Abstract

Laser frequencies were stabilized to the linear and saturated absorption spectral lines(LAS, SAS) in 87Rb vapors which were filled into two kinds of glass cell: cell A (87Rb vapor only) and cell B (87Rb vapor and buffer gases). The frequency shifts induced by the change of laser power density were −5 MHz/(mW/cm2) and −10 MHz/(mW/cm2) for cells A and B, respectively, when LAS was used. A frequency shift of −0.8 MHz/K was observed for cell B, which underwent a temperature change. However, such a temperature-induced shift was not observed for cell A. The highest frequency stability was 7.7 × 10−11 at a 70-s integration time.

© 1989 Optical Society of America

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References

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  1. J. L. Picque, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett., 27, 340–342 (1975).
    [CrossRef]
  2. H. Tsuchida, S. Sanpei, M. Ohtsu, T. Tako, “Frequency Stability Measurement of Feedback Stabilized AlGaAs DH Laser,” Jpn. J. Appl. Phys., 19, L721–L724 (1980).
    [CrossRef]
  3. T. Okoshi, K. Kikuchi, “Frequency Stabilization of Semiconductor Lasers for Heterodyne-Type Optical Communication Systems,” Electron. Lett., 16, 179–181 (1980).
    [CrossRef]
  4. T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
    [CrossRef]
  5. H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
    [CrossRef]
  6. C. J. Nielsen, G. Jacobsen, “Frequency Stabilization of Singlemode Semiconductor Lasers at 830 nm and 1.3 μm,” J. Opt. Commun., 4, 122–125 (1983).
  7. M. Ohtsu, T. Tako, “Coherence in Semiconductor Lasers,” in Progress in Optics XXV, E. Wolf, Ed. (Elsevier Science, Amsterdam, 1988) pp. 191–278.
    [CrossRef]
  8. T. Shiomi, “Highly Precise Positioning System Using GPS,” (in Japanese) J”. IEICE Jpn., 70, 521–523 (1987).
  9. L. L. Lewis, M. Feldman, “Optical Pumping by Lasers in Atomic Frequency Standards,” in Proceedings, Thirty-Fifth Annual Symposium on Frequency Control, Fort Monmouth, NJ (1981) pp. 612–624.
    [CrossRef]
  10. M. Hashimoto, M. Ohtsu, “Experiments on a Semiconductor Laser Pumped Rubidium Atomic Clock,” IEEE J. Quantum Electron., QE-23, 446–451 (1987).
    [CrossRef]
  11. M. Hashimoto, M. Ohtsu, H. Furuta, “Ultra-Sensitive Frequency Discrimination in a Diode Laser Pumped 87Rb Atomic Clock,” in Proceedings, Forty-First Annual Symposium on Frequency Control, Philadelphia, PA (1987), pp. 25–35.
  12. V. Pevtschin, S. Ezekiel, “Investigation of Absolute Stability of Water-Vapor-Stabilized Semiconductor Laser,” Opt. Lett., 12, 172–174 (1987).
    [CrossRef] [PubMed]
  13. D. W. Allan, “Statistics of Atomic Frequency Standards,” Proc. IEEE, 54, 221–230 (1966).
    [CrossRef]
  14. I. Siio, M. Ohtsu, T. Tako, “Development of the Allan Variance Real-Time Processor,” (in Japanese) Trans. IECE Jpn., J64-C, 204–208 (1981).
  15. M. Ohtsu, M. Hashimoto, H. Ozawa, “A Highly Stabilized Semiconductor Laser and Its Application to Optically Pumped Rb Atomic Clock,” in Proceedings, Thirty-Ninth Annual Symposium on Frequency Control, Philadelphia, PA (1985), pp. 43–53.
  16. G. P. Barwood, P. Gill, W. R. C. Rowley, “Laser Diode Frequency Stabilization to Doppler-Free Rubidium Spectra,” Electron. Lett. 24, 769–770 (1988).
    [CrossRef]
  17. R. E. Beehler, R. C. Mockler, J. M. Richardson, “Cesium Beam Atomic Time and Frequency Standards,” Metrologia, 1, 114–131 (1965).
    [CrossRef]
  18. R. E. Beehler, D. J. Glaze, “The Performance and Capability of Cesium Beam Standards at the National Bureau of Standards,” IEEE Trans. Instrum. Meas., IM-15, 48–55 (1966).
    [CrossRef]
  19. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, 1968).
  20. E. Arimondo, M. Inguscio, P. Violino, “Experimental Determinations of the Hyperfine Structure in the Alkali Atoms,” Rev. Mod. Phys., 49, 31–75 (1977).
    [CrossRef]

