Abstract

The well-known theory of absorption and fluorescence is briefly reviewed in a systematic manner for the Na D transitions. The resulting formalism is applied to simulation of Doppler-free saturation fluorescence spectra. With only one adjusting parameter, the nonradiative rate chosen to represent the time a thermal atom takes to move across the laser beams, the simulated Doppler-free spectra match the measured ones well for both D 1 and D 2 transitions over one decade of excitation intensities. Relative to the weighted center of the six D 2 hyperfine transition lines, the frequencies of the dominant Doppler-free features have been determined from a simulated spectrum to within ±0.1 MHz to be −651.4, 187.8, and 1068.0 MHz, respectively, for D 2 a, crossover, and D 2 b resonances. These features may be used as accurate frequency references for atmospheric spectroscopy. They are essential for the operation of the newly developed narrow-band Na fluorescence lidar for wind and temperature measurements in the mesopause region.

© 1995 Optical Society of America

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References

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  1. T. W. Hansch, I. S. Shahin, A. L. Schawlow, “High-resolution saturation spectroscopy of the sodium D lines with a pulsed tunable dye laser,” Phys. Rev. Lett. 27, 707–710 (1971).
    [Crossref]
  2. C. Wieman, T. W. Hansch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
    [Crossref]
  3. T. P. Duffey, D. Kammen, A. L. Schawlow, S. Svanberg, H. X. Xia, G. G. Xiao, G. Y. Yan, “Laser spectroscopy using beam overlap modulation,” Opt. Lett. 10, 597–599 (1985).
    [Crossref] [PubMed]
  4. M. S. Sorem, A. L. Schawlow, “Saturated spectroscopy in molecular iodine by intermodulated fluorescence,” Opt. Commun. 5, 148–152 (1972).
    [Crossref]
  5. G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15–18 (1980).
    [Crossref] [PubMed]
  6. J. J. L. Mulders, L. W. G. Steenhuysen, “Experimental comparison of two Doppler-free detection methods with a new technique: differential saturation spectroscopy,” Opt. Commun. 55, 105–109 (1985).
    [Crossref]
  7. S. Nakayama, “Doppler-free laser spectroscopic techniques with optical pumping in D1 lines of alkali atoms,” J. Opt. Soc. Am. B 2, 1431–1437 (1985).
    [Crossref]
  8. S. Svanberg, G. Y. Yan, T. P. Duffey, A. L. Schawlow, “High-contrast Doppler-free transmission spectroscopy,” Opt. Lett. 11, 138–140 (1986).
    [Crossref] [PubMed]
  9. P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, A. Lurio, “Frequency-locking of organic dye lasers to atomic resonance lines,” Appl. Phys. Lett. 15, 179–181 (1969).
    [Crossref]
  10. C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
    [Crossref]
  11. A. Corney, Atomic and Laser Spectroscopy (Claredon, Oxford, 1977), Chap. 4.
  12. C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
    [Crossref] [PubMed]
  13. W. Hartig, H. Walther, “High-resolution spectroscopy and frequency stabilization of a cw laser,” Appl. Phys. 1, 171–174 (1973).
    [Crossref]
  14. W. L. Wiese, M. W. Smith, B. M. Miles, “Atomic transition probabilities,” Nat. Stand. Ref. Data Ser. Nat. Bur. Stand. 22 (National Bureau of Standards, Washington, D.C., 1969).
  15. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957), Chap. 5.
  16. V. B. Berestetski, E. M. Lifshitz, L. P. Pitevski, Relativistic Quantum Theory: Part I (Addison-Wesley, Reading, Mass., 1971), Chap. 5.
  17. L. M. Zheng, G. W. Xu, Atomic Structure and Spectroscopy (Peking U. Press, Peking, 1988), Chap. 1 (in Chinese).
  18. O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), Chap. 2.
  19. C. Y. She, W. M. Fairbank, K. W. Billman, “Measuring the velocity of individual atoms in real time,” Opt. Lett. 2, 30–32 (1978).
    [Crossref] [PubMed]
  20. C. L. Pan, J. V. Prodan, W. M. Fairbank, C. Y. She, “Detection of individual atoms in helium buffer gas and observation of their real-time motion,” Opt. Lett. 5, 459–461 (1980).
    [Crossref] [PubMed]
  21. M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
    [Crossref]
  22. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 7.
  23. Ref. 22, Chap. 30.
  24. A. Schawlow, Department of Physics, Stanford University, Stanford, Calif. 94305 (personal communication, October1992).
  25. P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955–1968 (1980).
    [Crossref]
  26. J. R. Yu, C. Y. She, “Lidar-observed temperature structures and gravity-wave perturbations of the mesopause region in the Springs of 1990–1992 over Fort Collins, CO,” Appl. Phys. B 57, 231–238 (1993).
    [Crossref]
  27. H. Moosmuller, C. Y. She, “Equal intensity and phase contours in focused Gaussian laser beams,” IEEE J. Quantum Electron. 27, 869–874 (1991).
    [Crossref]
  28. S. Y. Tang, C. Y. She, S. A. Lee, “Continuous-wave Rayleigh–Brillouin-gain spectroscopy in SF6,” Opt. Lett. 12, 870–872 (1987).
    [Crossref] [PubMed]
  29. L. Hlousek, S. A. Lee, W. M. Fairbank, “Precision wavelength measurements and new experimental Lamb shifts in helium,” Phys. Rev. Lett. 50, 328–331 (1983).
    [Crossref]
  30. M. A. Kasevich, E. Riis, S. Chu, R. G. Devoe, “RF spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
    [Crossref] [PubMed]

