Abstract

The main task of this paper is to identify a number of physical problems that must be successfully addressed to achieve stabilized laser linewidths well below 1 Hz. After presentation of the basic stability characteristics of available laser sources, we show that if any of these lasers were optimally locked to a high-finesse Fabry–Perot cavity it would be theoretically possible to obtain a laser linewidth in the millihertz domain. Problems of optical feedback, modulation waveform errors, mechanical support and isolation of the reference cavity, thermal stabilization of the environment, etc. are considered, and interim solutions are discussed. Experimentally, locking accuracy to successive cavity orders of <2 × 10−5 linewidths (±1.5 Hz) was achieved; mirror birefringence pulled the lock point approximately 10-fold more. Relative phase coherence between two independent lasers locked onto adjacent cavity orders was preserved for 8 sec, corresponding to a linewidth of each optical source of ∼50 mHz.

© 1988 Optical Society of America

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References

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  1. J. E. Faller, P. L. Bender, J. L. Hall, D. Hils, and M. A. Vincent, in Kilometric Optical Arrays in Space (European Space Agency, Paris, 1985), p. 157.
  2. The content of this paragraph is developed in detail by J. L. Hall, in Quantum Optics IV, J. D. Harvey and D. F. Walls, eds. (Springer-Verlag, Heidelberg, 1986), p. 273.
    [Crossref]
  3. T. Baer, F. V. Kowalski, and J. L. Hall, Appl. Opt. 19, 3173 (1980).
    [Crossref] [PubMed]
  4. J. L. Hall, L.-S. Ma, and G. Kramer, IEEE J. Quantum Electron. QE-23, 427 (1987).
    [Crossref]
  5. B. Welleghausen, IEEE J. Quantum Electron. QE-15, 1108 (1979).
    [Crossref]
  6. A. Brillet, J. Dallarosa, J. L. Hall, and R. Drullinger, J. Opt. Soc. Am. 68, 635 (1978).
  7. L. Hollberg and J. L. Hall, in Lasers’ 80 (Society for Optical and Quantum Electronics, McLean, Va., 1980).
  8. K. J. Seimsen, E. Williams, and J. Reid, Opt. Lett. 24, 879 (1987).
    [Crossref]
  9. B. Zhou, T. J. Kane, G. J. Dixon, and R. L. Byer, Opt. Lett. 10, 62 (1985).
    [Crossref] [PubMed]
  10. A. Szabo, National Research Council, Ottawa ONK1A 0R8, Ontario, Canada (personal communication).
  11. K.-C. Peng, Ling-An Wu, and H. J. Kimble, Appl. Opt. 24, 938 (1985);T. L. Boyd and H. J. Kimble, J. Opt. Soc. Am. A 3(13), P120 (1986).
    [Crossref] [PubMed]
  12. Some additional discussion of these points may be found in J. Helmcke, S. A. Lee, and J. L. Hall, Appl. Opt. 21, 1686 (1982).
    [Crossref] [PubMed]
  13. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
    [Crossref]
  14. Some additional data on optical phase-locking experiments can be found in Ref. 4 and in J. L. Hall, in Proceedings of the Beijing/Shanghai International Conference on Lasers (Wiley, New York, 1983), p. 15.
  15. Somewhat promising experiments were carried out in 1985 by Yiqui Wang in his laboratory (Peking University, Beijing, China).
  16. B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876 (1987).
    [Crossref] [PubMed]
  17. T. W. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
    [Crossref]
  18. R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
    [Crossref] [PubMed]
  19. D. K. Owens and R. Weiss, Rev. Sci. Instrum. 45, 1060 (1974).
    [Crossref]
  20. D. S. Elliott, R. Roy, and S. J. Smith, Phys. Rev. A 26, 12 (1982).
    [Crossref]
  21. J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
    [Crossref]
  22. D. Hils and J. L. Hall, “Response of a Fabry–Perot cavity to frequency-modulated light,” Rev. Sci. Instrum. 58, 1406 (1987).(Unfortunately, in the printed version, pp. 1408 and 1409 are reversed.)
    [Crossref]
  23. F. Walls and H. Hellwig, National Bureau of Standards, Boulder, Colorado 80303 (personal communication).
  24. F. W. Walls, in IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-34, 592 (1986).
  25. A powerful technique to sense and control the laser beam to cavity mode match has been introduced;see D. Z. Anderson, Appl. Opt. 23, 2944 (1984).
    [Crossref]
  26. N. M. Sampas and D. Z. Anderson, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 308, paper FA5.
  27. J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
    [Crossref]
  28. N. C. Wong and J. L. Hall, J. Opt. Soc. Am. B 2, 1527 (1985).
    [Crossref]
  29. D. Z. Anderson, Department of Physics, University of Colorado, Campus Box 390, Boulder, Colorado 80309 (personal communication).
  30. R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
    [Crossref]
  31. We are using CW Radiation’s Model LT1R.
  32. Schott Glass Technologies, Inc., Duryea, Penn.
  33. D. Hils, J. E. Faller, and J. L. Hall, Rev. Sci. Instrum. 57, 2532 (1986).
    [Crossref]
  34. D. Hils and J. L. Hall, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1987), p. 102.
  35. R. G. DeVoe, C. Fabre, K. Jungmann, K. L. Foster, and R. G. Brewster, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 80.
  36. D. Hils and J. L. Hall, “A new laser-based Kennedy-Thorndike experiment,” submitted to Phys. Rev. Lett.

