Abstract

Transmission of light through an atomic sample placed between crossed polarizers in a magnetic field is jointly determined by Faraday rotation and net absorption: Transmission increases with rotation and decreases with absorption. Both rotation and absorption are proportional to the atomic density N0; hence, in a certain range of N0, the two effects may compete, yielding a distinct density dependence of the transmitted light. We have studied such dependence in rubidium vapor for N0 of approximately 6.0×109 to 3.0×1011 atoms/cm3 with resonant laser light. We present interpretation of the competition effect and discuss its possible application for atomic density determination.

© 2005 Optical Society of America

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  1. D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
    [CrossRef]
  2. W. Seka and F. L. Curzon, "Measurements of relative transition probabilities using Faraday effect," J. Quant. Spectrosc. Radiat. Transf. 8, 1147-1162 (1968).
    [CrossRef]
  3. W. Gawlik, J. Kowalski, R. Neumann, and H. B. Wiegemann, "A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light," J. Phys. B 12, 3873-3882 (1979).
    [CrossRef]
  4. E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
    [CrossRef]
  5. A. Corney, B. P. Kibble, and G. W. Series, "Forward scattering of resonance radiation with special reference to double resonance and level-crossing experiments," Proc. R. Soc. London, Ser. A 293, 70-93 (1966).
    [CrossRef]
  6. W. Gawlik, J. Kowalski, R. Neumann, and F. Träger, "Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment," Opt. Commun. 12, 400-404 (1974).
    [CrossRef]
  7. S. Giraud-Cotton, V. P. Kaftandjian, and L. Klein, "Forward scattering of resonant radiation as a function of applied magnetic field: theoretical study of the hyperfine lines of the sodium doublet," Phys. Lett. A 88, 453-436 (1982).
    [CrossRef]
  8. X. Chen, V. L. Telegdi, and A. Weis, "Quantitative study of the nonlinear Macaluso-Corbino (resonant Faraday) effect in Cs," Opt. Commun. 74, 301-305 (1990).
    [CrossRef]
  9. B. Ståhlberg, P. Jungner, T. Fellman, and A. Lindberg, "Nonlinear forward scattering of resonant laser-light from excited neon systems," Appl. Phys. B 50, 547-551 (1990).
    [CrossRef]
  10. F. Schuller and D. N. Stacey, "Magneto-optical rotation in atomic transitions between levels with J=0 and J=1," Phys. Rev. A 60, 973-981 (1999).
    [CrossRef]
  11. B. W. Holmes and J. A. R. Griffith, "A detailed study of the effects of weak magnetic fields on the forward scattering of resonant laser light by sodium vapor," J. Phys. B 28, 2829-2846 (1995).
    [CrossRef]
  12. B. Lobodzin´ski and W. Gawlik, "Multipole moments and trap states in forward scattering of resonance light," Phys. Rev. A 54, 2238-2252 (1996).
    [CrossRef] [PubMed]
  13. G. Wa¸sik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "Laser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613-619 (2002).
    [CrossRef]
  14. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1972), Chap. 7.
  15. R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 3.
  16. E. Arimondo, "Coherent population trapping in laser spectroscopy," in Progress in Optics, Vol. XXXV , E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1996), pp. 259-354.
  17. B. Fried and S. Conte, The Plasma Dispersion Function (Academic, New York, 1961).
  18. M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), p. 297.
  19. E. Arimondo, "Relaxation processes in coherent-population trapping," Phys. Rev. A 54, 2216-2223 (1996).
    [CrossRef] [PubMed]
  20. A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media," Phys. Rev. Lett. 87, 133601 (2001).
    [CrossRef] [PubMed]
  21. CRC Handbook of Chemistry and Physics , 73rd ed., D. R. Lide, ed. (CRC Press, Boca Raton, Fla., 1992), pp. 5-80.
  22. A. N. Nesmyanov, Vapor Pressures of the Chemical Elements (Elsevier, New York, 1963).
  23. D. C. Thompson and G.-X. Xu, "Optical measurements of vapor pressures of Rb and a Rb-K mixture," Can. J. Phys. 60, 1496-1501 (1982).
    [CrossRef]

2002

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

G. Wa¸sik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "Laser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613-619 (2002).
[CrossRef]

2001

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media," Phys. Rev. Lett. 87, 133601 (2001).
[CrossRef] [PubMed]

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

1999

F. Schuller and D. N. Stacey, "Magneto-optical rotation in atomic transitions between levels with J=0 and J=1," Phys. Rev. A 60, 973-981 (1999).
[CrossRef]