1993 (1)

J. R. Yu, C. Y. She, “Lidar-observed temperature structures and gravity-wave perturbations of the mesopause region in the Springs of 1990–1992 over Fort Collins, CO,” Appl. Phys. B 57, 231–238 (1993).
[Crossref]

1992 (1)

1991 (1)

H. Moosmuller, C. Y. She, “Equal intensity and phase contours in focused Gaussian laser beams,” IEEE J. Quantum Electron. 27, 869–874 (1991).
[Crossref]

1990 (1)

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

1989 (1)

M. A. Kasevich, E. Riis, S. Chu, R. G. Devoe, “RF spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[Crossref] [PubMed]

1987 (1)

1986 (1)

1985 (3)

1983 (1)

L. Hlousek, S. A. Lee, W. M. Fairbank, “Precision wavelength measurements and new experimental Lamb shifts in helium,” Phys. Rev. Lett. 50, 328–331 (1983).
[Crossref]

1980 (3)

1978 (1)

1976 (1)

C. Wieman, T. W. Hansch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

1973 (1)

W. Hartig, H. Walther, “High-resolution spectroscopy and frequency stabilization of a cw laser,” Appl. Phys. 1, 171–174 (1973).
[Crossref]

1972 (2)

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[Crossref]

M. S. Sorem, A. L. Schawlow, “Saturated spectroscopy in molecular iodine by intermodulated fluorescence,” Opt. Commun. 5, 148–152 (1972).
[Crossref]

1971 (1)

T. W. Hansch, I. S. Shahin, A. L. Schawlow, “High-resolution saturation spectroscopy of the sodium D lines with a pulsed tunable dye laser,” Phys. Rev. Lett. 27, 707–710 (1971).
[Crossref]

1969 (1)

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, A. Lurio, “Frequency-locking of organic dye lasers to atomic resonance lines,” Appl. Phys. Lett. 15, 179–181 (1969).
[Crossref]

Alvarez, R. J.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

Berestetski, V. B.

V. B. Berestetski, E. M. Lifshitz, L. P. Pitevski, Relativistic Quantum Theory: Part I (Addison-Wesley, Reading, Mass., 1971), Chap. 5.

Billman, K. W.

Bills, R. E.

C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
[Crossref] [PubMed]

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

Bjorklund, G. C.

Burns, M. M.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955–1968 (1980).
[Crossref]

Chu, S.

M. A. Kasevich, E. Riis, S. Chu, R. G. Devoe, “RF spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[Crossref] [PubMed]

Corney, A.

A. Corney, Atomic and Laser Spectroscopy (Claredon, Oxford, 1977), Chap. 4.

Devoe, R. G.

M. A. Kasevich, E. Riis, S. Chu, R. G. Devoe, “RF spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[Crossref] [PubMed]

Duffey, T. P.

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957), Chap. 5.

Fairbank, W. M.

Feld, M. S.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955–1968 (1980).
[Crossref]

Gardner, C. S.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

Hansch, T. W.