1987 (4)

K. J. Seimsen, E. Williams, and J. Reid, Opt. Lett. 24, 879 (1987).
[Crossref]

J. L. Hall, L.-S. Ma, and G. Kramer, IEEE J. Quantum Electron. QE-23, 427 (1987).
[Crossref]

B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876 (1987).
[Crossref] [PubMed]

D. Hils and J. L. Hall, “Response of a Fabry–Perot cavity to frequency-modulated light,” Rev. Sci. Instrum. 58, 1406 (1987).(Unfortunately, in the printed version, pp. 1408 and 1409 are reversed.)
[Crossref]

1986 (2)

F. W. Walls, in IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-34, 592 (1986).

D. Hils, J. E. Faller, and J. L. Hall, Rev. Sci. Instrum. 57, 2532 (1986).
[Crossref]

1985 (3)

1984 (3)

A powerful technique to sense and control the laser beam to cavity mode match has been introduced;see D. Z. Anderson, Appl. Opt. 23, 2944 (1984).
[Crossref]

R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[Crossref]

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

1982 (2)

1981 (1)

J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
[Crossref]

1980 (2)

1979 (1)

B. Welleghausen, IEEE J. Quantum Electron. QE-15, 1108 (1979).
[Crossref]

1978 (1)

A. Brillet, J. Dallarosa, J. L. Hall, and R. Drullinger, J. Opt. Soc. Am. 68, 635 (1978).

1974 (1)

D. K. Owens and R. Weiss, Rev. Sci. Instrum. 45, 1060 (1974).
[Crossref]

1946 (1)

R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
[Crossref] [PubMed]

Anderson, D. Z.

A powerful technique to sense and control the laser beam to cavity mode match has been introduced;see D. Z. Anderson, Appl. Opt. 23, 2944 (1984).
[Crossref]

N. M. Sampas and D. Z. Anderson, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 308, paper FA5.

D. Z. Anderson, Department of Physics, University of Colorado, Campus Box 390, Boulder, Colorado 80309 (personal communication).

Baer, T.

J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
[Crossref]

T. Baer, F. V. Kowalski, and J. L. Hall, Appl. Opt. 19, 3173 (1980).
[Crossref] [PubMed]

Bender, P. L.

J. E. Faller, P. L. Bender, J. L. Hall, D. Hils, and M. A. Vincent, in Kilometric Optical Arrays in Space (European Space Agency, Paris, 1985), p. 157.

Brewer, R. G.

R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[Crossref]

Brewster, R. G.

R. G. DeVoe, C. Fabre, K. Jungmann, K. L. Foster, and R. G. Brewster, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 80.

Brillet, A.

A. Brillet, J. Dallarosa, J. L. Hall, and R. Drullinger, J. Opt. Soc. Am. 68, 635 (1978).

Byer, R. L.

Couillaud, B.

T. W. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
[Crossref]

Dahmani, B.

Dallarosa, J.

A. Brillet, J. Dallarosa, J. L. Hall, and R. Drullinger, J. Opt. Soc. Am. 68, 635 (1978).

DeVoe, R. G.

R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[Crossref]

R. G. DeVoe, C. Fabre, K. Jungmann, K. L. Foster, and R. G. Brewster, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 80.

Dixon, G. J.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

Drullinger, R.

B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876 (1987).
[Crossref] [PubMed]

A. Brillet, J. Dallarosa, J. L. Hall, and R. Drullinger, J. Opt. Soc. Am. 68, 635 (1978).

Elliott, D. S.

