Abstract

We report on the frequency stabilization and on the measurement of the spectral density of frequency fluctuations (range 20 Hz to 20 kHz) and of the Allan variance (0.02 ms to 105 s) of a Nd:YAG laser for the VIRGO interferometric detector of gravitational waves. The short-term frequency fluctuations presented here compare favorably with those of other known oscillators. The Allan variance is better than 10−14 for all measurement times below 0.1 s.

© 1996 Optical Society of America

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  1. R. W. P. Drever, J. L. Hall, F. V. Kovalsky, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  2. D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
    [CrossRef]
  3. Corning Glass Works specification sheet ULE 7971.
  4. P. R. Saulson, Phys. Rev. D 42, 2437 (1994).
    [CrossRef]
  5. M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
    [CrossRef]
  6. K. Nakagawa, A. S. Shelkovnikov, T. Katsuda, M. Ohtsu, Appl. Opt. 33, 6383 (1994).
    [CrossRef] [PubMed]
  7. N. M. Sampas, E. K. Gustafson, R. L. Byer, Opt. Lett. 18, 947 (1993).
    [CrossRef] [PubMed]
  8. Y. R. Jafry, J. Cornelisse, R. Reinhard, Eur. Space Adm. J. 18, 219 (1994).

1994

P. R. Saulson, Phys. Rev. D 42, 2437 (1994).
[CrossRef]

M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
[CrossRef]

Y. R. Jafry, J. Cornelisse, R. Reinhard, Eur. Space Adm. J. 18, 219 (1994).

K. Nakagawa, A. S. Shelkovnikov, T. Katsuda, M. Ohtsu, Appl. Opt. 33, 6383 (1994).
[CrossRef] [PubMed]

1993

1989

D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
[CrossRef]

1983

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

Blair, D. G.

M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
[CrossRef]

Brillet, A.

D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
[CrossRef]

Byer, R. L.

Cornelisse, J.

Y. R. Jafry, J. Cornelisse, R. Reinhard, Eur. Space Adm. J. 18, 219 (1994).

Costa, M. E.

M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
[CrossRef]

Cregut, O.

D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
[CrossRef]

Drever, R. W. P.

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

Ford, G. M.

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

Gustafson, E. K.

Hall, J. L.

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

He, J. W.

M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
[CrossRef]

Hough, J.

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

Jafry, Y. R.

Y. R. Jafry, J. Cornelisse, R. Reinhard, Eur. Space Adm. J. 18, 219 (1994).

Katsuda, T.

Kerr, G.

D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
[CrossRef]

Kovalsky, F. V.

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

Luiten, A. N.

M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
[CrossRef]

Man, C. N.

D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
[CrossRef]

Mann, A. S.

M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
[CrossRef]

Munley, A. J.

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

Nakagawa, K.

Ohtsu, M.

Reinhard, R.

Y. R. Jafry, J. Cornelisse, R. Reinhard, Eur. Space Adm. J. 18, 219 (1994).

Sampas, N. M.

Saulson, P. R.

P. R. Saulson, Phys. Rev. D 42, 2437 (1994).
[CrossRef]

Shelkovnikov, A. S.

Shoemaker, D.

D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
[CrossRef]

Ward, H.

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

Appl. Opt.

Appl. Phys. B

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

Electron. Lett.

M. E. Costa, J. W. He, A. S. Mann, A. N. Luiten, D. G. Blair, Electron. Lett. 30, 2119 (1994).
[CrossRef]

Eur. Space Adm. J.

Y. R. Jafry, J. Cornelisse, R. Reinhard, Eur. Space Adm. J. 18, 219 (1994).

Opt. Lett.

N. M. Sampas, E. K. Gustafson, R. L. Byer, Opt. Lett. 18, 947 (1993).
[CrossRef] [PubMed]

D. Shoemaker, A. Brillet, C. N. Man, O. Cregut, G. Kerr, Opt. Lett. 12, 609 (1989).
[CrossRef]

Phys. Rev. D

P. R. Saulson, Phys. Rev. D 42, 2437 (1994).
[CrossRef]

Other

Corning Glass Works specification sheet ULE 7971.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of frequency stabilization on a cavity and measurement of the absolute frequency noise. For a high unity-gain bandwidth (1 MHz), we use three loops. The transmitted light is used for an autolocking system. E-O, electro-optic; A-O, acousto-optic; FP1, FP2, Fabry–Perot cavities.

Fig. 2
Fig. 2

Frequency noise measurement. The lowest curve is the error signal for cavity FP1, the middle solid one is the error signal from FP2 (sum of the noises of the two cavities), and the top curve is the free-running laser spectrum (measured on a low-finesse cavity). The dashed curve shows the requirement for the use in VIRGO.

Fig. 3
Fig. 3

Allan root variance: (1) frequency noise spectrum (middle solid curve in Fig. 4); (2), (3) long-term drifts in this experiment, (4) stability of the University of Western Australia’s sapphire oscillator; (5) stability of the Shanghai Observatory’s hydrogen maser; (6) stability of the Tokyo Institute of Technology’s Nd:YAG laser (see text and references).

Equations (2)

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σ y 2 ( T ) = 0 2 ν ˜ ( f ) ν 0 sin 2 ( π τ f ) [ sin ( π τ f ) π τ f ] 2 d f .
σ y 2 ( T ) = 1 2 ( y i ¯ - y i + 1 ¯ ) 2 , y i ¯ ( T ) = i T ( i + 1 ) T ν ( T ) ν 0 d t ,

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