Abstract

An intracavity polarimeter for measuring small optical anisotropies is described. It is based on an optically pumped sodium dimer ring laser that supports two counterpropagating, orthogonally polarized modes. The optical anisot-ropy of an intracavity sample is detected by its effect on the beat frequency between the two modes. An analysis of the noise shows that a phase-retardation sensitivity of 6 × 10−8 rad can be achieved. A preliminary measurement of the Kerr effect in CO2 is reported.

© 1988 Optical Society of America

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References

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  1. C. G. Lefevre and R. J. W. Lefevre, “The Kerr effect,” in Techniques of Chemistry, A. Weissberger, ed. (Wiley Interscience, New York, 1972), Vol. 1, Part 3C,pp. 399–427.
  2. A. D. Buckingham and D. A. Dunmur, “Kerr effect in inert gases and sulphur hexafluoride,” Trans. Faraday Soc,  64, 1776 (1968).
    [CrossRef]
  3. A. K. Burnham, L. W. Buxton, and W. H. Flygare, “Kerr constants, depolarization. ratios, and hyperpolarizabilities of substituted methanes,” J. Chem. Phys. 67, 4990 (1977).
    [CrossRef]
  4. A. D. Buckingham and H. Sutter, “Gas phase measurements of the Kerr effect in some n-alkanes and cyclohexane,” J. Chem. Phys. 64, 364 (1976).
    [CrossRef]
  5. One of us has recently shown that it is possible to achieve the shot-noise limit of the conventional technique [D. P. Shelton and R. E. Cameron, Rev. Sci. Instrum. (to be published)]. The fundamental sensitivity of the intracavity technique is better and will be discussed in a future publication.
  6. W. M. Doyle and M. B. White, “Generation of combination tones by the interaction of orthogonal oscillations in a gas laser,” Appl. Phys. Lett. 10, 224 (1967).
    [CrossRef]
  7. S. C. Read, “Measurement of the Kerr effect in carbon dioxide using intracavity polarimetry,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1987).
  8. Lai Ming, “Frequency stabilization of an argon ion laser and a sodium dimer ring laser for use in optical anisotropy measurements,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1985).
  9. T. B. Cave, “An investigation of the sodium dimer ring laser for use in optical anisotropy measurements,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1983).
  10. A. D. Guest, “Dispersion measurements with a dual-frequency infrared helium-neon laser for use in optical anisotropy measurements,” M.Sc. Thesis (University of Toronto, Toronto, Canada, 1981).
  11. B. Wellegehausen, “Optically pumped cw dimer lasers,” IEEE J. Quantum Electron. QE-15, 1108 (1979).
    [CrossRef]
  12. H. Scheingraber and C. R. Vidal, “Heat pipe oven of well-defined column density,” Rev. Sci. Instrum. 52, 1010 (1981).
    [CrossRef]
  13. C. N. Man and C.N. Brillet, “Gain lineshapes in optically pumped dimer lasers,” Opt. Commun. 45, 95 (1983).
    [CrossRef]
  14. W. R. Bennett, “Gaseous optical masers,” Phys. Rev. 126, 580 (1962).
    [CrossRef]
  15. G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55, 703 (1985).
    [CrossRef] [PubMed]
  16. J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
    [CrossRef]
  17. A. D. Buckingham and B. J. Orr, “Electric birefringence in molecular hydrogen,” Proc. R. Soc. London Ser. A 305, 259 (1968).
    [CrossRef]
  18. J. H. Dymond and E. B. Smith, The Virial Coefficients of Gases: A Critical Compilation (Clarendon, Oxford, 1980), p. 37.
  19. G. G. Quarles, “The dispersion of the electro-optical Kerr effect in carbon dioxide,” Phys. Rev. 46, 692 (1934).
    [CrossRef]
  20. A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
    [CrossRef]

1985 (1)

G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55, 703 (1985).
[CrossRef] [PubMed]

1983 (1)

C. N. Man and C.N. Brillet, “Gain lineshapes in optically pumped dimer lasers,” Opt. Commun. 45, 95 (1983).
[CrossRef]

1981 (1)

H. Scheingraber and C. R. Vidal, “Heat pipe oven of well-defined column density,” Rev. Sci. Instrum. 52, 1010 (1981).
[CrossRef]

