Abstract

We describe a method for determining the number density of the alkali metal vapor by use of an evanescent wave in a single total internal reflection. The method is simple to use, and it has the following useful features: It is most suitable for determining the number density of dense (>1013 cm-3) alkali metal vapor and it permits the measurement of the alkali metal vapor number density in the vicinity (10-5 cm) of cell surfaces. Using this method, we measured the number density of Rb metal vapor in the vicinity (10-5 cm) of the cell wall in cells that contain only Rb metal and no buffer gas; we found that there is no systematic difference between the Rb number density near the surface and that in the bulk.

© 2001 Optical Society of America

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  1. M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on paraffin-coated walls,” Phys. Rev. A 147, 41–54 (1965).
    [CrossRef]
  2. T. Killian, “Thermionic phenomena caused by vapors of rubidium and potassium,” Phys. Rev. 27, 578–587 (1926).
    [CrossRef]
  3. A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1934).
  4. J. Carlsten, “Laser selective excitation of a three-level atom: barium,” J. Phys. B 7, 1620–1632 (1974).
    [CrossRef]
  5. B. Shirinzadeh and C. C. Wang, “Accurate determination of the vapor pressure of potassium using optical absorption,” Appl. Opt. 22, 3265–3270 (1983).
    [CrossRef] [PubMed]
  6. N. Gershenfeld, “The measurement of optically thick atomic vapor densities by the nonlinear least-squares fitting of absorption or fluorescence spectra,” Nucl. Instrum. Methods Phys. Res. A 224, 570–572 (1984).
    [CrossRef]
  7. Z. Wu, M. Kitano, W. Happer, M. Hou, and J. Daniels, “Optical determination of alkali metal vapor number density using Faraday rotation,” Appl. Opt. 25, 4483–4492 (1986).
    [CrossRef] [PubMed]
  8. Z. Wu, W. Happer, and J. Daniels, “Coherent nuclear-spin interactions of adsorbed 131Xe gas with surfaces,” Phys. Rev. Lett. 59, 1480–1483 (1987).
    [CrossRef] [PubMed]
  9. D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
    [CrossRef] [PubMed]
  10. M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
    [CrossRef] [PubMed]
  11. T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
    [CrossRef]
  12. V. G. Bordo, J. Loerke, and H. G. Rubahn, “Two-photon evanescent-volume wave spectroscopy: a new account of gas–solid dynamics in the boundary layer,” Phys. Rev. Lett. 86, 1490–1493 (2001).
    [CrossRef] [PubMed]
  13. P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
    [CrossRef]
  14. P. Boissel and F. Kerherve, “Absorption de lumiere par des atomes dans une onde evanescente,” Opt. Commun. 37, 397–402 (1981).
    [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).
  16. M. V. Klein, Optics (Wiley, New York, 1970), pp. 570–573.
  17. X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
    [CrossRef] [PubMed]
  18. E. Arimondo, M. Inguscio, and P. Violino, “Experimental determination of the hyperfine structure in the alkali atom,” Rev. Mod. Phys. 49, 31–75 (1977).
    [CrossRef]
  19. K. Niemax and G. Pichler, “New aspects in the self-broadening of alkali resonance lines,” J. Phys. B 8, 179–184 (1975).
    [CrossRef]
  20. S. Y. Chen, “Pressure effect of homogeneous Rb vapor on its resonance line,” Phys. Rev. 58, 884–887 (1940).
    [CrossRef]

2001 (1)

V. G. Bordo, J. Loerke, and H. G. Rubahn, “Two-photon evanescent-volume wave spectroscopy: a new account of gas–solid dynamics in the boundary layer,” Phys. Rev. Lett. 86, 1490–1493 (2001).
[CrossRef] [PubMed]

1994 (1)

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

1990 (1)

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

1987 (2)

Z. Wu, W. Happer, and J. Daniels, “Coherent nuclear-spin interactions of adsorbed 131Xe gas with surfaces,” Phys. Rev. Lett. 59, 1480–1483 (1987).
[CrossRef] [PubMed]

T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
[CrossRef]

1986 (2)

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

Z. Wu, M. Kitano, W. Happer, M. Hou, and J. Daniels, “Optical determination of alkali metal vapor number density using Faraday rotation,” Appl. Opt. 25, 4483–4492 (1986).
[CrossRef] [PubMed]

1985 (1)

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

1984 (1)

N. Gershenfeld, “The measurement of optically thick atomic vapor densities by the nonlinear least-squares fitting of absorption or fluorescence spectra,” Nucl. Instrum. Methods Phys. Res. A 224, 570–572 (1984).
[CrossRef]

1983 (1)

1981 (1)

P. Boissel and F. Kerherve, “Absorption de lumiere par des atomes dans une onde evanescente,” Opt. Commun. 37, 397–402 (1981).
[CrossRef]

