Abstract

We have observed 79 two-photon transitions in Na2 by using cw dye-laser excitation. The transitions are enhanced by the near coincidence of the laser frequency with a suitable one-photon transition. Of these two-photon lines, 57 have been assigned to transitions from the X 1g+ ground state to two recently reported 1g+ and one 1Πg state at 33000 cm−1. We discuss the spectral structures of the observed lines that arise from the requirements of near-resonant enhancement.

© 1982 Optical Society of America

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  1. L. S. Vasilenko, V. P. Chebotayev, and A. V. Shishaev, “Line shape of two-photon absorption in a standing-wave field in a gas,” JETP Lett. 12, 113–116 (1970).
  2. F. Biraben, B. Cagnac, and G. Grynberg, “Experimental evidence of two-photon transitions without Doppler broadening,” Phys. Rev. Lett. 32, 643–645 (1974).
    [Crossref]
  3. M. D. Levenson and N. Bloembergen, “Observation of two-photon absorption without Doppler broadening on the 3S–5S transition in sodium vapor,” Phys. Rev. Lett. 32, 645–648 (1974).
    [Crossref]
  4. T. W. Hänsch, K. C. Harvey, G. Meisel, and A. L. Schawlow, “Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a c.w. dye laser,” Opt. Commun. 11, 50–53 (1974).
    [Crossref]
  5. K. C. Harvey, “Doppler-free two-photon spectroscopy,” , (Stanford University, Stanford, Calif., 1975) (unpublished).
  6. J. P. Woerdman, “Doppler-free two-photon transitions of the sodium molecule,” Chem. Phys. Lett. 43, 279–282 (1976).
    [Crossref]
  7. N. Bloembergen and M. D. Levenson, “Doppler-free two-photon absorption spectroscopy,” in Topics in Applied Physics, High Resolution Laser Spectroscopy, K. Shimoda, ed. (Springer-Verlag, Berlin, 1976), Vol. 13.
    [Crossref]
  8. G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 1 of Spectra of Diatomic Molecules (Van Nostrand, Princeton, N.J., 1950).
  9. H.-R. Xia, G.-Y. Yan, and A. L. Schawlow, “Two photon line shapes with year-resonant enhancement,” Opt. Commun. 39, 153–158 (1981).
    [Crossref]
  10. P. Kusch and M. M. Hessel, “An analysis of the B1Πu–X1∑g+ band system of Na2,” J. Chem. Phys. 68, 2591–2606 (1978).
    [Crossref]
  11. P. Kusch and M. M. Hessel, Department of Physics, University of Texas, Richardson, Texas 75080 (personal communication).
  12. A. J. Taylor, K. M. Jones, and A. L. Schawlow, “A study of the excited 1∑g+ states in Na2,” Opt. Commun. 39, 47–50 (1981).
    [Crossref]
  13. N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2,” Phys. Rev. A 24, 822–834 (1981).
    [Crossref]
  14. H. R. Xia, S. V. Benson, and T. W. Hinsch, “A toy-train wavemeter,” Laser Focus 17(3), 54–58 (1981).
  15. J. P. Woerdman and M. F. H. Schuurmans, “Doppler-free three-photon cross-resonances in Na2vapor,” Opt. Commun. 21, 243–246 (1977).
    [Crossref]

1981 (4)

A. J. Taylor, K. M. Jones, and A. L. Schawlow, “A study of the excited 1∑g+ states in Na2,” Opt. Commun. 39, 47–50 (1981).
[Crossref]

N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2,” Phys. Rev. A 24, 822–834 (1981).
[Crossref]

H. R. Xia, S. V. Benson, and T. W. Hinsch, “A toy-train wavemeter,” Laser Focus 17(3), 54–58 (1981).

H.-R. Xia, G.-Y. Yan, and A. L. Schawlow, “Two photon line shapes with year-resonant enhancement,” Opt. Commun. 39, 153–158 (1981).
[Crossref]

1978 (1)

P. Kusch and M. M. Hessel, “An analysis of the B1Πu–X1∑g+ band system of Na2,” J. Chem. Phys. 68, 2591–2606 (1978).
[Crossref]

1977 (1)

J. P. Woerdman and M. F. H. Schuurmans, “Doppler-free three-photon cross-resonances in Na2vapor,” Opt. Commun. 21, 243–246 (1977).
[Crossref]

1976 (1)