1979 (1)

B. Wellegehausen, “Optically pumped cw dimer lasers,” IEEE J. Quantum Electron. QE-15, 1108 (1979).
[CrossRef]

1977 (1)

A. K. Burnham, L. W. Buxton, and W. H. Flygare, “Kerr constants, depolarization. ratios, and hyperpolarizabilities of substituted methanes,” J. Chem. Phys. 67, 4990 (1977).
[CrossRef]

1976 (1)

A. D. Buckingham and H. Sutter, “Gas phase measurements of the Kerr effect in some n-alkanes and cyclohexane,” J. Chem. Phys. 64, 364 (1976).
[CrossRef]

1971 (1)

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

1970 (1)

A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
[CrossRef]

1968 (2)

A. D. Buckingham and B. J. Orr, “Electric birefringence in molecular hydrogen,” Proc. R. Soc. London Ser. A 305, 259 (1968).
[CrossRef]

A. D. Buckingham and D. A. Dunmur, “Kerr effect in inert gases and sulphur hexafluoride,” Trans. Faraday Soc,  64, 1776 (1968).
[CrossRef]

1967 (1)

W. M. Doyle and M. B. White, “Generation of combination tones by the interaction of orthogonal oscillations in a gas laser,” Appl. Phys. Lett. 10, 224 (1967).
[CrossRef]

1962 (1)

W. R. Bennett, “Gaseous optical masers,” Phys. Rev. 126, 580 (1962).
[CrossRef]

1934 (1)

G. G. Quarles, “The dispersion of the electro-optical Kerr effect in carbon dioxide,” Phys. Rev. 46, 692 (1934).
[CrossRef]

Barnes, J. A.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Bennett, W. R.

W. R. Bennett, “Gaseous optical masers,” Phys. Rev. 126, 580 (1962).
[CrossRef]

Bogaard, M. P.

A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
[CrossRef]

Brillet, C.N.

C. N. Man and C.N. Brillet, “Gain lineshapes in optically pumped dimer lasers,” Opt. Commun. 45, 95 (1983).
[CrossRef]

Buckingham, A. D.

A. D. Buckingham and H. Sutter, “Gas phase measurements of the Kerr effect in some n-alkanes and cyclohexane,” J. Chem. Phys. 64, 364 (1976).
[CrossRef]

A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
[CrossRef]

A. D. Buckingham and D. A. Dunmur, “Kerr effect in inert gases and sulphur hexafluoride,” Trans. Faraday Soc,  64, 1776 (1968).
[CrossRef]

A. D. Buckingham and B. J. Orr, “Electric birefringence in molecular hydrogen,” Proc. R. Soc. London Ser. A 305, 259 (1968).
[CrossRef]

Burnham, A. K.

A. K. Burnham, L. W. Buxton, and W. H. Flygare, “Kerr constants, depolarization. ratios, and hyperpolarizabilities of substituted methanes,” J. Chem. Phys. 67, 4990 (1977).
[CrossRef]

Buxton, L. W.

A. K. Burnham, L. W. Buxton, and W. H. Flygare, “Kerr constants, depolarization. ratios, and hyperpolarizabilities of substituted methanes,” J. Chem. Phys. 67, 4990 (1977).
[CrossRef]

Cave, T. B.

T. B. Cave, “An investigation of the sodium dimer ring laser for use in optical anisotropy measurements,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1983).

Chi, A. R.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Cutler, L. S.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Doyle, W. M.

W. M. Doyle and M. B. White, “Generation of combination tones by the interaction of orthogonal oscillations in a gas laser,” Appl. Phys. Lett. 10, 224 (1967).
[CrossRef]

Dunmur, D. A.

A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
[CrossRef]

A. D. Buckingham and D. A. Dunmur, “Kerr effect in inert gases and sulphur hexafluoride,” Trans. Faraday Soc,  64, 1776 (1968).
[CrossRef]

Dymond, J. H.

J. H. Dymond and E. B. Smith, The Virial Coefficients of Gases: A Critical Compilation (Clarendon, Oxford, 1980), p. 37.

Flygare, W. H.