1988 (1)

G. P. Barwood, P. Gill, W. R. C. Rowley, “Laser Diode Frequency Stabilization to Doppler-Free Rubidium Spectra,” Electron. Lett. 24, 769–770 (1988).
[CrossRef]

1987 (3)

V. Pevtschin, S. Ezekiel, “Investigation of Absolute Stability of Water-Vapor-Stabilized Semiconductor Laser,” Opt. Lett., 12, 172–174 (1987).
[CrossRef] [PubMed]

T. Shiomi, “Highly Precise Positioning System Using GPS,” (in Japanese) J”. IEICE Jpn., 70, 521–523 (1987).

M. Hashimoto, M. Ohtsu, “Experiments on a Semiconductor Laser Pumped Rubidium Atomic Clock,” IEEE J. Quantum Electron., QE-23, 446–451 (1987).
[CrossRef]

1983 (1)

C. J. Nielsen, G. Jacobsen, “Frequency Stabilization of Singlemode Semiconductor Lasers at 830 nm and 1.3 μm,” J. Opt. Commun., 4, 122–125 (1983).

1982 (1)

H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
[CrossRef]

1981 (2)

T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
[CrossRef]

I. Siio, M. Ohtsu, T. Tako, “Development of the Allan Variance Real-Time Processor,” (in Japanese) Trans. IECE Jpn., J64-C, 204–208 (1981).

1980 (2)

H. Tsuchida, S. Sanpei, M. Ohtsu, T. Tako, “Frequency Stability Measurement of Feedback Stabilized AlGaAs DH Laser,” Jpn. J. Appl. Phys., 19, L721–L724 (1980).
[CrossRef]

T. Okoshi, K. Kikuchi, “Frequency Stabilization of Semiconductor Lasers for Heterodyne-Type Optical Communication Systems,” Electron. Lett., 16, 179–181 (1980).
[CrossRef]

1977 (1)

E. Arimondo, M. Inguscio, P. Violino, “Experimental Determinations of the Hyperfine Structure in the Alkali Atoms,” Rev. Mod. Phys., 49, 31–75 (1977).
[CrossRef]

1975 (1)

J. L. Picque, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett., 27, 340–342 (1975).
[CrossRef]

1966 (2)

D. W. Allan, “Statistics of Atomic Frequency Standards,” Proc. IEEE, 54, 221–230 (1966).
[CrossRef]

R. E. Beehler, D. J. Glaze, “The Performance and Capability of Cesium Beam Standards at the National Bureau of Standards,” IEEE Trans. Instrum. Meas., IM-15, 48–55 (1966).
[CrossRef]

1965 (1)

R. E. Beehler, R. C. Mockler, J. M. Richardson, “Cesium Beam Atomic Time and Frequency Standards,” Metrologia, 1, 114–131 (1965).
[CrossRef]

Allan, D. W.

D. W. Allan, “Statistics of Atomic Frequency Standards,” Proc. IEEE, 54, 221–230 (1966).
[CrossRef]

Arimondo, E.

