Abstract

We have developed an optical-cavity system comprising birefringent mirrors for a vibration transducer. To obtain a dispersive-shape signal necessary for reading out the information of mirror vibration, we measure the polarization change of the cavity transmission light caused by the natural birefringence appearing on interferential mirrors; this effect is enhanced by the cavity resonance. Since there are no additional polarization-changing elements inside the cavity, we can achieve the high finesse that is indispensable for a highly sensitive vibration measurement. The principle and an experimental demonstration of the system are reported here.

© 1998 Optical Society of America

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References

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  1. J. -P. Richard, “Approaching the quantum limit with optically instrumented multimode gravitational-wave detectors,” Phys. Rev. D 46, 2309–2317 (1992).
    [CrossRef]
  2. Y. Pang, J. -P. Richard, “Room-temperature test of an optical transducer for resonant gravitational wave detectors,” Appl. Opt. 34, 4982–4988 (1995).
    [CrossRef] [PubMed]
  3. N. Mio, K. Tsubono, “Vibration transducer using an ultrashort Fabry–Perot cavity,” Appl. Opt. 34, 186–189 (1995).
    [CrossRef] [PubMed]
  4. A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
    [CrossRef]
  5. K. Tsubono, N. Mio, A. Mizutani, “Laser interferometer instrumented in a disk antenna for gravitational radiation,” Jpn. J. Appl. Phys. 30, 1326–1330 (1991).
    [CrossRef]
  6. G. Rempe, R. J. Thompson, H. J. Kimble, R. Lalezari, “Measurement of ultralow losses in an optical interferometer,” Opt. Lett. 17, 363–365 (1992).
    [CrossRef] [PubMed]
  7. A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
    [CrossRef]
  8. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  9. T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
    [CrossRef]
  10. M. Kourogi, M. Ohtsu, “Novel optical frequency discriminator of FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
    [CrossRef]
  11. S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
    [CrossRef]
  12. P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
    [CrossRef]
  13. D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, M. Oger, “Supermirror phase anisotropy measurement,” Opt. Lett. 20, 671–673 (1995).
    [CrossRef] [PubMed]
  14. S. Moriwaki, H. Sakaida, T. Yuzawa, N. Mio, “Measurement of the residual birefringence of interferential mirrors using Fabry–Perot cavity,” Appl. Phys. B 65, 347–350 (1997).
    [CrossRef]

1997 (1)

S. Moriwaki, H. Sakaida, T. Yuzawa, N. Mio, “Measurement of the residual birefringence of interferential mirrors using Fabry–Perot cavity,” Appl. Phys. B 65, 347–350 (1997).
[CrossRef]

1996 (1)

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

1995 (4)

1993 (1)

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

1992 (2)

J. -P. Richard, “Approaching the quantum limit with optically instrumented multimode gravitational-wave detectors,” Phys. Rev. D 46, 2309–2317 (1992).
[CrossRef]

G. Rempe, R. J. Thompson, H. J. Kimble, R. Lalezari, “Measurement of ultralow losses in an optical interferometer,” Opt. Lett. 17, 363–365 (1992).
[CrossRef] [PubMed]

1991 (2)

K. Tsubono, N. Mio, A. Mizutani, “Laser interferometer instrumented in a disk antenna for gravitational radiation,” Jpn. J. Appl. Phys. 30, 1326–1330 (1991).
[CrossRef]

M. Kourogi, M. Ohtsu, “Novel optical frequency discriminator of FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[CrossRef]

1989 (1)

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1980 (1)

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

Bretenaker, F.

Carusotto, S.

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

Couillaud, B.

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

Della Valle, F.

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Gillespie, A.

A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Iacopini, E.

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

Jacob, D.

Kataoka, I.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Kimble, H. J.

Kitajima, N.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Kourogi, M.

M. Kourogi, M. Ohtsu, “Novel optical frequency discriminator of FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Lalezari, R.

Le Floch, A.

Micossi, P.

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Milotti, E.

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Mio, N.

S. Moriwaki, H. Sakaida, T. Yuzawa, N. Mio, “Measurement of the residual birefringence of interferential mirrors using Fabry–Perot cavity,” Appl. Phys. B 65, 347–350 (1997).
[CrossRef]

N. Mio, K. Tsubono, “Vibration transducer using an ultrashort Fabry–Perot cavity,” Appl. Opt. 34, 186–189 (1995).
[CrossRef] [PubMed]

K. Tsubono, N. Mio, A. Mizutani, “Laser interferometer instrumented in a disk antenna for gravitational radiation,” Jpn. J. Appl. Phys. 30, 1326–1330 (1991).
[CrossRef]

Mitake, T.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Mizutani, A.

K. Tsubono, N. Mio, A. Mizutani, “Laser interferometer instrumented in a disk antenna for gravitational radiation,” Jpn. J. Appl. Phys. 30, 1326–1330 (1991).
[CrossRef]

Moriwaki, S.

S. Moriwaki, H. Sakaida, T. Yuzawa, N. Mio, “Measurement of the residual birefringence of interferential mirrors using Fabry–Perot cavity,” Appl. Phys. B 65, 347–350 (1997).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Nakamura, K.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Oger, M.

Ohtsu, M.

M. Kourogi, M. Ohtsu, “Novel optical frequency discriminator of FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[CrossRef]

Pang, Y.

Polacco, E.

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

Raab, F.

A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

Rempe, G.

Richard, J. -P.