D. S. Elliott, R. Roy, and S. J. Smith, Phys. Rev. A 26, 12 (1982).
[Crossref]

Fabre, C.

R. G. DeVoe, C. Fabre, K. Jungmann, K. L. Foster, and R. G. Brewster, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 80.

Faller, J. E.

D. Hils, J. E. Faller, and J. L. Hall, Rev. Sci. Instrum. 57, 2532 (1986).
[Crossref]

J. E. Faller, P. L. Bender, J. L. Hall, D. Hils, and M. A. Vincent, in Kilometric Optical Arrays in Space (European Space Agency, Paris, 1985), p. 157.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

Foster, K. L.

R. G. DeVoe, C. Fabre, K. Jungmann, K. L. Foster, and R. G. Brewster, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 80.

Hall, J. L.

J. L. Hall, L.-S. Ma, and G. Kramer, IEEE J. Quantum Electron. QE-23, 427 (1987).
[Crossref]

D. Hils and J. L. Hall, “Response of a Fabry–Perot cavity to frequency-modulated light,” Rev. Sci. Instrum. 58, 1406 (1987).(Unfortunately, in the printed version, pp. 1408 and 1409 are reversed.)
[Crossref]

D. Hils, J. E. Faller, and J. L. Hall, Rev. Sci. Instrum. 57, 2532 (1986).
[Crossref]

N. C. Wong and J. L. Hall, J. Opt. Soc. Am. B 2, 1527 (1985).
[Crossref]

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

Some additional discussion of these points may be found in J. Helmcke, S. A. Lee, and J. L. Hall, Appl. Opt. 21, 1686 (1982).
[Crossref] [PubMed]

J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
[Crossref]

T. Baer, F. V. Kowalski, and J. L. Hall, Appl. Opt. 19, 3173 (1980).
[Crossref] [PubMed]

A. Brillet, J. Dallarosa, J. L. Hall, and R. Drullinger, J. Opt. Soc. Am. 68, 635 (1978).

L. Hollberg and J. L. Hall, in Lasers’ 80 (Society for Optical and Quantum Electronics, McLean, Va., 1980).

J. E. Faller, P. L. Bender, J. L. Hall, D. Hils, and M. A. Vincent, in Kilometric Optical Arrays in Space (European Space Agency, Paris, 1985), p. 157.

The content of this paragraph is developed in detail by J. L. Hall, in Quantum Optics IV, J. D. Harvey and D. F. Walls, eds. (Springer-Verlag, Heidelberg, 1986), p. 273.
[Crossref]

Some additional data on optical phase-locking experiments can be found in Ref. 4 and in J. L. Hall, in Proceedings of the Beijing/Shanghai International Conference on Lasers (Wiley, New York, 1983), p. 15.

D. Hils and J. L. Hall, “A new laser-based Kennedy-Thorndike experiment,” submitted to Phys. Rev. Lett.

D. Hils and J. L. Hall, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1987), p. 102.

Hänsch, T. W.

T. W. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
[Crossref]

Hellwig, H.

F. Walls and H. Hellwig, National Bureau of Standards, Boulder, Colorado 80303 (personal communication).

Helmcke, J.

Hils, D.

D. Hils and J. L. Hall, “Response of a Fabry–Perot cavity to frequency-modulated light,” Rev. Sci. Instrum. 58, 1406 (1987).(Unfortunately, in the printed version, pp. 1408 and 1409 are reversed.)
[Crossref]

D. Hils, J. E. Faller, and J. L. Hall, Rev. Sci. Instrum. 57, 2532 (1986).
[Crossref]

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

D. Hils and J. L. Hall, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1987), p. 102.

D. Hils and J. L. Hall, “A new laser-based Kennedy-Thorndike experiment,” submitted to Phys. Rev. Lett.

J. E. Faller, P. L. Bender, J. L. Hall, D. Hils, and M. A. Vincent, in Kilometric Optical Arrays in Space (European Space Agency, Paris, 1985), p. 157.

Hollberg, L.

B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876 (1987).
[Crossref] [PubMed]

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
[Crossref]

L. Hollberg and J. L. Hall, in Lasers’ 80 (Society for Optical and Quantum Electronics, McLean, Va., 1980).

Hough, J.

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

Jungmann, K.

R. G. DeVoe, C. Fabre, K. Jungmann, K. L. Foster, and R. G. Brewster, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 80.

Kane, T. J.

