Abstract

We demonstrate that a laser can be directly locked to a cavity when the laser linewidth is much greater than the cavity linewidth. We lock an external-cavity diode laser with more than 1 MHz of added frequency noise to a 3.5 kHz wide cavity resonance. Our analog servo acquires lock even though the laser frequency sweeps through the cavity resonance in less than the cavity buildup time. Our theoretical analysis fully describes our measurements and explains why lock can be acquired.

© 2005 Optical Society of America

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References

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  1. P. Gill, Metrologia 42, S125 (2005).
    [CrossRef]
  2. B. Abbot and the LIGO Scientific Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
    [CrossRef]
  3. B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
    [CrossRef]
  4. J. Camp, L. Sievers, R. Bork, and J. Heefner, Opt. Lett. 20, 2463 (1995).
    [CrossRef]
  5. M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson, and R. L. Byer, J. Opt. Soc. Am. B 16, 523 (1999).
    [CrossRef]
  6. H. Rohde, J. Eschner, F. Schmidt-Kaler, and R. Blatt, J. Opt. Soc. Am. B 19, 1425 (2002).
    [CrossRef]
  7. U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
    [CrossRef]
  8. A. Schoof, J. Grünert, S. Ritter, and A. Hemmerich, Opt. Lett. 26, 1562 (2001).
    [CrossRef]
  9. 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]
  10. For gravity wave detectors, the mode splittings are so small that adjacent modes must be considered.
  11. L. Duan and K. Gibble, “Locking lasers with large FM noise to high Q cavities,” in Proceedings of the 2005 Joint IEEE Frequency Control Symposium and Precise Time and Time Interval Meeting (Institute of Electrical and Electronics Engineers, to be published).

2005 (1)

P. Gill, Metrologia 42, S125 (2005).
[CrossRef]

2004 (2)

B. Abbot and the LIGO Scientific Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
[CrossRef]

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

2002 (1)

2001 (1)

1999 (2)

M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson, and R. L. Byer, J. Opt. Soc. Am. B 16, 523 (1999).
[CrossRef]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

1995 (1)

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]

Abbot, B.

B. Abbot and the LIGO Scientific Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
[CrossRef]

Bergquist, J. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Blatt, R.

Bork, R.

Byer, R. L.

Camp, J.

Cruz, F. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Degenhardt, C.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

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]

Duan, L.

L. Duan and K. Gibble, “Locking lasers with large FM noise to high Q cavities,” in Proceedings of the 2005 Joint IEEE Frequency Control Symposium and Precise Time and Time Interval Meeting (Institute of Electrical and Electronics Engineers, to be published).

Eschner, J.

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]

Gibble, K.

L. Duan and K. Gibble, “Locking lasers with large FM noise to high Q cavities,” in Proceedings of the 2005 Joint IEEE Frequency Control Symposium and Precise Time and Time Interval Meeting (Institute of Electrical and Electronics Engineers, to be published).

Gill, P.

P. Gill, Metrologia 42, S125 (2005).
[CrossRef]

Grünert, J.

Gustafson, E. K.

Hall, J. L.

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]

Heefner, J.

Helmcke, J.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

Hemmerich, A.

Hollberg, L.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

Hough, 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]

Husman, M. E.

Itano, W. M.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

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]

Lawrence, M. J.

Lisdat, C.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[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]

Oates, C. W.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

Riehle, F.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

Ritter, S.

Rohde, H.

Schmidt-Kaler, F.

Schnatz, H.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

Schoof, A.

Sievers, L.

Sterr, U.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

Stoehr, H.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

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]

Willke, B.

Wilpers, G.

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

Young, B. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Appl. Phys. B (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]

C. R. Phys. (1)

U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. W. Oates, and L. Hollberg, C. R. Phys. 5, 845 (2004).
[CrossRef]

J. Opt. Soc. Am. B (2)

Metrologia (1)

P. Gill, Metrologia 42, S125 (2005).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

B. Abbot and the LIGO Scientific Collaboration, Nucl. Instrum. Methods Phys. Res. A 517, 154 (2004).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Other (2)

For gravity wave detectors, the mode splittings are so small that adjacent modes must be considered.

L. Duan and K. Gibble, “Locking lasers with large FM noise to high Q cavities,” in Proceedings of the 2005 Joint IEEE Frequency Control Symposium and Precise Time and Time Interval Meeting (Institute of Electrical and Electronics Engineers, to be published).

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Figures (4)

Fig. 1
Fig. 1

We treat the real laser 1 as an ideal laser with added phase noise. We lock it to a high-finesse cavity after it passes through an optical isolator, acousto-optic modulator AOM1, a 2 m optical fiber, and an electro-optic modulator. The light reflected from the cavity is detected on photodiode PD 1. Laser 2 is phase locked to laser 1 via PD 2 and scanned over the cavity resonance with AOM 2. EOM 1 and EOM 2 operate at 56 and 72 MHz, and servos 1 and 2 have bandwidths of 2 and 4 MHz, respectively.

Fig. 2
Fig. 2

PDH error signal S PDH for a cavity linewidth of 3.46 kHz and noise at (a) f n = 0.8 kHz with depths 0.8, 1.6, 3.2, 6.4, 12.8, 51.2, 204.8, and 819.2 kHz and (b) f n = 10 kHz and noise depths 10, 20, 40, 80, and 200 kHz. Experiment (solid) and theory (dashed) agree well. The theory curves include the 16.34 kHz pole of the low-pass filter. For (a) f FM = 12.8 kHz corresponds to v ω = 0.85 , and v ω increases linearly with f FM .

Fig. 3
Fig. 3

Regions of the response of Pound–Drever–Hall error signal S PDH as a function of noise frequency f n and noise depth f FM , scaled by cavity linewidth Δ ν .

Fig. 4
Fig. 4

(a) Magnitude and (b) phase of S PDH at noise frequency Ω = 2 π f n as a function of noise depth f FM and β = f FM f n for f n Δ ν = 0.23 , 1.15, 2.9, 10, 100. Data points are squares (circles, diamonds) for f n Δ ν = 0.23 (1.15, 2.9). The response falls for large FM depths at all f n . For f n > Δ ν , the phase oscillates between a phase lag and a phase lead for β > 2 .

Equations (2)

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S PDH = 2 β p , k = 0 J k p ( β ) J k + p + 1 ( β ) ( 2 k + 1 ) Δ ω Ω [ ( k p ) ( k + p + 1 ) Ω 2 + Δ ω 2 ] cos [ ( 2 p + 1 ) Ω t ] + ( 2 p + 1 ) Δ ω Ω sin [ ( 2 p + 1 ) Ω t ] [ ( k p ) 2 Ω 2 + Δ ω 2 ] [ ( k + p + 1 ) 2 Ω 2 + Δ ω 2 ] .
S PDH β f FM Δ ν cos ( Ω t ) + f n sin ( Ω t ) f n 2 + Δ ν 2 .

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