C. Wieman, T. W. Hansch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

T. W. Hansch, I. S. Shahin, A. L. Schawlow, “High-resolution saturation spectroscopy of the sodium D lines with a pulsed tunable dye laser,” Phys. Rev. Lett. 27, 707–710 (1971).
[Crossref]

Hartig, W.

W. Hartig, H. Walther, “High-resolution spectroscopy and frequency stabilization of a cw laser,” Appl. Phys. 1, 171–174 (1973).
[Crossref]

Hinshelwood, D. D.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955–1968 (1980).
[Crossref]

Hlousek, L.

L. Hlousek, S. A. Lee, W. M. Fairbank, “Precision wavelength measurements and new experimental Lamb shifts in helium,” Phys. Rev. Lett. 50, 328–331 (1983).
[Crossref]

Kammen, D.

Kasevich, M. A.

M. A. Kasevich, E. Riis, S. Chu, R. G. Devoe, “RF spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[Crossref] [PubMed]

Lankard, J. R.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, A. Lurio, “Frequency-locking of organic dye lasers to atomic resonance lines,” Appl. Phys. Lett. 15, 179–181 (1969).
[Crossref]

Latifi, H.

C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
[Crossref] [PubMed]

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

Lee, S. A.

S. Y. Tang, C. Y. She, S. A. Lee, “Continuous-wave Rayleigh–Brillouin-gain spectroscopy in SF6,” Opt. Lett. 12, 870–872 (1987).
[Crossref] [PubMed]

L. Hlousek, S. A. Lee, W. M. Fairbank, “Precision wavelength measurements and new experimental Lamb shifts in helium,” Phys. Rev. Lett. 50, 328–331 (1983).
[Crossref]

Levenson, M. D.

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[Crossref]

Lifshitz, E. M.

V. B. Berestetski, E. M. Lifshitz, L. P. Pitevski, Relativistic Quantum Theory: Part I (Addison-Wesley, Reading, Mass., 1971), Chap. 5.

Lurio, A.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, A. Lurio, “Frequency-locking of organic dye lasers to atomic resonance lines,” Appl. Phys. Lett. 15, 179–181 (1969).
[Crossref]

Miles, B. M.

W. L. Wiese, M. W. Smith, B. M. Miles, “Atomic transition probabilities,” Nat. Stand. Ref. Data Ser. Nat. Bur. Stand. 22 (National Bureau of Standards, Washington, D.C., 1969).

Moosmuller, H.

H. Moosmuller, C. Y. She, “Equal intensity and phase contours in focused Gaussian laser beams,” IEEE J. Quantum Electron. 27, 869–874 (1991).
[Crossref]

Moruzzi, V. L.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, A. Lurio, “Frequency-locking of organic dye lasers to atomic resonance lines,” Appl. Phys. Lett. 15, 179–181 (1969).
[Crossref]

Mulders, J. J. L.

J. J. L. Mulders, L. W. G. Steenhuysen, “Experimental comparison of two Doppler-free detection methods with a new technique: differential saturation spectroscopy,” Opt. Commun. 55, 105–109 (1985).
[Crossref]

Murnick, D. E.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955–1968 (1980).
[Crossref]

Nakayama, S.

Pan, C. L.

Pappas, P. G.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955–1968 (1980).
[Crossref]

Pitevski, L. P.

V. B. Berestetski, E. M. Lifshitz, L. P. Pitevski, Relativistic Quantum Theory: Part I (Addison-Wesley, Reading, Mass., 1971), Chap. 5.

Prodan, J. V.

Riis, E.

M. A. Kasevich, E. Riis, S. Chu, R. G. Devoe, “RF spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[Crossref] [PubMed]

Schawlow, A.

A. Schawlow, Department of Physics, Stanford University, Stanford, Calif. 94305 (personal communication, October1992).

Schawlow, A. L.

