Abstract

Spurious coherent reflections from optical elements that re-enter an exit port of a two-mirror ring-down cavity can significantly change the effective reflectivity of the cavity mirrors, thus altering the cavity decay time. For a 25-cm-long Fabry–Perot cavity with a decay constant of 40 µs, we find that a specular reflection of only 10-4 of the transmitted ring-down power that is mode matched back toward the cavity could change the decay time by as much as ±0.4 µs, depending on the phase of the returning reflection. The perturbation of the decay time is proportional to the electric field, so a decrease in the spurious reflected power of 100 times will result in a perturbation that is only 10 times smaller. We demonstrate the effect with a cw system by purposely introducing a spurious reflection.

© 2002 Optical Society of America

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  1. P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, Spectrochim. Acta B 56, 1277 (2001), and references therein.
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. J. Ye and J. L. Hall, Phys. Rev. A 61, 061802(R) (2000).
    [CrossRef]
  6. M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
    [CrossRef]
  7. M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).
  8. 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]

2001

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, Spectrochim. Acta B 56, 1277 (2001), and references therein.
[CrossRef]

2000

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

J. Ye and J. L. Hall, Phys. Rev. A 61, 061802(R) (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
[CrossRef]

1998

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

1995

P. Zalicki and R. N. Zare, J. Chem. Phys. 102, 2708 (1995).

1985

1983

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]

Axner, O.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, Spectrochim. Acta B 56, 1277 (2001), and references therein.
[CrossRef]

Byer, R. L.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
[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]

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]

Gustafsson, J.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, Spectrochim. Acta B 56, 1277 (2001), and references therein.
[CrossRef]

Hall, J. L.

J. Ye and J. L. Hall, Phys. Rev. A 61, 061802(R) (2000).
[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]

Harb, C. C.

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
[CrossRef]

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

Harris, J. S.

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

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]

Kluczynski, P.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, Spectrochim. Acta B 56, 1277 (2001), and references therein.
[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.

Levenson, M. D.

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

Lindberg, A. M.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, Spectrochim. Acta B 56, 1277 (2001), and references therein.
[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]

Paldus, B. A.

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
[CrossRef]

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

Spence, T. G.

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
[CrossRef]

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

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]

Webster, C. R.

Willke, B.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

Ye, J.

J. Ye and J. L. Hall, Phys. Rev. A 61, 061802(R) (2000).
[CrossRef]

Zalicki, P.

P. Zalicki and R. N. Zare, J. Chem. Phys. 102, 2708 (1995).

Zare, R. N.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, R. N. Zare, M. J. Lawrence, and R. L. Byer, Opt. Lett. 25, 920 (2000).
[CrossRef]

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

P. Zalicki and R. N. Zare, J. Chem. Phys. 102, 2708 (1995).

Appl. Phys. B

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]

Chem. Phys. Lett.

M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris, and R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).

J. Chem. Phys.

P. Zalicki and R. N. Zare, J. Chem. Phys. 102, 2708 (1995).

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

J. Ye and J. L. Hall, Phys. Rev. A 61, 061802(R) (2000).
[CrossRef]

Rev. Sci. Instrum.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

Spectrochim. Acta B

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, Spectrochim. Acta B 56, 1277 (2001), and references therein.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Typical thin-film high-finesse mirror with the intracavity wave incident from the right. L and H refer to layers whose relative refraction index is low or high, respectively. The resultant reflection is determined by the coherent superposition of the individual reflections, including the back-surface reflection Er and reflections from surfaces some distance away, as designated by Es. Back-surface reflections may be avoided by angle polishing of the substrate.

Fig. 2
Fig. 2

Curves marked with squares and diamonds, calculated maximum deviations of the apparent reflectivity of the high-finesse mirror, caused by a retroreflection of a fraction of the beam transmitted from the cavity. For instance, a mode-matched retroreflection of 10-3 will change the effective reflectivity by -1.4 to +1.4 parts in 106 (ppm), depending on the relative phase of the returning light (dotted lines). The corresponding change of the ring-down time constant for such a retroreflection entering one port, assuming a two-mirror cavity, a round-trip cavity length of 50 cm, and a nominal decay constant of 40 µs, is shown by the line marked with triangles. That change would be approximately ±1 µs for a spurious retroreflection of 10-3, equivalent to an apparent change of an intracavity absorption of ±2×10-8 cm-1.

Fig. 3
Fig. 3

Measured time constants of a two-mirror cavity with no antireflection coating on either mirror’s back surface. Each point is the exponential time constant determined from a fit of the ring-down signal of a TEM00 mode. The open circles were obtained on day 1, and the data indicated by the squares were from the following day. A reflectivity of 3.4% is expected at the fused-silica–air interfaces. From Fig. 2, we expect a maximum perturbation from each mirror of ±7.4 µs. The data show a perturbation of the total cavity time constant of ±5.5 µs, consistent with a partial cancellation of the contribution from each mirror because of a slight difference in mirror thickness.

Fig. 4
Fig. 4

Measurement of 3000 sequential cavity decay time constants. Each point represents a time constant determined by an exponential fit to 175 µs of a decay from a TEM00 mode. The laser is then relocked to the same mode, and the next decay is triggered approximately 5 ms later. At 4.5 s into the data set, a spurious reflection of 7.5×10-4 was introduced by means of unblocking a piezoelectric transducer–mounted mirror positioned 50 cm from the cavity. The mirror motion is unidirectional (toward the cavity) for the entire data set. The data show a deviation of the ring-down time constant that is due to the spurious reflection of ±0.25 µs, which is consistent with an expected deviation of ±1 µs that should occur from a mode-matched reflection, as shown by Fig. 2.

Equations (3)

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τ-1=αL+i=1k1-RinL/c,
dτdα=-cnτ2,
α=nc1τ-1τ0.

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