E. Arimondo, M. Inguscio, P. Violino, “Experimental Determinations of the Hyperfine Structure in the Alkali Atoms,” Rev. Mod. Phys., 49, 31–75 (1977).
[CrossRef]

Barwood, G. P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “Laser Diode Frequency Stabilization to Doppler-Free Rubidium Spectra,” Electron. Lett. 24, 769–770 (1988).
[CrossRef]

Beehler, R. E.

R. E. Beehler, D. J. Glaze, “The Performance and Capability of Cesium Beam Standards at the National Bureau of Standards,” IEEE Trans. Instrum. Meas., IM-15, 48–55 (1966).
[CrossRef]

R. E. Beehler, R. C. Mockler, J. M. Richardson, “Cesium Beam Atomic Time and Frequency Standards,” Metrologia, 1, 114–131 (1965).
[CrossRef]

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, 1968).

Ezekiel, S.

Feldman, M.

L. L. Lewis, M. Feldman, “Optical Pumping by Lasers in Atomic Frequency Standards,” in Proceedings, Thirty-Fifth Annual Symposium on Frequency Control, Fort Monmouth, NJ (1981) pp. 612–624.
[CrossRef]

Furuta, H.

M. Hashimoto, M. Ohtsu, H. Furuta, “Ultra-Sensitive Frequency Discrimination in a Diode Laser Pumped 87Rb Atomic Clock,” in Proceedings, Forty-First Annual Symposium on Frequency Control, Philadelphia, PA (1987), pp. 25–35.

Gill, P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “Laser Diode Frequency Stabilization to Doppler-Free Rubidium Spectra,” Electron. Lett. 24, 769–770 (1988).
[CrossRef]

Glaze, D. J.

R. E. Beehler, D. J. Glaze, “The Performance and Capability of Cesium Beam Standards at the National Bureau of Standards,” IEEE Trans. Instrum. Meas., IM-15, 48–55 (1966).
[CrossRef]

Hashimoto, M.

M. Hashimoto, M. Ohtsu, “Experiments on a Semiconductor Laser Pumped Rubidium Atomic Clock,” IEEE J. Quantum Electron., QE-23, 446–451 (1987).
[CrossRef]

M. Hashimoto, M. Ohtsu, H. Furuta, “Ultra-Sensitive Frequency Discrimination in a Diode Laser Pumped 87Rb Atomic Clock,” in Proceedings, Forty-First Annual Symposium on Frequency Control, Philadelphia, PA (1987), pp. 25–35.

M. Ohtsu, M. Hashimoto, H. Ozawa, “A Highly Stabilized Semiconductor Laser and Its Application to Optically Pumped Rb Atomic Clock,” in Proceedings, Thirty-Ninth Annual Symposium on Frequency Control, Philadelphia, PA (1985), pp. 43–53.

Hori, H.

T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
[CrossRef]

Ibaragi, A.

T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
[CrossRef]

Inguscio, M.

E. Arimondo, M. Inguscio, P. Violino, “Experimental Determinations of the Hyperfine Structure in the Alkali Atoms,” Rev. Mod. Phys., 49, 31–75 (1977).
[CrossRef]

Jacobsen, G.

C. J. Nielsen, G. Jacobsen, “Frequency Stabilization of Singlemode Semiconductor Lasers at 830 nm and 1.3 μm,” J. Opt. Commun., 4, 122–125 (1983).

Kikuchi, K.

T. Okoshi, K. Kikuchi, “Frequency Stabilization of Semiconductor Lasers for Heterodyne-Type Optical Communication Systems,” Electron. Lett., 16, 179–181 (1980).
[CrossRef]

Kitano, M.

T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
[CrossRef]

Kuramochi, N.

H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
[CrossRef]

Lewis, L. L.

L. L. Lewis, M. Feldman, “Optical Pumping by Lasers in Atomic Frequency Standards,” in Proceedings, Thirty-Fifth Annual Symposium on Frequency Control, Fort Monmouth, NJ (1981) pp. 612–624.
[CrossRef]

Mockler, R. C.