1996

B. Lobodzin´ski and W. Gawlik, "Multipole moments and trap states in forward scattering of resonance light," Phys. Rev. A 54, 2238-2252 (1996).
[CrossRef] [PubMed]

E. Arimondo, "Relaxation processes in coherent-population trapping," Phys. Rev. A 54, 2216-2223 (1996).
[CrossRef] [PubMed]

1995

B. W. Holmes and J. A. R. Griffith, "A detailed study of the effects of weak magnetic fields on the forward scattering of resonant laser light by sodium vapor," J. Phys. B 28, 2829-2846 (1995).
[CrossRef]

1990

X. Chen, V. L. Telegdi, and A. Weis, "Quantitative study of the nonlinear Macaluso-Corbino (resonant Faraday) effect in Cs," Opt. Commun. 74, 301-305 (1990).
[CrossRef]

B. Ståhlberg, P. Jungner, T. Fellman, and A. Lindberg, "Nonlinear forward scattering of resonant laser-light from excited neon systems," Appl. Phys. B 50, 547-551 (1990).
[CrossRef]

1982

S. Giraud-Cotton, V. P. Kaftandjian, and L. Klein, "Forward scattering of resonant radiation as a function of applied magnetic field: theoretical study of the hyperfine lines of the sodium doublet," Phys. Lett. A 88, 453-436 (1982).
[CrossRef]

D. C. Thompson and G.-X. Xu, "Optical measurements of vapor pressures of Rb and a Rb-K mixture," Can. J. Phys. 60, 1496-1501 (1982).
[CrossRef]

1979

W. Gawlik, J. Kowalski, R. Neumann, and H. B. Wiegemann, "A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light," J. Phys. B 12, 3873-3882 (1979).
[CrossRef]

1974

W. Gawlik, J. Kowalski, R. Neumann, and F. Träger, "Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment," Opt. Commun. 12, 400-404 (1974).
[CrossRef]

1968

W. Seka and F. L. Curzon, "Measurements of relative transition probabilities using Faraday effect," J. Quant. Spectrosc. Radiat. Transf. 8, 1147-1162 (1968).
[CrossRef]

1966

A. Corney, B. P. Kibble, and G. W. Series, "Forward scattering of resonance radiation with special reference to double resonance and level-crossing experiments," Proc. R. Soc. London, Ser. A 293, 70-93 (1966).
[CrossRef]

Anderson, L. W.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

Arimondo, E.

E. Arimondo, "Relaxation processes in coherent-population trapping," Phys. Rev. A 54, 2216-2223 (1996).
[CrossRef] [PubMed]

Budker, D.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

Chen, X.

X. Chen, V. L. Telegdi, and A. Weis, "Quantitative study of the nonlinear Macaluso-Corbino (resonant Faraday) effect in Cs," Opt. Commun. 74, 301-305 (1990).
[CrossRef]

Corney, A.

A. Corney, B. P. Kibble, and G. W. Series, "Forward scattering of resonance radiation with special reference to double resonance and level-crossing experiments," Proc. R. Soc. London, Ser. A 293, 70-93 (1966).
[CrossRef]

Curzon, F. L.

W. Seka and F. L. Curzon, "Measurements of relative transition probabilities using Faraday effect," J. Quant. Spectrosc. Radiat. Transf. 8, 1147-1162 (1968).
[CrossRef]

Erickson, C. J.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

Fellman, T.

B. Ståhlberg, P. Jungner, T. Fellman, and A. Lindberg, "Nonlinear forward scattering of resonant laser-light from excited neon systems," Appl. Phys. B 50, 547-551 (1990).
[CrossRef]

Gawlik, W.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

G. Wa¸sik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "Laser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613-619 (2002).
[CrossRef]

B. Lobodzin´ski and W. Gawlik, "Multipole moments and trap states in forward scattering of resonance light," Phys. Rev. A 54, 2238-2252 (1996).
[CrossRef] [PubMed]

W. Gawlik, J. Kowalski, R. Neumann, and H. B. Wiegemann, "A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light," J. Phys. B 12, 3873-3882 (1979).
[CrossRef]

W. Gawlik, J. Kowalski, R. Neumann, and F. Träger, "Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment," Opt. Commun. 12, 400-404 (1974).
[CrossRef]

Giraud-Cotton, S.

S. Giraud-Cotton, V. P. Kaftandjian, and L. Klein, "Forward scattering of resonant radiation as a function of applied magnetic field: theoretical study of the hyperfine lines of the sodium doublet," Phys. Lett. A 88, 453-436 (1982).
[CrossRef]

Griffith, J. A. R.