1977 (1)

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determination of the hyperfine structure in the alkali atom,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

1975 (1)

K. Niemax and G. Pichler, “New aspects in the self-broadening of alkali resonance lines,” J. Phys. B 8, 179–184 (1975).
[CrossRef]

1974 (1)

J. Carlsten, “Laser selective excitation of a three-level atom: barium,” J. Phys. B 7, 1620–1632 (1974).
[CrossRef]

1965 (1)

M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on paraffin-coated walls,” Phys. Rev. A 147, 41–54 (1965).
[CrossRef]

1940 (1)

S. Y. Chen, “Pressure effect of homogeneous Rb vapor on its resonance line,” Phys. Rev. 58, 884–887 (1940).
[CrossRef]

1926 (1)

T. Killian, “Thermionic phenomena caused by vapors of rubidium and potassium,” Phys. Rev. 27, 578–587 (1926).
[CrossRef]

Albert, M. S.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

Arimondo, E.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determination of the hyperfine structure in the alkali atom,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Benton, D. R.

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

Bloch, D.

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

Boissel, P.

P. Boissel and F. Kerherve, “Absorption de lumiere par des atomes dans une onde evanescente,” Opt. Commun. 37, 397–402 (1981).
[CrossRef]

Bordo, V. G.

V. G. Bordo, J. Loerke, and H. G. Rubahn, “Two-photon evanescent-volume wave spectroscopy: a new account of gas–solid dynamics in the boundary layer,” Phys. Rev. Lett. 86, 1490–1493 (2001).
[CrossRef] [PubMed]

Bouchiat, M. A.

M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on paraffin-coated walls,” Phys. Rev. A 147, 41–54 (1965).
[CrossRef]

Brossel, J.

M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on paraffin-coated walls,” Phys. Rev. A 147, 41–54 (1965).
[CrossRef]

Call, T.

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

Carlsten, J.

J. Carlsten, “Laser selective excitation of a three-level atom: barium,” J. Phys. B 7, 1620–1632 (1974).
[CrossRef]

Cates, G. D.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

Chen, S. Y.

S. Y. Chen, “Pressure effect of homogeneous Rb vapor on its resonance line,” Phys. Rev. 58, 884–887 (1940).
[CrossRef]

Chupp, T. E.

T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
[CrossRef]

Coulter, K. P.

T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
[CrossRef]

Daniels, J.

Z. Wu, W. Happer, and J. Daniels, “Coherent nuclear-spin interactions of adsorbed 131Xe gas with surfaces,” Phys. Rev. Lett. 59, 1480–1483 (1987).
[CrossRef] [PubMed]

Z. Wu, M. Kitano, W. Happer, M. Hou, and J. Daniels, “Optical determination of alkali metal vapor number density using Faraday rotation,” Appl. Opt. 25, 4483–4492 (1986).
[CrossRef] [PubMed]

De Araujo, C. B.

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

Driehuys, B.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

Ducloy, M.

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

Gatzky, M.

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

Gershenfeld, N.

N. Gershenfeld, “The measurement of optically thick atomic vapor densities by the nonlinear least-squares fitting of absorption or fluorescence spectra,” Nucl. Instrum. Methods Phys. Res. A 224, 570–572 (1984).
[CrossRef]

Happer, W.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

Z. Wu, W. Happer, and J. Daniels, “Coherent nuclear-spin interactions of adsorbed 131Xe gas with surfaces,” Phys. Rev. Lett. 59, 1480–1483 (1987).
[CrossRef] [PubMed]

T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
[CrossRef]

Z. Wu, M. Kitano, W. Happer, M. Hou, and J. Daniels, “Optical determination of alkali metal vapor number density using Faraday rotation,” Appl. Opt. 25, 4483–4492 (1986).
[CrossRef] [PubMed]

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

Hasson, K. C.

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

Hou, M.

Inguscio, M.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determination of the hyperfine structure in the alkali atom,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Kerherve, F.

P. Boissel and F. Kerherve, “Absorption de lumiere par des atomes dans une onde evanescente,” Opt. Commun. 37, 397–402 (1981).
[CrossRef]

Killian, T.

T. Killian, “Thermionic phenomena caused by vapors of rubidium and potassium,” Phys. Rev. 27, 578–587 (1926).
[CrossRef]

Kitano, M.

Le Boiteaux, S.

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

Leite, J. R. Rios

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

Loerke, J.

V. G. Bordo, J. Loerke, and H. G. Rubahn, “Two-photon evanescent-volume wave spectroscopy: a new account of gas–solid dynamics in the boundary layer,” Phys. Rev. Lett. 86, 1490–1493 (2001).
[CrossRef] [PubMed]

McDonald, A. B.