S. Svanberg, G. Y. Yan, T. P. Duffey, A. L. Schawlow, “High-contrast Doppler-free transmission spectroscopy,” Opt. Lett. 11, 138–140 (1986).
[Crossref] [PubMed]

T. P. Duffey, D. Kammen, A. L. Schawlow, S. Svanberg, H. X. Xia, G. G. Xiao, G. Y. Yan, “Laser spectroscopy using beam overlap modulation,” Opt. Lett. 10, 597–599 (1985).
[Crossref] [PubMed]

M. S. Sorem, A. L. Schawlow, “Saturated spectroscopy in molecular iodine by intermodulated fluorescence,” Opt. Commun. 5, 148–152 (1972).
[Crossref]

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[Crossref]

T. W. Hansch, I. S. Shahin, A. L. Schawlow, “High-resolution saturation spectroscopy of the sodium D lines with a pulsed tunable dye laser,” Phys. Rev. Lett. 27, 707–710 (1971).
[Crossref]

Shahin, I. S.

T. W. Hansch, I. S. Shahin, A. L. Schawlow, “High-resolution saturation spectroscopy of the sodium D lines with a pulsed tunable dye laser,” Phys. Rev. Lett. 27, 707–710 (1971).
[Crossref]

She, C. Y.

J. R. Yu, C. Y. She, “Lidar-observed temperature structures and gravity-wave perturbations of the mesopause region in the Springs of 1990–1992 over Fort Collins, CO,” Appl. Phys. B 57, 231–238 (1993).
[Crossref]

C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
[Crossref] [PubMed]

H. Moosmuller, C. Y. She, “Equal intensity and phase contours in focused Gaussian laser beams,” IEEE J. Quantum Electron. 27, 869–874 (1991).
[Crossref]

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

S. Y. Tang, C. Y. She, S. A. Lee, “Continuous-wave Rayleigh–Brillouin-gain spectroscopy in SF6,” Opt. Lett. 12, 870–872 (1987).
[Crossref] [PubMed]

C. L. Pan, J. V. Prodan, W. M. Fairbank, C. Y. She, “Detection of individual atoms in helium buffer gas and observation of their real-time motion,” Opt. Lett. 5, 459–461 (1980).
[Crossref] [PubMed]

C. Y. She, W. M. Fairbank, K. W. Billman, “Measuring the velocity of individual atoms in real time,” Opt. Lett. 2, 30–32 (1978).
[Crossref] [PubMed]

Siegman, A.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 7.

Smith, M. W.

W. L. Wiese, M. W. Smith, B. M. Miles, “Atomic transition probabilities,” Nat. Stand. Ref. Data Ser. Nat. Bur. Stand. 22 (National Bureau of Standards, Washington, D.C., 1969).

Sorem, M. S.

M. S. Sorem, A. L. Schawlow, “Saturated spectroscopy in molecular iodine by intermodulated fluorescence,” Opt. Commun. 5, 148–152 (1972).
[Crossref]

Sorokin, P. P.

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, A. Lurio, “Frequency-locking of organic dye lasers to atomic resonance lines,” Appl. Phys. Lett. 15, 179–181 (1969).
[Crossref]

Steenhuysen, L. W. G.

J. J. L. Mulders, L. W. G. Steenhuysen, “Experimental comparison of two Doppler-free detection methods with a new technique: differential saturation spectroscopy,” Opt. Commun. 55, 105–109 (1985).
[Crossref]

Svanberg, S.

Svelto, O.

O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), Chap. 2.

Tang, S. Y.

Walther, H.

W. Hartig, H. Walther, “High-resolution spectroscopy and frequency stabilization of a cw laser,” Appl. Phys. 1, 171–174 (1973).
[Crossref]

Wieman, C.

C. Wieman, T. W. Hansch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

Wiese, W. L.

W. L. Wiese, M. W. Smith, B. M. Miles, “Atomic transition probabilities,” Nat. Stand. Ref. Data Ser. Nat. Bur. Stand. 22 (National Bureau of Standards, Washington, D.C., 1969).

Xia, H. X.

Xiao, G. G.

Xu, G. W.

L. M. Zheng, G. W. Xu, Atomic Structure and Spectroscopy (Peking U. Press, Peking, 1988), Chap. 1 (in Chinese).

Yan, G. Y.

Yu, J. R.

J. R. Yu, C. Y. She, “Lidar-observed temperature structures and gravity-wave perturbations of the mesopause region in the Springs of 1990–1992 over Fort Collins, CO,” Appl. Phys. B 57, 231–238 (1993).
[Crossref]

C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
[Crossref] [PubMed]

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

Zheng, L. M.