B. W. Holmes and J. A. R. Griffith, "A detailed study of the effects of weak magnetic fields on the forward scattering of resonant laser light by sodium vapor," J. Phys. B 28, 2829-2846 (1995).
[CrossRef]

Happer, W.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

Holmes , B. W.

B. W. Holmes and J. A. R. Griffith, "A detailed study of the effects of weak magnetic fields on the forward scattering of resonant laser light by sodium vapor," J. Phys. B 28, 2829-2846 (1995).
[CrossRef]

Jungner, P.

B. Ståhlberg, P. Jungner, T. Fellman, and A. Lindberg, "Nonlinear forward scattering of resonant laser-light from excited neon systems," Appl. Phys. B 50, 547-551 (1990).
[CrossRef]

Kadlecek, S.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

Kaftandjian, V. P.

S. Giraud-Cotton, V. P. Kaftandjian, and L. Klein, "Forward scattering of resonant radiation as a function of applied magnetic field: theoretical study of the hyperfine lines of the sodium doublet," Phys. Lett. A 88, 453-436 (1982).
[CrossRef]

Kibble, B. P.

A. Corney, B. P. Kibble, and G. W. Series, "Forward scattering of resonance radiation with special reference to double resonance and level-crossing experiments," Proc. R. Soc. London, Ser. A 293, 70-93 (1966).
[CrossRef]

Kimball, D. F.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

Klein, L.

S. Giraud-Cotton, V. P. Kaftandjian, and L. Klein, "Forward scattering of resonant radiation as a function of applied magnetic field: theoretical study of the hyperfine lines of the sodium doublet," Phys. Lett. A 88, 453-436 (1982).
[CrossRef]

Kowalski, J.

W. Gawlik, J. Kowalski, R. Neumann, and H. B. Wiegemann, "A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light," J. Phys. B 12, 3873-3882 (1979).
[CrossRef]

W. Gawlik, J. Kowalski, R. Neumann, and F. Träger, "Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment," Opt. Commun. 12, 400-404 (1974).
[CrossRef]

Lindberg, A.

B. Ståhlberg, P. Jungner, T. Fellman, and A. Lindberg, "Nonlinear forward scattering of resonant laser-light from excited neon systems," Appl. Phys. B 50, 547-551 (1990).
[CrossRef]

Lobodzin´ski , B.

B. Lobodzin´ski and W. Gawlik, "Multipole moments and trap states in forward scattering of resonance light," Phys. Rev. A 54, 2238-2252 (1996).
[CrossRef] [PubMed]

Matsko, A. B.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media," Phys. Rev. Lett. 87, 133601 (2001).
[CrossRef] [PubMed]

Neumann, R.

W. Gawlik, J. Kowalski, R. Neumann, and H. B. Wiegemann, "A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light," J. Phys. B 12, 3873-3882 (1979).
[CrossRef]

W. Gawlik, J. Kowalski, R. Neumann, and F. Träger, "Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment," Opt. Commun. 12, 400-404 (1974).
[CrossRef]

Novikova, I.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media," Phys. Rev. Lett. 87, 133601 (2001).
[CrossRef] [PubMed]

Rochester, S. M.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

Schuller , F.

F. Schuller and D. N. Stacey, "Magneto-optical rotation in atomic transitions between levels with J=0 and J=1," Phys. Rev. A 60, 973-981 (1999).
[CrossRef]

Scully, M. O.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media," Phys. Rev. Lett. 87, 133601 (2001).
[CrossRef] [PubMed]

Seka , W.

W. Seka and F. L. Curzon, "Measurements of relative transition probabilities using Faraday effect," J. Quant. Spectrosc. Radiat. Transf. 8, 1147-1162 (1968).
[CrossRef]

Series, G. W.

A. Corney, B. P. Kibble, and G. W. Series, "Forward scattering of resonance radiation with special reference to double resonance and level-crossing experiments," Proc. R. Soc. London, Ser. A 293, 70-93 (1966).
[CrossRef]

Stacey, D. N.

F. Schuller and D. N. Stacey, "Magneto-optical rotation in atomic transitions between levels with J=0 and J=1," Phys. Rev. A 60, 973-981 (1999).
[CrossRef]

Ståhlberg, B.

B. Ståhlberg, P. Jungner, T. Fellman, and A. Lindberg, "Nonlinear forward scattering of resonant laser-light from excited neon systems," Appl. Phys. B 50, 547-551 (1990).
[CrossRef]

Telegdi, V. L.