R. E. Beehler, R. C. Mockler, J. M. Richardson, “Cesium Beam Atomic Time and Frequency Standards,” Metrologia, 1, 114–131 (1965).
[CrossRef]

Nielsen, C. J.

C. J. Nielsen, G. Jacobsen, “Frequency Stabilization of Singlemode Semiconductor Lasers at 830 nm and 1.3 μm,” J. Opt. Commun., 4, 122–125 (1983).

Ogawa, T.

T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
[CrossRef]

Ohtsu, M.

M. Hashimoto, M. Ohtsu, “Experiments on a Semiconductor Laser Pumped Rubidium Atomic Clock,” IEEE J. Quantum Electron., QE-23, 446–451 (1987).
[CrossRef]

H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
[CrossRef]

I. Siio, M. Ohtsu, T. Tako, “Development of the Allan Variance Real-Time Processor,” (in Japanese) Trans. IECE Jpn., J64-C, 204–208 (1981).

H. Tsuchida, S. Sanpei, M. Ohtsu, T. Tako, “Frequency Stability Measurement of Feedback Stabilized AlGaAs DH Laser,” Jpn. J. Appl. Phys., 19, L721–L724 (1980).
[CrossRef]

M. Ohtsu, T. Tako, “Coherence in Semiconductor Lasers,” in Progress in Optics XXV, E. Wolf, Ed. (Elsevier Science, Amsterdam, 1988) pp. 191–278.
[CrossRef]

M. Ohtsu, M. Hashimoto, H. Ozawa, “A Highly Stabilized Semiconductor Laser and Its Application to Optically Pumped Rb Atomic Clock,” in Proceedings, Thirty-Ninth Annual Symposium on Frequency Control, Philadelphia, PA (1985), pp. 43–53.

M. Hashimoto, M. Ohtsu, H. Furuta, “Ultra-Sensitive Frequency Discrimination in a Diode Laser Pumped 87Rb Atomic Clock,” in Proceedings, Forty-First Annual Symposium on Frequency Control, Philadelphia, PA (1987), pp. 25–35.

Okoshi, T.

T. Okoshi, K. Kikuchi, “Frequency Stabilization of Semiconductor Lasers for Heterodyne-Type Optical Communication Systems,” Electron. Lett., 16, 179–181 (1980).
[CrossRef]

Oura, N.

H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
[CrossRef]

Ozawa, H.

M. Ohtsu, M. Hashimoto, H. Ozawa, “A Highly Stabilized Semiconductor Laser and Its Application to Optically Pumped Rb Atomic Clock,” in Proceedings, Thirty-Ninth Annual Symposium on Frequency Control, Philadelphia, PA (1985), pp. 43–53.

Pevtschin, V.

Picque, J. L.

J. L. Picque, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett., 27, 340–342 (1975).
[CrossRef]

Richardson, J. M.

R. E. Beehler, R. C. Mockler, J. M. Richardson, “Cesium Beam Atomic Time and Frequency Standards,” Metrologia, 1, 114–131 (1965).
[CrossRef]

Roizen, S.

J. L. Picque, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett., 27, 340–342 (1975).
[CrossRef]

Rowley, W. R. C.

G. P. Barwood, P. Gill, W. R. C. Rowley, “Laser Diode Frequency Stabilization to Doppler-Free Rubidium Spectra,” Electron. Lett. 24, 769–770 (1988).
[CrossRef]

Sanpei, S.

H. Tsuchida, S. Sanpei, M. Ohtsu, T. Tako, “Frequency Stability Measurement of Feedback Stabilized AlGaAs DH Laser,” Jpn. J. Appl. Phys., 19, L721–L724 (1980).
[CrossRef]

Shiomi, T.

T. Shiomi, “Highly Precise Positioning System Using GPS,” (in Japanese) J”. IEICE Jpn., 70, 521–523 (1987).

Siio, I.