J. P. Woerdman, “Doppler-free two-photon transitions of the sodium molecule,” Chem. Phys. Lett. 43, 279–282 (1976).
[Crossref]

1974 (3)

F. Biraben, B. Cagnac, and G. Grynberg, “Experimental evidence of two-photon transitions without Doppler broadening,” Phys. Rev. Lett. 32, 643–645 (1974).
[Crossref]

M. D. Levenson and N. Bloembergen, “Observation of two-photon absorption without Doppler broadening on the 3S–5S transition in sodium vapor,” Phys. Rev. Lett. 32, 645–648 (1974).
[Crossref]

T. W. Hänsch, K. C. Harvey, G. Meisel, and A. L. Schawlow, “Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a c.w. dye laser,” Opt. Commun. 11, 50–53 (1974).
[Crossref]

1970 (1)

L. S. Vasilenko, V. P. Chebotayev, and A. V. Shishaev, “Line shape of two-photon absorption in a standing-wave field in a gas,” JETP Lett. 12, 113–116 (1970).

Benson, S. V.

H. R. Xia, S. V. Benson, and T. W. Hinsch, “A toy-train wavemeter,” Laser Focus 17(3), 54–58 (1981).

Biraben, F.

F. Biraben, B. Cagnac, and G. Grynberg, “Experimental evidence of two-photon transitions without Doppler broadening,” Phys. Rev. Lett. 32, 643–645 (1974).
[Crossref]

Bloembergen, N.

M. D. Levenson and N. Bloembergen, “Observation of two-photon absorption without Doppler broadening on the 3S–5S transition in sodium vapor,” Phys. Rev. Lett. 32, 645–648 (1974).
[Crossref]

N. Bloembergen and M. D. Levenson, “Doppler-free two-photon absorption spectroscopy,” in Topics in Applied Physics, High Resolution Laser Spectroscopy, K. Shimoda, ed. (Springer-Verlag, Berlin, 1976), Vol. 13.
[Crossref]

Cagnac, B.

F. Biraben, B. Cagnac, and G. Grynberg, “Experimental evidence of two-photon transitions without Doppler broadening,” Phys. Rev. Lett. 32, 643–645 (1974).
[Crossref]

Carlson, N. W.

N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2,” Phys. Rev. A 24, 822–834 (1981).
[Crossref]

Chebotayev, V. P.

L. S. Vasilenko, V. P. Chebotayev, and A. V. Shishaev, “Line shape of two-photon absorption in a standing-wave field in a gas,” JETP Lett. 12, 113–116 (1970).

Grynberg, G.

F. Biraben, B. Cagnac, and G. Grynberg, “Experimental evidence of two-photon transitions without Doppler broadening,” Phys. Rev. Lett. 32, 643–645 (1974).
[Crossref]

Hänsch, T. W.

T. W. Hänsch, K. C. Harvey, G. Meisel, and A. L. Schawlow, “Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a c.w. dye laser,” Opt. Commun. 11, 50–53 (1974).
[Crossref]

Harvey, K. C.

T. W. Hänsch, K. C. Harvey, G. Meisel, and A. L. Schawlow, “Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a c.w. dye laser,” Opt. Commun. 11, 50–53 (1974).
[Crossref]

K. C. Harvey, “Doppler-free two-photon spectroscopy,” , (Stanford University, Stanford, Calif., 1975) (unpublished).

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 1 of Spectra of Diatomic Molecules (Van Nostrand, Princeton, N.J., 1950).

Hessel, M. M.

P. Kusch and M. M. Hessel, “An analysis of the B1Πu–X1∑g+ band system of Na2,” J. Chem. Phys. 68, 2591–2606 (1978).
[Crossref]

P. Kusch and M. M. Hessel, Department of Physics, University of Texas, Richardson, Texas 75080 (personal communication).

Hinsch, T. W.

H. R. Xia, S. V. Benson, and T. W. Hinsch, “A toy-train wavemeter,” Laser Focus 17(3), 54–58 (1981).

Jones, K. M.

N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2,” Phys. Rev. A 24, 822–834 (1981).
[Crossref]

A. J. Taylor, K. M. Jones, and A. L. Schawlow, “A study of the excited 1∑g+ states in Na2,” Opt. Commun. 39, 47–50 (1981).
[Crossref]

Kusch, P.