X. Chen, V. L. Telegdi, and A. Weis, "Quantitative study of the nonlinear Macaluso-Corbino (resonant Faraday) effect in Cs," Opt. Commun. 74, 301-305 (1990).
[CrossRef]

Thompson , D. C.

D. C. Thompson and G.-X. Xu, "Optical measurements of vapor pressures of Rb and a Rb-K mixture," Can. J. Phys. 60, 1496-1501 (1982).
[CrossRef]

Träger, F.

W. Gawlik, J. Kowalski, R. Neumann, and F. Träger, "Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment," Opt. Commun. 12, 400-404 (1974).
[CrossRef]

Vliegen, E.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

Wa¸sik, G.

G. Wa¸sik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "Laser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613-619 (2002).
[CrossRef]

Walker, T. G.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

Weis, A.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

X. Chen, V. L. Telegdi, and A. Weis, "Quantitative study of the nonlinear Macaluso-Corbino (resonant Faraday) effect in Cs," Opt. Commun. 74, 301-305 (1990).
[CrossRef]

Welch, G. R.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media," Phys. Rev. Lett. 87, 133601 (2001).
[CrossRef] [PubMed]

Wiegemann, H. B.

W. Gawlik, J. Kowalski, R. Neumann, and H. B. Wiegemann, "A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light," J. Phys. B 12, 3873-3882 (1979).
[CrossRef]

Xu, G.-X.

D. C. Thompson and G.-X. Xu, "Optical measurements of vapor pressures of Rb and a Rb-K mixture," Can. J. Phys. 60, 1496-1501 (1982).
[CrossRef]

Yashchuk, V. V.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

Zachorowski, J.

G. Wa¸sik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "Laser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613-619 (2002).
[CrossRef]

Zawadzki, W.

G. Wa¸sik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "Laser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613-619 (2002).
[CrossRef]

Appl. Phys. B

B. Ståhlberg, P. Jungner, T. Fellman, and A. Lindberg, "Nonlinear forward scattering of resonant laser-light from excited neon systems," Appl. Phys. B 50, 547-551 (1990).
[CrossRef]

G. Wa¸sik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "Laser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613-619 (2002).
[CrossRef]

Can. J. Phys.

D. C. Thompson and G.-X. Xu, "Optical measurements of vapor pressures of Rb and a Rb-K mixture," Can. J. Phys. 60, 1496-1501 (1982).
[CrossRef]

J. Phys. B

B. W. Holmes and J. A. R. Griffith, "A detailed study of the effects of weak magnetic fields on the forward scattering of resonant laser light by sodium vapor," J. Phys. B 28, 2829-2846 (1995).
[CrossRef]

W. Gawlik, J. Kowalski, R. Neumann, and H. B. Wiegemann, "A new method for measuring oscillator strengths using the resonant Faraday effect in monochromatic light," J. Phys. B 12, 3873-3882 (1979).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf.

W. Seka and F. L. Curzon, "Measurements of relative transition probabilities using Faraday effect," J. Quant. Spectrosc. Radiat. Transf. 8, 1147-1162 (1968).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, "Faraday rotation density mea-surements of optically thick alkali metal vapors," Nucl. Instrum. Methods Phys. Res. A 460, 444-450 (2001).
[CrossRef]

Opt. Commun.

W. Gawlik, J. Kowalski, R. Neumann, and F. Träger, "Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment," Opt. Commun. 12, 400-404 (1974).
[CrossRef]

X. Chen, V. L. Telegdi, and A. Weis, "Quantitative study of the nonlinear Macaluso-Corbino (resonant Faraday) effect in Cs," Opt. Commun. 74, 301-305 (1990).
[CrossRef]

Phys. Lett. A

S. Giraud-Cotton, V. P. Kaftandjian, and L. Klein, "Forward scattering of resonant radiation as a function of applied magnetic field: theoretical study of the hyperfine lines of the sodium doublet," Phys. Lett. A 88, 453-436 (1982).
[CrossRef]

Phys. Rev. A

F. Schuller and D. N. Stacey, "Magneto-optical rotation in atomic transitions between levels with J=0 and J=1," Phys. Rev. A 60, 973-981 (1999).
[CrossRef]

E. Arimondo, "Relaxation processes in coherent-population trapping," Phys. Rev. A 54, 2216-2223 (1996).
[CrossRef] [PubMed]

B. Lobodzin´ski and W. Gawlik, "Multipole moments and trap states in forward scattering of resonance light," Phys. Rev. A 54, 2238-2252 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media," Phys. Rev. Lett. 87, 133601 (2001).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A

A. Corney, B. P. Kibble, and G. W. Series, "Forward scattering of resonance radiation with special reference to double resonance and level-crossing experiments," Proc. R. Soc. London, Ser. A 293, 70-93 (1966).
[CrossRef]

Rev. Mod. Phys.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
[CrossRef]

Other

CRC Handbook of Chemistry and Physics , 73rd ed., D. R. Lide, ed. (CRC Press, Boca Raton, Fla., 1992), pp. 5-80.