A. K. Burnham, L. W. Buxton, and W. H. Flygare, “Kerr constants, depolarization. ratios, and hyperpolarizabilities of substituted methanes,” J. Chem. Phys. 67, 4990 (1977).
[CrossRef]

Guest, A. D.

A. D. Guest, “Dispersion measurements with a dual-frequency infrared helium-neon laser for use in optical anisotropy measurements,” M.Sc. Thesis (University of Toronto, Toronto, Canada, 1981).

Healy, D. J.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Hobbs, C. P.

A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
[CrossRef]

Hugon, D.

G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55, 703 (1985).
[CrossRef] [PubMed]

Leeson, D. B.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Lefevre, C. G.

C. G. Lefevre and R. J. W. Lefevre, “The Kerr effect,” in Techniques of Chemistry, A. Weissberger, ed. (Wiley Interscience, New York, 1972), Vol. 1, Part 3C,pp. 399–427.

Lefevre, R. J. W.

C. G. Lefevre and R. J. W. Lefevre, “The Kerr effect,” in Techniques of Chemistry, A. Weissberger, ed. (Wiley Interscience, New York, 1972), Vol. 1, Part 3C,pp. 399–427.

Man, C. N.

C. N. Man and C.N. Brillet, “Gain lineshapes in optically pumped dimer lasers,” Opt. Commun. 45, 95 (1983).
[CrossRef]

Mcgunigal, T. E.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Ming, Lai

Lai Ming, “Frequency stabilization of an argon ion laser and a sodium dimer ring laser for use in optical anisotropy measurements,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1985).

Mullen, J. A.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Orr, B. J.

A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
[CrossRef]

A. D. Buckingham and B. J. Orr, “Electric birefringence in molecular hydrogen,” Proc. R. Soc. London Ser. A 305, 259 (1968).
[CrossRef]

Quarles, G. G.

G. G. Quarles, “The dispersion of the electro-optical Kerr effect in carbon dioxide,” Phys. Rev. 46, 692 (1934).
[CrossRef]

Read, S. C.

S. C. Read, “Measurement of the Kerr effect in carbon dioxide using intracavity polarimetry,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1987).

Scheingraber, H.

H. Scheingraber and C. R. Vidal, “Heat pipe oven of well-defined column density,” Rev. Sci. Instrum. 52, 1010 (1981).
[CrossRef]

Smith, E. B.

J. H. Dymond and E. B. Smith, The Virial Coefficients of Gases: A Critical Compilation (Clarendon, Oxford, 1980), p. 37.

Smith, W. L.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Stephan, G.

G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55, 703 (1985).
[CrossRef] [PubMed]

Sutter, H.

A. D. Buckingham and H. Sutter, “Gas phase measurements of the Kerr effect in some n-alkanes and cyclohexane,” J. Chem. Phys. 64, 364 (1976).
[CrossRef]

Sydnor, R. L.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Vessot, R. F. C.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Vidal, C. R.

H. Scheingraber and C. R. Vidal, “Heat pipe oven of well-defined column density,” Rev. Sci. Instrum. 52, 1010 (1981).
[CrossRef]

Wellegehausen, B.

B. Wellegehausen, “Optically pumped cw dimer lasers,” IEEE J. Quantum Electron. QE-15, 1108 (1979).
[CrossRef]

White, M. B.

W. M. Doyle and M. B. White, “Generation of combination tones by the interaction of orthogonal oscillations in a gas laser,” Appl. Phys. Lett. 10, 224 (1967).
[CrossRef]

Winkler, G. M. R.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Appl. Phys. Lett. (1)

W. M. Doyle and M. B. White, “Generation of combination tones by the interaction of orthogonal oscillations in a gas laser,” Appl. Phys. Lett. 10, 224 (1967).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. Wellegehausen, “Optically pumped cw dimer lasers,” IEEE J. Quantum Electron. QE-15, 1108 (1979).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healy, D. B. Leeson, T. E. Mcgunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

J. Chem. Phys. (2)

A. K. Burnham, L. W. Buxton, and W. H. Flygare, “Kerr constants, depolarization. ratios, and hyperpolarizabilities of substituted methanes,” J. Chem. Phys. 67, 4990 (1977).
[CrossRef]

A. D. Buckingham and H. Sutter, “Gas phase measurements of the Kerr effect in some n-alkanes and cyclohexane,” J. Chem. Phys. 64, 364 (1976).
[CrossRef]