I. Siio, M. Ohtsu, T. Tako, “Development of the Allan Variance Real-Time Processor,” (in Japanese) Trans. IECE Jpn., J64-C, 204–208 (1981).

Tako, T.

H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
[CrossRef]

I. Siio, M. Ohtsu, T. Tako, “Development of the Allan Variance Real-Time Processor,” (in Japanese) Trans. IECE Jpn., J64-C, 204–208 (1981).

H. Tsuchida, S. Sanpei, M. Ohtsu, T. Tako, “Frequency Stability Measurement of Feedback Stabilized AlGaAs DH Laser,” Jpn. J. Appl. Phys., 19, L721–L724 (1980).
[CrossRef]

M. Ohtsu, T. Tako, “Coherence in Semiconductor Lasers,” in Progress in Optics XXV, E. Wolf, Ed. (Elsevier Science, Amsterdam, 1988) pp. 191–278.
[CrossRef]

Tsuchida, H.

H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
[CrossRef]

H. Tsuchida, S. Sanpei, M. Ohtsu, T. Tako, “Frequency Stability Measurement of Feedback Stabilized AlGaAs DH Laser,” Jpn. J. Appl. Phys., 19, L721–L724 (1980).
[CrossRef]

Violino, P.

E. Arimondo, M. Inguscio, P. Violino, “Experimental Determinations of the Hyperfine Structure in the Alkali Atoms,” Rev. Mod. Phys., 49, 31–75 (1977).
[CrossRef]

Yabuzaki, T.

T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
[CrossRef]

(in Japanese) Trans. IECE Jpn. (1)

I. Siio, M. Ohtsu, T. Tako, “Development of the Allan Variance Real-Time Processor,” (in Japanese) Trans. IECE Jpn., J64-C, 204–208 (1981).

Appl. Phys. Lett. (1)

J. L. Picque, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett., 27, 340–342 (1975).
[CrossRef]

Electron. Lett. (2)

T. Okoshi, K. Kikuchi, “Frequency Stabilization of Semiconductor Lasers for Heterodyne-Type Optical Communication Systems,” Electron. Lett., 16, 179–181 (1980).
[CrossRef]

G. P. Barwood, P. Gill, W. R. C. Rowley, “Laser Diode Frequency Stabilization to Doppler-Free Rubidium Spectra,” Electron. Lett. 24, 769–770 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Hashimoto, M. Ohtsu, “Experiments on a Semiconductor Laser Pumped Rubidium Atomic Clock,” IEEE J. Quantum Electron., QE-23, 446–451 (1987).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

R. E. Beehler, D. J. Glaze, “The Performance and Capability of Cesium Beam Standards at the National Bureau of Standards,” IEEE Trans. Instrum. Meas., IM-15, 48–55 (1966).
[CrossRef]

IEICE Jpn. (1)

T. Shiomi, “Highly Precise Positioning System Using GPS,” (in Japanese) J”. IEICE Jpn., 70, 521–523 (1987).

J. Opt. Commun. (1)

C. J. Nielsen, G. Jacobsen, “Frequency Stabilization of Singlemode Semiconductor Lasers at 830 nm and 1.3 μm,” J. Opt. Commun., 4, 122–125 (1983).

Jpn. J. Appl. Phys. (3)

T. Yabuzaki, A. Ibaragi, H. Hori, M. Kitano, T. Ogawa, “Frequency-Locking of a GaAlAs Laser to a Doppler-Free Spectrum of Cs-D2 Line,” Jpn. J. Appl. Phys., 20, L451–L454 (1981).
[CrossRef]

H. Tsuchida, M. Ohtsu, T. Tako, N. Kuramochi, N. Oura, “Frequency Stabilization of AlGaAs Semiconductor Laser Based on the 85Rb-D2 Line,” Jpn. J. Appl. Phys., 21, L561–L563 (1982).
[CrossRef]