A. N. Nesmyanov, Vapor Pressures of the Chemical Elements (Elsevier, New York, 1963).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1972), Chap. 7.

R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), Chap. 3.

E. Arimondo, "Coherent population trapping in laser spectroscopy," in Progress in Optics, Vol. XXXV , E. Wolf, ed. (Elsevier, North-Holland, Amsterdam, 1996), pp. 259-354.

B. Fried and S. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), p. 297.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup: BS is the beam splitter; P, A are polarizer and analyzer, respectively; λ/2 is half-wave plate; D is photodetector.

Fig. 2
Fig. 2

Typical forward scattering signal IFS(B) recorded for cell temperature 29.5 °C and light intensity I0=2.2 mW/cm2. (a) FS signals calculated with the X model (solid curve) and Λ model (dashed curve). (b) AFS denotes the amplitude of the FS signal. The theoretical signals correspond to incident light intensity I0=0.6 mW/cm2. They are presented in the domain of Larmor frequency over the effective width (Γef=Γ for the X model and Γef=γg for the Λ model) and are normalized to the same AFS.

Fig. 3
Fig. 3

Amplitudes of the FS signals (AFS) versus temperature for various intensities of the incident light.

Fig. 4
Fig. 4

Amplitude of the FS signal (AFS) versus temperature for very high light intensity I0=130 mW/cm2.

Fig. 5
Fig. 5

Energy level structure for (a) the X model, (b) the Λ model.

Fig. 6
Fig. 6

Results of numerical simulations of the FS signal amplitudes versus atomic concentration for the same incident light intensities as used in the experiment.

Fig. 7
Fig. 7

Results of numerical simulations of the FS signal amplitudes versus vapor temperature for the light intensities as used in the experiment (compare with Fig. 3).

Equations (25)

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IFS=I04[exp(-κ+kL)-exp(-κ-kL)]2+I0 sin2n+-n-2kLexp[-(κ++κ-)kL],
IFSI0=sin2 (αN0) exp(-βN0),
n-1=Ridiρcoh(i)vE0,
κ=Iidiρcoh(i)vE0,
n+-1=dRρaBvE0,n--1=dRρbAvE0,
κ+=dIρaBvE0,κ-=dIρbAvE0.
H=ω0(ρAA+ρBB)+/2ggωB(ρaa-ρbb)+/2geωB(ρAA-ρBB)+dE(ρaB+ρbA+h.c.),
ρ˙=-i[H, ρ]-Γ˜ρ,
ρ˙aB=i(ω0+ωB+iΓ)ρaB+iβ(ρaa-ρBB),
ρ˙bA=i(ω0-ωB+iΓ)ρbA+iβ(ρbb-ρAA),
ρ˜aB=-βδ+ωB+iΓ(ρaa-ρBB),
ρ˜bA=-βδ-ωB+iΓ(ρbb-ρAA),
ρ˜aB
=βneq(δ+ωB-iΓ)×MA(δ)+2rGMA(δ)MB(δ)+rG[MA(δ)+MB(δ)]+2rG2,
MA(δ)=(δ-ωB)2+Γ2,
MB(δ)=(δ+ωB)2+Γ2,
r=γe3γg,G=2β2Γγe,
ρ˜aB=-neqβA+(ωB)δ+δ1(ωB)+A-(ωB)δ-δ1(ωB)+B+(ωB)δ+δ2(ωB)+B-(ωB)δ-δ2(ωB),
δ1,22=B2-γ2-rG±[r2G2-4B2(γ2+rG)-2rG2]1/2
A±=12δ13aδ12+bδ1cδ1(δ12-δ22),
B±=-12δ23aδ22+bδ2cδ2(δ12-δ22),
ρ˜aBv=-neqβN0πuA+(ωB)-exp(-v2/u2)dvδ-kv+δ1(ωB)+A-(ωB)-exp(-v2/u2)dvδ-kv-δ1(ωB)+B+(ωB)-exp(-v2/u2)dvδ-kv+δ2(ωB)+B-(ωB)-exp(-v2/u2)dvδ-kv-δ2(ωB),
IFS=I0 sin2n+-n-2kLexp(-2κkL),
log10 p(T)=A-BT.
log10 p(T)=A+BT+CT+D log10 T,

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