Kimble, H. J.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

T. Baer, F. V. Kowalski, and J. L. Hall, Appl. Opt. 19, 3173 (1980).
[Crossref] [PubMed]

Kramer, G.

J. L. Hall, L.-S. Ma, and G. Kramer, IEEE J. Quantum Electron. QE-23, 427 (1987).
[Crossref]

Lee, S. A.

Ma, L.-S.

J. L. Hall, L.-S. Ma, and G. Kramer, IEEE J. Quantum Electron. QE-23, 427 (1987).
[Crossref]

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
[Crossref]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

Owens, D. K.

D. K. Owens and R. Weiss, Rev. Sci. Instrum. 45, 1060 (1974).
[Crossref]

Peng, K.-C.

Pound, R. V.

R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
[Crossref] [PubMed]

Rayman, M. D.

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

Reid, J.

K. J. Seimsen, E. Williams, and J. Reid, Opt. Lett. 24, 879 (1987).
[Crossref]

Robinson, H. G.

J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
[Crossref]

Roy, R.

D. S. Elliott, R. Roy, and S. J. Smith, Phys. Rev. A 26, 12 (1982).
[Crossref]

Sampas, N. M.

N. M. Sampas and D. Z. Anderson, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 308, paper FA5.

Seimsen, K. J.

K. J. Seimsen, E. Williams, and J. Reid, Opt. Lett. 24, 879 (1987).
[Crossref]

Smith, S. J.

D. S. Elliott, R. Roy, and S. J. Smith, Phys. Rev. A 26, 12 (1982).
[Crossref]

Szabo, A.

A. Szabo, National Research Council, Ottawa ONK1A 0R8, Ontario, Canada (personal communication).

Vincent, M. A.

J. E. Faller, P. L. Bender, J. L. Hall, D. Hils, and M. A. Vincent, in Kilometric Optical Arrays in Space (European Space Agency, Paris, 1985), p. 157.

Walls, F.

F. Walls and H. Hellwig, National Bureau of Standards, Boulder, Colorado 80303 (personal communication).

Walls, F. W.

F. W. Walls, in IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-34, 592 (1986).

Wang, Yiqui

Somewhat promising experiments were carried out in 1985 by Yiqui Wang in his laboratory (Peking University, Beijing, China).

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

Weiss, R.

D. K. Owens and R. Weiss, Rev. Sci. Instrum. 45, 1060 (1974).
[Crossref]

Welleghausen, B.

B. Welleghausen, IEEE J. Quantum Electron. QE-15, 1108 (1979).
[Crossref]

Williams, E.

K. J. Seimsen, E. Williams, and J. Reid, Opt. Lett. 24, 879 (1987).
[Crossref]

Wong, N. C.

Wu, Ling-An

Zhou, B.

Appl. Opt. (4)

Appl. Phys. B (2)

J. Hough, D. Hils, M. D. Rayman, L.-S. Ma, L. Hollberg, and J. L. Hall, Appl. Phys. B 33, 179 (1984).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[Crossref]

IEEE J. Quantum Electron. (2)

J. L. Hall, L.-S. Ma, and G. Kramer, IEEE J. Quantum Electron. QE-23, 427 (1987).
[Crossref]

B. Welleghausen, IEEE J. Quantum Electron. QE-15, 1108 (1979).
[Crossref]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

F. W. Walls, in IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-34, 592 (1986).

J. Opt. Soc. Am. (1)

A. Brillet, J. Dallarosa, J. L. Hall, and R. Drullinger, J. Opt. Soc. Am. 68, 635 (1978).

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

J. Phys. Colloq. (1)

J. L. Hall, L. Hollberg, L.-S. Ma, T. Baer, and H. G. Robinson, J. Phys. Colloq. 42, Suppl. 12, C8, 59 (1981).
[Crossref]

Opt. Commun. (1)

T. W. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (2)

D. S. Elliott, R. Roy, and S. J. Smith, Phys. Rev. A 26, 12 (1982).
[Crossref]

R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[Crossref]

Rev. Sci. Instrum. (4)

D. Hils, J. E. Faller, and J. L. Hall, Rev. Sci. Instrum. 57, 2532 (1986).
[Crossref]

D. Hils and J. L. Hall, “Response of a Fabry–Perot cavity to frequency-modulated light,” Rev. Sci. Instrum. 58, 1406 (1987).(Unfortunately, in the printed version, pp. 1408 and 1409 are reversed.)
[Crossref]

R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
[Crossref] [PubMed]

D. K. Owens and R. Weiss, Rev. Sci. Instrum. 45, 1060 (1974).
[Crossref]

Other (14)

Some additional data on optical phase-locking experiments can be found in Ref. 4 and in J. L. Hall, in Proceedings of the Beijing/Shanghai International Conference on Lasers (Wiley, New York, 1983), p. 15.

