. G. Brewer, Phys. Rev. Lett. 28, 1430 (1972).
[CrossRef]

J. Mlynek, N. C. Wong, R. G. DeVoe, E. S. Kintzer, R. G. Brewer, Phys. Rev. Lett. 50, 993 (1983).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of the Raman-scattering processes. For simplicity, only the two F = 2 multiplets of the Na D1 transition are shown. The curved arrows indicate two ground-state coherences, the solid lines represent the incident light, and the wavy lines mark the resulting optical polarization. (b) Relevant geometry and choice of coordinate system.

Fig. 2
Fig. 2

Schematic representation of the detection setup for (a) conventional heterodyne detection and (b) balanced heterodyne detection. P, polarizer; PBS, polarizing beam splitter; PD's, photodiode's; AMP, amplifier.

Fig. 3
Fig. 3

Experimental signals observed in the case of a single Raman frequency. The left-hand column contains time-domain data for the analyzer oriented parallel (top) and perpendicular (center) to the polarization of the incident beam. The signal at the bottom was recorded with the balanced heterodyne detection scheme of Fig. 2(b). The Raman spectra in the right-hand column were obtained by Fourier transformation of the time-domain data.

Fig. 4
Fig. 4

Experimental signal observed for the case of multiple sublevel frequencies: the upper trace shows the complete Raman spectrum, and the lower traces contain expansions of the regions close to the first and third harmonics of the Larmor frequency.

Equations (4)

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E x = c tot ( t ) E , E x = c tot ( t ) E ,
c tot ( t ) = c 0 Re [ ρ 12 ( t ) + ρ 23 ( t ) + 2 ρ 45 ( t ) + 3 ρ 56 ( t ) + 3 ρ 67 ( t ) + 2 ρ 78 ( t ) ] .
E = E 0 cos ( c tot x ) , E = E 0 sin ( c tot x ) ,
S 45 ( 1 ) = l c o Re ( ρ 12 + ρ 23 + 2 ρ 45 + 3 ρ 56 + 3 ρ 67 + 2 ρ 78 ) .

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