T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
[CrossRef]

Miron, E.

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

Newbury, N. R.

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

Niemax, K.

K. Niemax and G. Pichler, “New aspects in the self-broadening of alkali resonance lines,” J. Phys. B 8, 179–184 (1975).
[CrossRef]

Pichler, G.

K. Niemax and G. Pichler, “New aspects in the self-broadening of alkali resonance lines,” J. Phys. B 8, 179–184 (1975).
[CrossRef]

Rubahn, H. G.

V. G. Bordo, J. Loerke, and H. G. Rubahn, “Two-photon evanescent-volume wave spectroscopy: a new account of gas–solid dynamics in the boundary layer,” Phys. Rev. Lett. 86, 1490–1493 (2001).
[CrossRef] [PubMed]

Saam, B.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

Schreiber, D.

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

Shirinzadeh, B.

Simoneau, P.

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

Springer Jr., C. S.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

Violino, P.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determination of the hyperfine structure in the alkali atom,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Wagshul, M. E.

T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
[CrossRef]

Wang, C. C.

Wishnia, A.

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

Wu, Z.

Z. Wu, W. Happer, and J. Daniels, “Coherent nuclear-spin interactions of adsorbed 131Xe gas with surfaces,” Phys. Rev. Lett. 59, 1480–1483 (1987).
[CrossRef] [PubMed]

Z. Wu, M. Kitano, W. Happer, M. Hou, and J. Daniels, “Optical determination of alkali metal vapor number density using Faraday rotation,” Appl. Opt. 25, 4483–4492 (1986).
[CrossRef] [PubMed]

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

Zeng, X.

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Phys. B (2)

K. Niemax and G. Pichler, “New aspects in the self-broadening of alkali resonance lines,” J. Phys. B 8, 179–184 (1975).
[CrossRef]

J. Carlsten, “Laser selective excitation of a three-level atom: barium,” J. Phys. B 7, 1620–1632 (1974).
[CrossRef]

Nature (1)

M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, Jr., and A. Wishnia, “Biological magnetic resonance imaging using laser-polarized 129Xe,” Nature 370, 199–201 (1994).
[CrossRef] [PubMed]

Nucl. Instrum. Methods Phys. Res. A (1)

N. Gershenfeld, “The measurement of optically thick atomic vapor densities by the nonlinear least-squares fitting of absorption or fluorescence spectra,” Nucl. Instrum. Methods Phys. Res. A 224, 570–572 (1984).
[CrossRef]

Opt. Commun. (2)

P. Simoneau, S. Le Boiteaux, C. B. De Araujo, D. Bloch, J. R. Rios Leite, and M. Ducloy, “Doppler-free evanescent wave spectroscopy,” Opt. Commun. 59, 103–106 (1986).
[CrossRef]

P. Boissel and F. Kerherve, “Absorption de lumiere par des atomes dans une onde evanescente,” Opt. Commun. 37, 397–402 (1981).
[CrossRef]

Phys. Rev. (3)

S. Y. Chen, “Pressure effect of homogeneous Rb vapor on its resonance line,” Phys. Rev. 58, 884–887 (1940).
[CrossRef]

M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on paraffin-coated walls,” Phys. Rev. A 147, 41–54 (1965).
[CrossRef]

T. Killian, “Thermionic phenomena caused by vapors of rubidium and potassium,” Phys. Rev. 27, 578–587 (1926).
[CrossRef]

Phys. Rev. A (1)

X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber, and W. Happer, “Experimental determination of the rate constants for spin exchange between optically pumped K, Rb and Cs atoms and 129Xe nuclei in alkali-metal–noble-gas van der Waals molecules,” Phys. Rev. A 31, 260–278 (1985).
[CrossRef] [PubMed]

Phys. Rev. C (1)

T. E. Chupp, M. E. Wagshul, K. P. Coulter, A. B. McDonald, and W. Happer, “Polarized, high density, gaseous 3He targets,” Phys. Rev. C 36, 2244–2251 (1987).
[CrossRef]

Phys. Rev. Lett. (3)

V. G. Bordo, J. Loerke, and H. G. Rubahn, “Two-photon evanescent-volume wave spectroscopy: a new account of gas–solid dynamics in the boundary layer,” Phys. Rev. Lett. 86, 1490–1493 (2001).
[CrossRef] [PubMed]

Z. Wu, W. Happer, and J. Daniels, “Coherent nuclear-spin interactions of adsorbed 131Xe gas with surfaces,” Phys. Rev. Lett. 59, 1480–1483 (1987).
[CrossRef] [PubMed]

D. R. Benton, G. D. Cates, M. Gatzky, W. Happer, K. C. Hasson, and N. R. Newbury, “Laser production of large nuclear-spin polarization in frozen xenon,” Phys. Rev. Lett. 65, 2591–2594 (1990).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determination of the hyperfine structure in the alkali atom,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

M. V. Klein, Optics (Wiley, New York, 1970), pp. 570–573.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1934).

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Figures (7)

Fig. 1
Fig. 1

Calculated frequency dependence of reflectivity Rp(ν) for different angles of incidence about critical angle θ¯c. T=140 °C, N=6.2×1013 cm-3, and the values of γFF were obtained from Eqs. (26) and (27).