H. Tsuchida, S. Sanpei, M. Ohtsu, T. Tako, “Frequency Stability Measurement of Feedback Stabilized AlGaAs DH Laser,” Jpn. J. Appl. Phys., 19, L721–L724 (1980).
[CrossRef]

Metrologia (1)

R. E. Beehler, R. C. Mockler, J. M. Richardson, “Cesium Beam Atomic Time and Frequency Standards,” Metrologia, 1, 114–131 (1965).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

D. W. Allan, “Statistics of Atomic Frequency Standards,” Proc. IEEE, 54, 221–230 (1966).
[CrossRef]

Rev. Mod. Phys. (1)

E. Arimondo, M. Inguscio, P. Violino, “Experimental Determinations of the Hyperfine Structure in the Alkali Atoms,” Rev. Mod. Phys., 49, 31–75 (1977).
[CrossRef]

Other (5)

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, 1968).

M. Hashimoto, M. Ohtsu, H. Furuta, “Ultra-Sensitive Frequency Discrimination in a Diode Laser Pumped 87Rb Atomic Clock,” in Proceedings, Forty-First Annual Symposium on Frequency Control, Philadelphia, PA (1987), pp. 25–35.

M. Ohtsu, M. Hashimoto, H. Ozawa, “A Highly Stabilized Semiconductor Laser and Its Application to Optically Pumped Rb Atomic Clock,” in Proceedings, Thirty-Ninth Annual Symposium on Frequency Control, Philadelphia, PA (1985), pp. 43–53.

M. Ohtsu, T. Tako, “Coherence in Semiconductor Lasers,” in Progress in Optics XXV, E. Wolf, Ed. (Elsevier Science, Amsterdam, 1988) pp. 191–278.
[CrossRef]

L. L. Lewis, M. Feldman, “Optical Pumping by Lasers in Atomic Frequency Standards,” in Proceedings, Thirty-Fifth Annual Symposium on Frequency Control, Fort Monmouth, NJ (1981) pp. 612–624.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup for the frequency stabilization of a semiconductor laser. To obtain the frequency disciminator, the injection current was modulated at the modulation frequency fm = 2kHz, and a lock-in amplifier was used to obtain the first derivative of the spectral lineshape in 87Rb vapor. (a) Setup for linear absorption spectroscopy. (b) Setup for saturated absorption spectroscopy.

Fig. 2
Fig. 2

Energy levels of the 87Rb atom. The quantum numbers F and F′ represent the total angular momenta for the hyperfine levels in the ground state 5S1/2 and in the excited state 5P3/2, respectively. In this paper, the transitions from the hyperfine level of F = 2 in 5S1/2 to the levels of F′ = 1, 2, and 3 in 5P3/2 are referred to o, p, and q, and those from the level of F = 1 in 5S1/2 to the levels of F′ = 0, 1, and 2 in 5P3/2 to r, s, and t, respectively.

Fig. 3
Fig. 3

First derivative of the linear absorption spectral line (LAS) obtained by sweeping the injection current of the laser: (a) gas cell A; (b) gas cell B. The injection current was modulated at a frequency of fm = 2 kHz with the amplitude of im = 50 μApp. (c) The first derivative of the saturated absorption spectral line (SAS) obtained for gas cell A: at a frequency of fm = 2 kHz and im = 10 μApp. The spectral profiles #1 and #2 in these figures correspond to the transitions from the level of F = 1(r, s, and t in Fig. 2) and F = 2(o, p, and q in Fig. 2), respectively. The symbols st, rt, and rs represent the crossover resonances between a hyperfine level(F = 1) in 5S1/2 and two hyperfine levels in 5P3/2.

Fig. 4
Fig. 4

Experimental setup for the measurements of frequency shift and stability. Here, ARPS represents the Allan variance realtime processing system14.