P. Kusch and M. M. Hessel, “An analysis of the B1Πu–X1∑g+ band system of Na2,” J. Chem. Phys. 68, 2591–2606 (1978).
[Crossref]

P. Kusch and M. M. Hessel, Department of Physics, University of Texas, Richardson, Texas 75080 (personal communication).

Levenson, M. D.

M. D. Levenson and N. Bloembergen, “Observation of two-photon absorption without Doppler broadening on the 3S–5S transition in sodium vapor,” Phys. Rev. Lett. 32, 645–648 (1974).
[Crossref]

N. Bloembergen and M. D. Levenson, “Doppler-free two-photon absorption spectroscopy,” in Topics in Applied Physics, High Resolution Laser Spectroscopy, K. Shimoda, ed. (Springer-Verlag, Berlin, 1976), Vol. 13.
[Crossref]

Meisel, G.

T. W. Hänsch, K. C. Harvey, G. Meisel, and A. L. Schawlow, “Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a c.w. dye laser,” Opt. Commun. 11, 50–53 (1974).
[Crossref]

Schawlow, A. L.

H.-R. Xia, G.-Y. Yan, and A. L. Schawlow, “Two photon line shapes with year-resonant enhancement,” Opt. Commun. 39, 153–158 (1981).
[Crossref]

A. J. Taylor, K. M. Jones, and A. L. Schawlow, “A study of the excited 1∑g+ states in Na2,” Opt. Commun. 39, 47–50 (1981).
[Crossref]

N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2,” Phys. Rev. A 24, 822–834 (1981).
[Crossref]

T. W. Hänsch, K. C. Harvey, G. Meisel, and A. L. Schawlow, “Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a c.w. dye laser,” Opt. Commun. 11, 50–53 (1974).
[Crossref]

Schuurmans, M. F. H.

J. P. Woerdman and M. F. H. Schuurmans, “Doppler-free three-photon cross-resonances in Na2vapor,” Opt. Commun. 21, 243–246 (1977).
[Crossref]

Shishaev, A. V.

L. S. Vasilenko, V. P. Chebotayev, and A. V. Shishaev, “Line shape of two-photon absorption in a standing-wave field in a gas,” JETP Lett. 12, 113–116 (1970).

Taylor, A. J.

N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2,” Phys. Rev. A 24, 822–834 (1981).
[Crossref]

A. J. Taylor, K. M. Jones, and A. L. Schawlow, “A study of the excited 1∑g+ states in Na2,” Opt. Commun. 39, 47–50 (1981).
[Crossref]

Vasilenko, L. S.

L. S. Vasilenko, V. P. Chebotayev, and A. V. Shishaev, “Line shape of two-photon absorption in a standing-wave field in a gas,” JETP Lett. 12, 113–116 (1970).

Woerdman, J. P.

J. P. Woerdman and M. F. H. Schuurmans, “Doppler-free three-photon cross-resonances in Na2vapor,” Opt. Commun. 21, 243–246 (1977).
[Crossref]

J. P. Woerdman, “Doppler-free two-photon transitions of the sodium molecule,” Chem. Phys. Lett. 43, 279–282 (1976).
[Crossref]

Xia, H. R.

H. R. Xia, S. V. Benson, and T. W. Hinsch, “A toy-train wavemeter,” Laser Focus 17(3), 54–58 (1981).

Xia, H.-R.

H.-R. Xia, G.-Y. Yan, and A. L. Schawlow, “Two photon line shapes with year-resonant enhancement,” Opt. Commun. 39, 153–158 (1981).
[Crossref]

Yan, G.-Y.

H.-R. Xia, G.-Y. Yan, and A. L. Schawlow, “Two photon line shapes with year-resonant enhancement,” Opt. Commun. 39, 153–158 (1981).
[Crossref]

Chem. Phys. Lett. (1)

J. P. Woerdman, “Doppler-free two-photon transitions of the sodium molecule,” Chem. Phys. Lett. 43, 279–282 (1976).
[Crossref]

J. Chem. Phys. (1)

P. Kusch and M. M. Hessel, “An analysis of the B1Πu–X1∑g+ band system of Na2,” J. Chem. Phys. 68, 2591–2606 (1978).
[Crossref]

JETP Lett. (1)

L. S. Vasilenko, V. P. Chebotayev, and A. V. Shishaev, “Line shape of two-photon absorption in a standing-wave field in a gas,” JETP Lett. 12, 113–116 (1970).