Somewhat promising experiments were carried out in 1985 by Yiqui Wang in his laboratory (Peking University, Beijing, China).

A. Szabo, National Research Council, Ottawa ONK1A 0R8, Ontario, Canada (personal communication).

J. E. Faller, P. L. Bender, J. L. Hall, D. Hils, and M. A. Vincent, in Kilometric Optical Arrays in Space (European Space Agency, Paris, 1985), p. 157.

The content of this paragraph is developed in detail by J. L. Hall, in Quantum Optics IV, J. D. Harvey and D. F. Walls, eds. (Springer-Verlag, Heidelberg, 1986), p. 273.
[Crossref]

L. Hollberg and J. L. Hall, in Lasers’ 80 (Society for Optical and Quantum Electronics, McLean, Va., 1980).

F. Walls and H. Hellwig, National Bureau of Standards, Boulder, Colorado 80303 (personal communication).

N. M. Sampas and D. Z. Anderson, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), p. 308, paper FA5.

D. Z. Anderson, Department of Physics, University of Colorado, Campus Box 390, Boulder, Colorado 80309 (personal communication).

D. Hils and J. L. Hall, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1987), p. 102.

R. G. DeVoe, C. Fabre, K. Jungmann, K. L. Foster, and R. G. Brewster, in Digest of the International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 80.

D. Hils and J. L. Hall, “A new laser-based Kennedy-Thorndike experiment,” submitted to Phys. Rev. Lett.

We are using CW Radiation’s Model LT1R.

Schott Glass Technologies, Inc., Duryea, Penn.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup: EOM’s electro-optic modulator; F.I.’s, Faraday isolators (2 polarizers + Faraday crystal); L, lens; WP’s, λ/4 plates; det 1, det 2, detectors. The optical heterodyne frequency-diagnostics system consists of a computer-controlled reciprocal counter, a rf spectrum analyzer, a rf-frequency synthesizer and downconverter, a Fourier-transform audio spectrum analyzer, and a multichannel analyzer.

Fig. 2
Fig. 2

Fourier spectrum of the beat frequency between the two lasers locked to two adjacent modes of the Fabry–Perot cavity. (a) Logarithmic scale: 50 Hz/division, 10-Hz bandwidth, 10-sec recording time. (b) Linear scale: 0.5 Hz/division, 30-mHz bandwidth, 1-min recording time. The full width at half-maximum is approximately 50 mHz.

Fig. 3
Fig. 3

Beat frequency recorded during a 21-min time interval: 1000 points, 1.25 sec/point.

Fig. 4
Fig. 4

Allan variance of the beat frequency presented in Fig. 3. The optical frequency has been chosen as the reference frequency (474 THz).

Fig. 5
Fig. 5

Temporal analysis of the beat frequency heterodyned down to low frequency: (a) the beat frequency is ∼1 Hz: 512 points, 40 msec/point, 20.48-sec recording time; (b) the beat frequency is 0.6 Hz and still appears nicely sinusoidal; (c) the beat frequency is ∼0.4 Hz, and some phase reversal may be seen; (d) the beat frequency has been adjusted to be ∼0 Hz. Note that there is an 8-sec period during which the phase is stable within 1 rad. Each laser linewidth needs to be ∼50 mHz to give such a beat.

Tables (1)

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Table 1 Heterodyne Beat with Laser II Used as Reference When Laser I is Locked on Several Cavity Ordersa

Equations (4)

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δ ν ν I | cavity δ I Δ ν c δ I I 80 kHz × 15 × 10 6 = 1.2 Hz .
Δ = [ ( 2 e i dc ) 1 / 2 / i sig ] Δ ν c = [ 2 e 2 ( P η d h ν ) ] 1 / 2 e P η d h ν η c Δ ν c .
δ f = π Δ 2 = 2 π ( Δ ν c 2 ) ( η c ) 2 h ν P η d ( shot-noise-limited linewidth ) .
σ 2 ( 2 , τ , τ ) = 1 ( m 1 ) ν 0 2 k = 1 m 1 ( ν ¯ k + 1 ν ¯ k ) 2 2 ,

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