Fig. 5
Fig. 5

Frequency shift Δf of a semiconductor laser when the laser was locked to the LAS line center (F = 1) of gas cell A: (a) as a function of PL at TRb = 303 K; (b) as a function of TRb at PL = 1.6 mW/cm2. The reference (Δf = 0) was the beat frequency at TRb = 303 K and PL = 1.6 mW/cm2. Here ○, Δ, and × represent the results for the modulation amplitude im = 10, 20 and 50 μApp, respectively.

Fig. 6
Fig. 6

Frequency shift Δf of a semiconductor laser when the laser was locked to the LAS line center (F = 1) of gas cell B: (a) as a function of PL at TRb = 333 K; (b) as a function of TRb at PL = 1.6 mW/cm2. The reference (Δf = 0) was the beat frequency at TRb = 333 K and PL = 1.6 mW/cm2. Here Δ and × represent the results for the modulation amplitude im = 20 and 50 μApp, respectively.

Fig. 7
Fig. 7

(a) Values of I1, I2, γ1, and γ2 used for the least-square-fitting, given as a function of TRb of gas cell B at PL = 1.6 mW/cm2. In this figure, I1 and I2 were normalized to the values at TRb = 333 K. The values of I1 and I2 at TRb = 333 K were expressed as I10 and I20, respectively. The measured value of I20/I10 was 2.15. Open(○, ⋄) and solid(•, ♦) correspond to the spectral profiles #1 and #2 in Fig. 3(b), respectively. (b) Estimated results of frequency shift Δf as a function of TRb, using the values of (a) and Eqs. (1)(3). The reference (Δf = 0) was the estimated frequency at TRb = 333 K.

Fig. 8
Fig. 8

Frequency shift Δf of a semiconductor laser when the laser was locked to the SAS line centers [F = 1: t, rt, st, s, and rs in Fig. 3(c)] of gas cell A: (a) as a function of PL at TRb = 303 K; (b) as a function of TRb at PL = 2.6 mW/cm2. The reference (Δf = 0) was the beat frequency when the frequency of the test laser was locked to the component s when TRb = 303 K and PL = 2.6 mW/cm2. Solid(•, ♦, ▲, ■, ▼) and open(○, ⋄, Δ, □, ∇) represent the results for the modulation amplitude im = 10 and 20 μApp, respectively.

Fig. 9
Fig. 9

Square root of the Allan variance σ2(τ) for the residual beat frequency fluctuations of semiconductor lasers. The value of σ2(τ) was normalized to the optical frequency of a laser. A: Result of the free running lasers. B: Result of frequency stabilization by using the first derivative of the LAS of gas cell A. C: Result of frequency stabilization by using the first derivative LAS of gas cell B. D: Result of frequency stabilization by using the first derivative of SAS of gas cell A.

Equations (6)

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I ( ν ) = I 1 ( ν ) + I 2 ( ν ) ,
I 1 ( ν ) = I 1 i = 1 3 p i γ 1 2 ( ν ν i ) 2 + γ 1 2 ,
I 2 ( ν ) = I 2 i = 4 6 p i γ 2 2 ( ν ν i ) 2 + γ 2 2 .
7 . 7 × 10 11 ( at τ = 70 s ) ; LAS , gas cell A 1 . 5 × 10 10 ( at τ = 30 s ) ; SAS , gas cell A 3 . 0 × 10 10 ( at τ = 10 s ) ; LAS , gas cell B .
p 1 = 1 / 36 ( component r ) , p 2 = 5 / 72 ( component s ) , p 3 = 5 / 72 ( component t ) , p 4 = 1 / 120 ( component o ) , p 5 = 3 / 72 ( component p ) , p 6 = 7 / 60 ( component q ) .
ν 1 = ν 2 72 MHz , ν 3 = ν 2 + 157 MHz , ν 4 = ν 2 6834 MHz , ν 5 = ν 2 6677 MHz , ν 6 = ν 2 6410 MHz ,

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