Laser Focus (1)

H. R. Xia, S. V. Benson, and T. W. Hinsch, “A toy-train wavemeter,” Laser Focus 17(3), 54–58 (1981).

Opt. Commun. (4)

J. P. Woerdman and M. F. H. Schuurmans, “Doppler-free three-photon cross-resonances in Na2vapor,” Opt. Commun. 21, 243–246 (1977).
[Crossref]

A. J. Taylor, K. M. Jones, and A. L. Schawlow, “A study of the excited 1∑g+ states in Na2,” Opt. Commun. 39, 47–50 (1981).
[Crossref]

H.-R. Xia, G.-Y. Yan, and A. L. Schawlow, “Two photon line shapes with year-resonant enhancement,” Opt. Commun. 39, 153–158 (1981).
[Crossref]

T. W. Hänsch, K. C. Harvey, G. Meisel, and A. L. Schawlow, “Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a c.w. dye laser,” Opt. Commun. 11, 50–53 (1974).
[Crossref]

Phys. Rev. A (1)

N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2,” Phys. Rev. A 24, 822–834 (1981).
[Crossref]

Phys. Rev. Lett. (2)

F. Biraben, B. Cagnac, and G. Grynberg, “Experimental evidence of two-photon transitions without Doppler broadening,” Phys. Rev. Lett. 32, 643–645 (1974).
[Crossref]

M. D. Levenson and N. Bloembergen, “Observation of two-photon absorption without Doppler broadening on the 3S–5S transition in sodium vapor,” Phys. Rev. Lett. 32, 645–648 (1974).
[Crossref]

Other (4)

K. C. Harvey, “Doppler-free two-photon spectroscopy,” , (Stanford University, Stanford, Calif., 1975) (unpublished).

P. Kusch and M. M. Hessel, Department of Physics, University of Texas, Richardson, Texas 75080 (personal communication).

N. Bloembergen and M. D. Levenson, “Doppler-free two-photon absorption spectroscopy,” in Topics in Applied Physics, High Resolution Laser Spectroscopy, K. Shimoda, ed. (Springer-Verlag, Berlin, 1976), Vol. 13.
[Crossref]

G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 1 of Spectra of Diatomic Molecules (Van Nostrand, Princeton, N.J., 1950).

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Figures (7)

Fig. 1
Fig. 1

Energy-level schemes for (a) a two-photon transition (Δ, enhancing level offset; δ, laser-frequency detuning) and (b) a two-step transition with the same three energy levels as in (a).

Fig. 2
Fig. 2

Rotational-term curves for a two-photon-transition band. The curves are represented approximately by lines with the equation T = T + ωe(v + 0.5) + BeJ(J + 1). A vibrational level v′ enhances (a) one and (b) two of the two-photon-absorption bands for a certain lower vibrational level v″.

Fig. 3
Fig. 3

An example of how to predict observable two-photon transitions from X 1g+(v″ = 2) to 1g+(3s–5s) (v = 19) rotational–vibrational levels enhanced by A 1g+(v′ = 22). Only the individual frequencies with even J are plotted. The insert shows the relative rotational quantum numbers. On the left is shown the resulting spectrum; a dashed line represents the center frequency of each band.

Fig. 4
Fig. 4

The experimental setup.

Fig. 5
Fig. 5

Experimental traces of (a) the Doppler-free two-photon line at 17006.2945 cm−1 and (b) the I2 excitation spectrum in this region.

Fig. 6
Fig. 6

Graphical representations of (a) part of a two-photon fluorescence spectrogram with the laser frequency at 16704.169 cm−1 and (b) that which we would expect to see for a Q2-branch transition.

Fig. 7
Fig. 7

The vibrational structure of two-photon electronic transitions. Horizontal lines represent the v′ progressions of bands. The individual sequences of bands are indicated by brackets.

Tables (4)

Tables Icon

Table 1 Dunham Constants for 1g+ (3s + 5s) State

Tables Icon

Table 2 Assigned Two-Photon Transitions from X 1g+(3s + 5s) State

Tables Icon

Table 3 Assigned Two-Photon Transitions from X 1g+ to 1g+(3s + 4d) State

Tables Icon

Table 4 Assigned Two-Photon Transition from X 1g+ to 1Πg(3s+ 4d) State

Equations (2)

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Γ c a | b a r b b r c Δ b | 2 γ c 4 δ 2 + γ c 2 / 4 .
I N × 1 Δ 2 .