Opt. Commun. (1)

C. N. Man and C.N. Brillet, “Gain lineshapes in optically pumped dimer lasers,” Opt. Commun. 45, 95 (1983).
[CrossRef]

Phys. Rev. (2)

W. R. Bennett, “Gaseous optical masers,” Phys. Rev. 126, 580 (1962).
[CrossRef]

G. G. Quarles, “The dispersion of the electro-optical Kerr effect in carbon dioxide,” Phys. Rev. 46, 692 (1934).
[CrossRef]

Phys. Rev. Lett. (1)

G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55, 703 (1985).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

A. D. Buckingham and B. J. Orr, “Electric birefringence in molecular hydrogen,” Proc. R. Soc. London Ser. A 305, 259 (1968).
[CrossRef]

Rev. Sci. Instrum. (1)

H. Scheingraber and C. R. Vidal, “Heat pipe oven of well-defined column density,” Rev. Sci. Instrum. 52, 1010 (1981).
[CrossRef]

Trans. Faraday Soc (1)

A. D. Buckingham and D. A. Dunmur, “Kerr effect in inert gases and sulphur hexafluoride,” Trans. Faraday Soc,  64, 1776 (1968).
[CrossRef]

Trans. Faraday Soc. (1)

A. D. Buckingham, M. P. Bogaard, D. A. Dunmur, C. P. Hobbs, and B. J. Orr, “Kerr effect in some simple non-dipolar gases,” Trans. Faraday Soc. 66, 1548 (1970).
[CrossRef]

Other (7)

J. H. Dymond and E. B. Smith, The Virial Coefficients of Gases: A Critical Compilation (Clarendon, Oxford, 1980), p. 37.

C. G. Lefevre and R. J. W. Lefevre, “The Kerr effect,” in Techniques of Chemistry, A. Weissberger, ed. (Wiley Interscience, New York, 1972), Vol. 1, Part 3C,pp. 399–427.

One of us has recently shown that it is possible to achieve the shot-noise limit of the conventional technique [D. P. Shelton and R. E. Cameron, Rev. Sci. Instrum. (to be published)]. The fundamental sensitivity of the intracavity technique is better and will be discussed in a future publication.

S. C. Read, “Measurement of the Kerr effect in carbon dioxide using intracavity polarimetry,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1987).

Lai Ming, “Frequency stabilization of an argon ion laser and a sodium dimer ring laser for use in optical anisotropy measurements,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1985).

T. B. Cave, “An investigation of the sodium dimer ring laser for use in optical anisotropy measurements,” M.Sc. thesis (University of Toronto, Toronto, Canada, 1983).

A. D. Guest, “Dispersion measurements with a dual-frequency infrared helium-neon laser for use in optical anisotropy measurements,” M.Sc. Thesis (University of Toronto, Toronto, Canada, 1981).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the intracavity polarimeter. Abbreviations are defined in text.

Fig. 2
Fig. 2

Energy-level diagram of an optically pumped dimer laser. For our apparatus, ωP is the frequency of the Ar+ pump beam and ωD is the frequency of the Na2 laser.

Fig. 3
Fig. 3

Measured variation in the beat frequency of the bare laser, over a 3-min time interval. The mean beat frequency was approximately 400 kHz. Successive data points were measured for an integration time of 100 msec and separated by a 90-msec dead time. The expanded section shows the variation over a 15-sec period.

Fig. 4
Fig. 4

Plot of the average beat frequency νb0 times the square root σ(τ) of the Allan variance as a function of sampling time. This is a measure of the stability or rate of change of the beat frequency at various sampling times.

Fig. 5
Fig. 5

Density dependence of the change in the beat frequency due to the Kerr effect in CO2. The maximum density corresponds to a cell pressure of approximately 50 atm.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ν b = ν 2 ν 1 = c ( m 2 ϕ 2 / 2 π ) n ( L l ) + n 2 l c ( m 1 ϕ 1 / 2 π ) n ( L l ) + n 1 l .
ν b ν b 0 = f ν Δ n ,
A K = 2 27 Δ n ρ E 2 ,
l = 2 0 E 2 ( x ) d x E 2 ( 0 ) .

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