Abstract

We present a new method for locking the frequency of a laser to a reference-interferometer cavity. For a non-mode-matched input beam, the light reflected off a cavity contains an interference between the wave fronts corresponding to the various cavity modes. A detector placed at the proper position on the interference pattern provides a signal proportional to the imaginary component of the reflected field. As a function of laser frequency, this signal is dispersion shaped and can be used as the error signal for electronic frequency stabilization.

© 1982 Optical Society of America

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References

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  1. R. L. Barger, M. S. Sorem, J. L. Hall, Appl. Phys. Lett. 22, 573 (1973).
    [Crossref]
  2. A. D. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
    [Crossref]
  3. R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
    [Crossref] [PubMed]
  4. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).
  5. T. W. Hänsch, B. Couillaud, Opt. Commun. 35, 441 (1980).
    [Crossref]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 7.6;Ref. 5.
  7. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [Crossref] [PubMed]

1980 (1)

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

1973 (1)

R. L. Barger, M. S. Sorem, J. L. Hall, Appl. Phys. Lett. 22, 573 (1973).
[Crossref]

1966 (1)

1965 (1)

A. D. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
[Crossref]

1946 (1)

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

Barger, R. L.

R. L. Barger, M. S. Sorem, J. L. Hall, Appl. Phys. Lett. 22, 573 (1973).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 7.6;Ref. 5.

Couillaud, B.

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

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).

Hall, J. L.

R. L. Barger, M. S. Sorem, J. L. Hall, Appl. Phys. Lett. 22, 573 (1973).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).

Hänsch, T. W.

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

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).

Kogelnik, H.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).

Li, T.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).

Pound, R. V.

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

Sorem, M. S.

R. L. Barger, M. S. Sorem, J. L. Hall, Appl. Phys. Lett. 22, 573 (1973).
[Crossref]

White, A. D.

A. D. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 7.6;Ref. 5.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. L. Barger, M. S. Sorem, J. L. Hall, Appl. Phys. Lett. 22, 573 (1973).
[Crossref]

IEEE J. Quantum Electron. (1)

A. D. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
[Crossref]

Opt. Commun. (1)

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

Rev. Sci. Instrum. (1)

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

Other (2)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colorado 80309 (personal communication).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Chap. 7.6;Ref. 5.

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Figures (2)

Fig. 1
Fig. 1

A, Im(ERC)/Ei versus δ. B, solid curve, ( I 2 I 1 ) / ( 2 I 0 E i ); dashed curve, approximation from formula (8). Vertical scale is expanded by a factor of 5.76 from A.

Fig. 2
Fig. 2

Schematic showing laser-stabilizer concept.

Equations (9)

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E RC = E i [ R 1 T 1 R 1 R exp ( i δ ) 1 R exp ( i δ ) ] = E i [ R 1 ( T 1 R R 1 ) cos δ R + i sin δ ( 1 R ) 2 + 4 R sin 2 δ 2 ] .
I 2 = | E RC + E 0 | 2 = I 0 + I RC + 2 Re ( E RC ) Re ( E 0 ) + 2 Im ( E RC ) Im ( E 0 ) .
E 0 = I 0 cos θ + i I 0 sin θ ,
I 2 = I 0 + I RC + 2 I 0 cos θ Re ( E RC ) + 2 I 0 sin θ Im ( E RC ) .
I 2 = I 0 + I RC + 2 I 0 Im ( E RC ) .
I 1 = I 0 + I RC ,
I 2 I 1 = 2 I 0 [ Im ( E RC ) sin θ + Re ( E RC ) cos θ ] .
I 2 I 1 2 I 0 E i [ Im ( E RC ) E i sin θ + cos θ ] .
Φ m , n = ( m + n + 1 ) arctan ( λ z / π ω 0 2 ) ,

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