Fig. 2
Fig. 2

Experimental arrangement.

Fig. 3
Fig. 3

Attenuated total internal reflection signal S(ν) at a cell temperature of 140.2 °C and θ=θ¯c+10.2°. The horizontal axis represents the frequency of the probe beam, which scans across the D1 resonance line of both isotopes of Rb. The signal was averaged 50 times. The dashed line corresponds to no absorption and therefore is equal to C1/C2. Reflectivity Rp(ν) is obtained by division of signal Rp(ν)C1/C2 by C1/C2.

Fig. 4
Fig. 4

Measured reflectivities (solid curves) at T=122 °C. The signals were averaged 30 times. The dotted curves are the best fit by use of Eqs. (12), (20), and (21). Note the decrease in reflectivity when the angle of incidence becomes slightly smaller than the critical angle.

Fig. 5
Fig. 5

Measured Rb metal vapor number density versus temperature. The angles of incidence for the total internal reflection data are shown, and these data points represent the Rb number density in the vicinity of the cell wall. ○ and + represent the measured bulk and surface Rb number densities in a freshly made cell. The solid curve is obtained from Killian’s formula (29).

Fig. 6
Fig. 6

Rb metal vapor number density obtained for several angles of incidence. The penetration depths that correspond to these angles of incidence vary from 0.21 to 1.41 µm. Within experimental uncertainties the data show no systematic dependence of Rb number density on penetration depth of the probe beam.

Fig. 7
Fig. 7

Angular dependence of A(θ) and penetration depth [Eq. (10)].

Equations (36)

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(n2+in2)2=2+i2.
rs=kz(1)-kz(2)kz(1)+kz(2)(s polarization),
rp=kz(1)/1-kz(2)/2kz(1)/1+kz(2)/2(p polarization),
kz(i)2=4π2iν2/c2-kx(i)2,i=1, 2,
2=|2|exp(iβ)=22+22 exp(iβ),
kz(2)=ik ¯exp(-iα/2),
k¯/k(1)=[(sin2 θ-sin2 θc)2+(2/1)2]1/4,
tan α=2/1sin2 θ-sin2 θc.
d=1k¯cos(α/2),
d=λ02πn1 1(sin2 θ-sin2 θc)1/2,
Rs=|rs|2=1-4kz(1)k¯sin(α/2)kz(1)2+k¯2+2kz(1)k¯sin(α/2)
(spolarization),
Rp=|rp|2=1-4kz(1)k¯1|2|sin(α/2+β)kz(1)2|2|2+k¯212+2kz(1)k¯1|2|sin(α/2+β)
(ppolarization).
21,
α/21,
1-Rp=4n2n1 cos θ(2n12 sin2 θ-1)(n12 sin2 θ-1)1/2(cos2 θ+n14 sin2 θ-n12).
n2=Nσ(ν)λ04π,
[1-Rp(ν)]dν
=Ncrefλ0n1 cos θ(2n12 sin2 θ-1)(n12 sin2 θ-1)1/2(cos2 θ+n14 sin2 θ-n12).
σ(ν)dν=πcref,
NNmax=8π cot θcσmax λ0(θ-θc),
2=1+F,Ff¯FF 0 y2-xFF2(y2-xFF2)2+γ¯FF2xFF2×2Δπe-4(y-1)2Δ2 dy,
2=F,Ff¯FF 0 γ¯FFxFF(y2-xFF2)2+γ¯FF2xFF2×2Δπe-4(y-1)2Δ2dy
xFF=ν/νFF,
γ¯FF=γFF/νFF,
f¯FF=NFe2fFF/πmνFF2,
Δ=2c 2kTm.
fFF=fW2(JFJF;I1)(2J+1)(2F+1),
NF=2F+1(2J+1)(2I+1)ηN,
S(ν)=C1C2 Rp(ν),
γFFN=12πτ(2F+1)(2F+1)fFFF (2F+1)(2F+1)fFF.
γFFSB=(4π/3)C3N,
I(ν)=I0(ν)exp-2π2lλ0,
N=2.570×1026 exp(-9514/T)/T.
A(θ)=cos θ(2n12 sin2 θ-1)(n12 sin2 θ-1)1/2(cos2 θ+n14 sin2 θ-n12).

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