L. M. Zheng, G. W. Xu, Atomic Structure and Spectroscopy (Peking U. Press, Peking, 1988), Chap. 1 (in Chinese).

Appl. Opt. (1)

Appl. Phys. (1)

W. Hartig, H. Walther, “High-resolution spectroscopy and frequency stabilization of a cw laser,” Appl. Phys. 1, 171–174 (1973).
[Crossref]

Appl. Phys. B (1)

J. R. Yu, C. Y. She, “Lidar-observed temperature structures and gravity-wave perturbations of the mesopause region in the Springs of 1990–1992 over Fort Collins, CO,” Appl. Phys. B 57, 231–238 (1993).
[Crossref]

Appl. Phys. Lett. (1)

P. P. Sorokin, J. R. Lankard, V. L. Moruzzi, A. Lurio, “Frequency-locking of organic dye lasers to atomic resonance lines,” Appl. Phys. Lett. 15, 179–181 (1969).
[Crossref]

Geophys. Res. Lett. (1)

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[Crossref]

IEEE J. Quantum Electron. (1)

H. Moosmuller, C. Y. She, “Equal intensity and phase contours in focused Gaussian laser beams,” IEEE J. Quantum Electron. 27, 869–874 (1991).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

J. J. L. Mulders, L. W. G. Steenhuysen, “Experimental comparison of two Doppler-free detection methods with a new technique: differential saturation spectroscopy,” Opt. Commun. 55, 105–109 (1985).
[Crossref]

M. S. Sorem, A. L. Schawlow, “Saturated spectroscopy in molecular iodine by intermodulated fluorescence,” Opt. Commun. 5, 148–152 (1972).
[Crossref]

Opt. Lett. (6)

Phys. Rev. A (2)

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955–1968 (1980).
[Crossref]

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[Crossref]

Phys. Rev. Lett. (4)

T. W. Hansch, I. S. Shahin, A. L. Schawlow, “High-resolution saturation spectroscopy of the sodium D lines with a pulsed tunable dye laser,” Phys. Rev. Lett. 27, 707–710 (1971).
[Crossref]

C. Wieman, T. W. Hansch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett. 36, 1170–1173 (1976).
[Crossref]

L. Hlousek, S. A. Lee, W. M. Fairbank, “Precision wavelength measurements and new experimental Lamb shifts in helium,” Phys. Rev. Lett. 50, 328–331 (1983).
[Crossref]

M. A. Kasevich, E. Riis, S. Chu, R. G. Devoe, “RF spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[Crossref] [PubMed]

Other (9)

A. Corney, Atomic and Laser Spectroscopy (Claredon, Oxford, 1977), Chap. 4.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 7.

Ref. 22, Chap. 30.

A. Schawlow, Department of Physics, Stanford University, Stanford, Calif. 94305 (personal communication, October1992).

W. L. Wiese, M. W. Smith, B. M. Miles, “Atomic transition probabilities,” Nat. Stand. Ref. Data Ser. Nat. Bur. Stand. 22 (National Bureau of Standards, Washington, D.C., 1969).

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957), Chap. 5.

V. B. Berestetski, E. M. Lifshitz, L. P. Pitevski, Relativistic Quantum Theory: Part I (Addison-Wesley, Reading, Mass., 1971), Chap. 5.

L. M. Zheng, G. W. Xu, Atomic Structure and Spectroscopy (Peking U. Press, Peking, 1988), Chap. 1 (in Chinese).

O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), Chap. 2.

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Figures (10)

Fig. 1
Fig. 1

Energy-level diagrams of a Na atom described by three related models. The basic model is a two-state system (3s and 3p with respective degeneracies of 1 and 3). In the intermediate model, the electron spin is included, which doubles the degeneracies. The spin-orbit coupling splits the excited state into a doublet and a quartet, 2 P 1/2 and 2P 3/2, giving rise to D 1 and D 2 emission lines to the ground state 2 S 1/2 at 5896 and 5890 Å, respectively. In the final model, the nuclear spin of 3/2 and the associated hyperfine interaction lead to the energy-level structure with hyperfine splitting. The degeneracy then increases by another factor of 4, and the states 2 S 1/2, 2P 1/2, and 2P 3/2 split into 2, 2, and 4 hyperfine levels, respectively, labeled by total angular momentum of the atom, F, with the degeneracy 2f + 1. The numbers given in a transition arrow of each model are the transition line strength S (not bracketed) and the Einstein coefficient A (in the bracket) of that transition in the unit of the transition line strength S 0 and the spontaneous emission rate A 0 of the basic model.