Y. Pang, J. -P. Richard, “Room-temperature test of an optical transducer for resonant gravitational wave detectors,” Appl. Opt. 34, 4982–4988 (1995).
[CrossRef] [PubMed]

J. -P. Richard, “Approaching the quantum limit with optically instrumented multimode gravitational-wave detectors,” Phys. Rev. D 46, 2309–2317 (1992).
[CrossRef]

Rizzo, C.

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Ruoso, G.

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Sakaida, H.

S. Moriwaki, H. Sakaida, T. Yuzawa, N. Mio, “Measurement of the residual birefringence of interferential mirrors using Fabry–Perot cavity,” Appl. Phys. B 65, 347–350 (1997).
[CrossRef]

Scuri, F.

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

Sekiguchi, H.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Stefanini, G.

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

Thompson, R. J.

Tsubono, K.

N. Mio, K. Tsubono, “Vibration transducer using an ultrashort Fabry–Perot cavity,” Appl. Opt. 34, 186–189 (1995).
[CrossRef] [PubMed]

K. Tsubono, N. Mio, A. Mizutani, “Laser interferometer instrumented in a disk antenna for gravitational radiation,” Jpn. J. Appl. Phys. 30, 1326–1330 (1991).
[CrossRef]

Uchisawa, K.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Ueda, A.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Ueda, K.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Uehara, N.

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Vallet, M.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Yuzawa, T.

S. Moriwaki, H. Sakaida, T. Yuzawa, N. Mio, “Measurement of the residual birefringence of interferential mirrors using Fabry–Perot cavity,” Appl. Phys. B 65, 347–350 (1997).
[CrossRef]

Zavattini, E.

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (4)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

S. Carusotto, E. Polacco, E. Iacopini, G. Stefanini, E. Zavattini, F. Scuri, “The ellipticity induced by interferential mirrors on a linearly polarized light beam orthogonally reflected,” Appl. Phys. B 48, 231–234 (1989).
[CrossRef]

P. Micossi, F. Della Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

S. Moriwaki, H. Sakaida, T. Yuzawa, N. Mio, “Measurement of the residual birefringence of interferential mirrors using Fabry–Perot cavity,” Appl. Phys. B 65, 347–350 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Tsubono, N. Mio, A. Mizutani, “Laser interferometer instrumented in a disk antenna for gravitational radiation,” Jpn. J. Appl. Phys. 30, 1326–1330 (1991).
[CrossRef]

Opt. Commun. (2)

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[CrossRef]

M. Kourogi, M. Ohtsu, “Novel optical frequency discriminator of FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[CrossRef]

Opt. Lett. (2)

Opt. Rev. (1)

A. Ueda, N. Uehara, K. Uchisawa, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, I. Kataoka, “Ultra-high quality cavity with 1.5-ppm loss at 1064 nm,” Opt. Rev. 3, 369–372 (1996).
[CrossRef]

Phys. Rev. D (2)

J. -P. Richard, “Approaching the quantum limit with optically instrumented multimode gravitational-wave detectors,” Phys. Rev. D 46, 2309–2317 (1992).
[CrossRef]

A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic view of an OCT comprising birefringent mirrors. Two mirrors (M1 and M2) that form a Fabry–Perot cavity have orthogonal eigenaxes for the polarization denoted by slow and fast; they are set so that their optical eigenaxes are along the same direction. Transmitted light from the cavity is led to a polarizing beam splitter (PBS) and detected by two photodiodes (PD s and PD p ). The photocurrents from them are fed to a differential amplifier to obtain a signal necessary for extracting the information on mirror vibration.

Fig. 2
Fig. 2

Optical system of the experiment. A single-mode and linear polarization He–Ne laser (λ = 633 nm) is used as a light source; its output power is ∼1 mW. The laser light is incident on the cavity through three Faraday isolators (FI), a half-wave plate (H1), alignment mirrors, a mode-matching lens (L), a polarizing beam splitter (PBS1), and the second half-wave plate (H2). The transmitted light is fed to the third half-wave plate (H3) and the second polarizing beam splitter (PBS2). The two outputs detected by photodiodes (PD s and PD p ) are led to a differential amplifier to obtain a dispersive-shape signal. The signal is fed to the piezoactuators through an appropriate feedback circuit to maintain the operation point of the cavity.

Fig. 3
Fig. 3

Transmission intensities of the cavity, measured through the polarizing beam splitter, while sweeping the cavity length (a). A clear dispersive signal is observed at the output of the differential amplifier (b). The linear region is ∼60 pm at around x = 0.

Fig. 4
Fig. 4

Equivalent displacement noise spectrum. There are several complex structures around 5 kHz that may originate from the mechanical-structure resonance of the cavity. The floor noise, which is almost inverse proportional to the frequency, may originate from the frequency noise of the laser. The horizontal dashed line shows the estimated shot noise calculated from the dc photocurrents.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

δ x shot = γ hc λ P 1 / 2 ,
δ x FM = δ ν ν   L ,
R = r exp i δ / 2 0 0 exp - i δ / 2
d = λ Δ 4 π Δ = δ 1 + δ 2 ,
I s = I 0 1 + Γ x - a 2 ,
I p = I 0 1 + Γ x + a 2 ,
δ I d = I d x | x = 0   δ x = 4 a Γ I 0 1 + Γ a 2 2   δ x
SN = 4 a Γ I 0 1 + Γ a 2 2 2 δ x 2 2 e I p + I s | x = 0 ,
δ x min = 27 e 16 Γ I 0 1 / 2 = 27 128 1 / 2 × 1 hc λ η MP 1 / 2 .
I 0 = 1 2 e η MP λ hc ,
Δ opt = 2 π .

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