Fig. 2
Fig. 2

Initial Na D 2 fluorescence spectra with three Doppler-free features located at D 2 a peak ν a , D 2 b peak ν b , and crossover resonance ν c = (ν a + ν b )/2 from a laboratory Na cell at 325 K with the reflections from the cell window (solid curve) and an external mirror (short-dashed curve) are shown. Also shown is the fluorescence signal from a Na layer at 92 km (triangles) along with a theoretical thermal-broadened spectrum (long-dashed) at T = 187 K, which exhibits the familiar Doppler-broadened double humps without Doppler-free features.

Fig. 3
Fig. 3

Simulated Doppler-free fluorescence spectra of a three-level system with parameters that depict the poorly resolved Na D 2 transition with excitation laser intensities of (a) 7.7 × 10−4, (b) 5.8 × 10−3, and (c) 3.8 × 10−2 mW/mm2, along with a nonradiative rate of 2.5 × 105 s−1.

Fig. 4
Fig. 4

Pictorial descriptions of atoms with equilibrium velocity distribution interacting with counterpropagating laser beams, giving rise to Doppler-free Lamb dip and crossover resonances.

Fig. 5
Fig. 5

Schematic experimental setup for Doppler-free fluorescence spectroscopy. BS, beam splitter; PMT, photomultiplier tube.

Fig. 6
Fig. 6

Experimentally measured laser intensity cross-sectional profile, along with a Gaussian fit that yields an e −2 beam radius of w 0 = 0.81 mm

Fig. 7
Fig. 7

Simulated and measured laser-induced fluorescence spectra of Na D 1 transition normalized to the intensity at −1.60 GHz, with laser power P and peak intensity I 0 per beam of (a) 0.05 mW and 0.048 mW/mm2, (b) 0.10 mW and 0.097 mW/mm2, (c) 0.25 mW and 0.243 mW/mm2, and (d) 0.50 mW and 0.485 mW/mm2.

Fig. 8
Fig. 8

Simulated and measured laser-induced fluorescence spectra of Na D 2 transition normalized to the intensity at −1.32 GHz, with laser power P and peak intensity I 0 per beam of (a) 0.05 mW and 0.048 mW/mm2, (b) 0.10 mW and 0.097 mW/mm2, (c) 0.25 mW and 0.243 mW/mm2, and (d) 0.50 mW and 0.485 mW/mm2.

Fig. 9
Fig. 9

Simulated fluorescence (Theory D1 and D2), measured fluorescence (Exp. D1 and D2), and scattered background (Exp. D1.BG and D2.BG) light intensities are plotted as a function of laser excitation power (a) for the Na D 1 transition and (b) for the Na D 2 transition. These plots depict the saturation in the Doppler-broadened background fluorescence. Computer-fitted saturation power for both simulated and measured fluorescence intensities is marked by the curves.

Fig. 10
Fig. 10

Simulated and measured laser-induced fluorescence spectra of (a) the Na D 1 transition and (b) the Na D 2 transition at the excitation laser power of 0.1 mW in an expanded frequency scale for the determination of the absolute frequencies of the Doppler-free features.

Tables (1)

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Table 1 Frequencies of D 1 and D 2 Transitions Relative to the Weighted Group Center of the Respective Transitions

Equations (35)

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W = g 1 W i 2 = g 2 W k 1 = ( π / 3 ɛ 0 c 2 ) [ S g ( Δ ω ) ] I ,
g ( ω - ω 0 ) = ( 2 π ) - 1 g ( ν - ν 0 ) = ( 2 π 2 ) - 1 G ( ν - ν 0 ) ,
G ( ν - ν 0 ) = ( Δ ν ) / [ ( ν - ν 0 ) 2 + ( Δ ν ) 2 ] .
A k 1 = ( ω 3 / π 2 c 3 ) B k 1 = ( ω 3 / 3 π ɛ 0 c 3 ) ( S / g 2 ) .
S 0 = e 2 | R 30 ( r ) r 3 R 31 ( r ) d r | 2 = S l l .
A 0 = ( ω 0 3 / 3 π ɛ 0 c 3 ) ( S 0 / 3 ) = A l l .
j , m T q κ j , m = ( - 1 ) j - m ( j κ j m q m ) j T κ j ,
f μ f 2 = g f g f [ f 1 f j I j ] 2 j μ j 2 ,
j μ j 2 = g j g j [ j 1 j l S l ] l μ l 2 .
d N 2 / d t = d N 1 / d t = - W k 1 N 2 + W i 2 N 1 - N 2 / τ ,
N 2 / N 1 = W i 2 / [ W k 1 + ( 1 / τ ) ] = ( W i 2 τ ) / [ ( W k 1 τ ) + 1 ] = [ ( B i 2 τ ) ( I / c ) g ( ω - ω 0 ) ] / [ 1 + ( B k 1 τ ) ( I / c ) g ( ω - ω 0 ) ] .
R ( ν ) = ( N 2 / N 0 ) A k 1 = R s [ ( I / I s ) / ( 1 + I / I s ) ] ,
I s - 1 = ( 1 + g 2 / g 1 ) B k 1 τ g ( ω - ω 0 ) / c = ( π / 3 ɛ 0 c 2 ) ( 1 + g 2 / g 1 ) [ S g ( ω - ω 0 ) τ / g 2 ] .
( B k 1 / A k 1 ) ( I / 2 π c ) g ( ν - ν 0 ) = ξ I G ( ν - ν 0 ) ,
I s - 1 = ( 1 + g 2 / g 1 ) ξ G ( ν - ν 0 ) .
Fluo ( ν , I ) = ( D / π T ) exp ( - D z 2 / T ) R ( ν , z , I ) d z ,
d N 1 / d t = - ( W 13 + Γ ) N 1 + ( W 31 + A 31 ) N 3 + Γ N 01 ,
d N 2 / d t = - ( W 23 + Γ ) N 2 + ( W 32 + A 32 ) N 3 + Γ N 02 ,
d N 3 / d t = W 23 N 2 + W 13 N 1 - ( A 31 + W 31 + A 32 + W 32 + Γ ) N 3 ,
N 02 = N 0 g 2 exp ( - Δ E / k B T ) / [ g 1 + g 2 exp ( - Δ E / k B T ) ] ,
N 01 = N 0 g 1 / [ g 1 + g 2 exp ( - Δ E / k B T ) ] ,
I ( r , z ) = I ( r ) = I 0 exp [ - 2 ( r / w 0 ) 2 ] ,
I 0 = 2 P / π w 0 2 ,
Fluo ( ν ) = C ( 2 π r ) Fluo [ ν , I ( r ) ] d r ,
d N 1 / d t = - ( W 13 + W 14 + Γ ) N 1 + ( W 31 + A 31 ) N 3 + ( W 41 + A 41 ) N 4 + Γ N 01 ,
d N 2 / d t = - ( W 23 + W 24 + Γ ) N 2 + ( W 32 + A 32 ) N 3 + ( W 42 + A 42 ) N 4 + Γ N 02 ,
d N 3 / d t = W 23 N 2 + W 13 N 1 - ( A 31 + W 31 + A 32 + W 32 + Γ ) N 3 ,
d N 4 / d t = W 24 N 2 + W 14 N 1 - ( A 41 + W 41 + A 42 + W 42 + Γ ) N 4 .
d N 1 / d t = - ( W 15 + W 16 + W 17 + Γ ) N 1 + ( W 51 + A 51 ) N 5 + ( W 61 + A 61 ) N 6 + ( W 71 + A 71 ) N 7 + Γ N 01 ,
d N 2 / d t = - ( W 26 + W 27 + W 28 + Γ ) N 2 + ( W 62 + A 62 ) N 6 + ( W 72 + A 72 ) N 7 + ( W 82 + A 82 ) N 8 + Γ N 02 ,
d N 5 / d t = W 15 N 1 - ( A 51 + W 51 + Γ ) N 5 ,
d N 6 / d t = W 16 N 1 + W 26 N 2 - ( A 61 + W 61 + A 62 + W 62 + Γ ) N 6 ,
d N 7 / d t = W 17 N 1 + W 27 N 2 - ( A 71 + W 71 + A 72 + W 72 + Γ ) N 7 ,
d N 8 / d t = W 28 N 2 - ( A 82 + W 82 + Γ ) N 8 .
R [ ν , z , I ( r ) ] = n ( ν , z ) A 0 / N 0 ,

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