Abstract

We describe a balanced-heterodyne postmodulated Sagnac interferometer signal extraction method that is suitable for gravitational wave detection. The method is simple to implement by placement of a polarization-selective modulator after the beam splitter in the dark port of the interferometer. The postmodulated Sagnac interferometer retains its common path advantage and exhibits insensitivity to laser frequency noise below, at, and above the heterodyne frequency. Balanced detection reduces sensitivity to laser amplitude noise. In this scheme mirror displacement signals were rf demodulated and observed from 0.2 to 10  kHz.

© 1997 Optical Society of America

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  1. A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
    [CrossRef] [PubMed]
  2. R. Weiss, MIT Res. Lab. Electron. Q. Rep. 105, 54 (1972).
  3. D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, and R. Weiss, Appl. Opt. 30, 3133 (1991).
    [CrossRef] [PubMed]
  4. M. W. Regehr, F. J. Raab, and S. E. Whitcomb, Opt. Lett. 20, 1507 (1995).
    [CrossRef] [PubMed]
  5. K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, Phys. Rev. Lett. 76, 3053 (1996).
    [CrossRef] [PubMed]
  6. S. Ezekiel and H. J. Arditty, eds., Fiber-Optic Rotation Sensors (Springer-Verlag, Berlin, 1982).
    [CrossRef]
  7. C. N. Man, D. Shoemaker, M. P. Tu, and D. Dewey, Phys. Lett. 148, 8 (1990).
    [CrossRef]
  8. J. Giaime, “Studies of laser interferometer design and a vibration isolation system for interferometric gravitational wave detectors,” Ph.D dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1995).
  9. M. B. Gary, A. J. Stevenson, C. C. Harb, H.-A. Bachor, and D. E. McClelland, Appl. Opt. 35, 1623 (1996).
    [CrossRef]
  10. K.-X. Sun, E. K. Gustafson, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1359 (1997).
    [CrossRef]
  11. K. X. Sun, Bull. Am. Phys. Soc. 42, 1106 (1997).

1997

1996

K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, Phys. Rev. Lett. 76, 3053 (1996).
[CrossRef] [PubMed]

M. B. Gary, A. J. Stevenson, C. C. Harb, H.-A. Bachor, and D. E. McClelland, Appl. Opt. 35, 1623 (1996).
[CrossRef]

1995

1992

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

1991

1990

C. N. Man, D. Shoemaker, M. P. Tu, and D. Dewey, Phys. Lett. 148, 8 (1990).
[CrossRef]

1972

R. Weiss, MIT Res. Lab. Electron. Q. Rep. 105, 54 (1972).

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Bachor, H.-A.

Byer, R. L.

K.-X. Sun, E. K. Gustafson, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1359 (1997).
[CrossRef]

K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, Phys. Rev. Lett. 76, 3053 (1996).
[CrossRef] [PubMed]

Christensen, N.

Dewey, D.

C. N. Man, D. Shoemaker, M. P. Tu, and D. Dewey, Phys. Lett. 148, 8 (1990).
[CrossRef]

Drever, R. W. P.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Fejer, M. M.

K.-X. Sun, E. K. Gustafson, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1359 (1997).
[CrossRef]

K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, Phys. Rev. Lett. 76, 3053 (1996).
[CrossRef] [PubMed]

Fritschel, P.

Gary, M. B.

Giaime, J.

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, and R. Weiss, Appl. Opt. 30, 3133 (1991).
[CrossRef] [PubMed]

J. Giaime, “Studies of laser interferometer design and a vibration isolation system for interferometric gravitational wave detectors,” Ph.D dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1995).

Gursel, Y.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Gustafson, E. K.

K.-X. Sun, E. K. Gustafson, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1359 (1997).
[CrossRef]

K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, Phys. Rev. Lett. 76, 3053 (1996).
[CrossRef] [PubMed]

Harb, C. C.

Kawamura, S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Man, C. N.

C. N. Man, D. Shoemaker, M. P. Tu, and D. Dewey, Phys. Lett. 148, 8 (1990).
[CrossRef]

McClelland, D. E.

Raab, F. J.

M. W. Regehr, F. J. Raab, and S. E. Whitcomb, Opt. Lett. 20, 1507 (1995).
[CrossRef] [PubMed]

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Regehr, M. W.

Shoemaker, D.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, and R. Weiss, Appl. Opt. 30, 3133 (1991).
[CrossRef] [PubMed]

C. N. Man, D. Shoemaker, M. P. Tu, and D. Dewey, Phys. Lett. 148, 8 (1990).
[CrossRef]

Sievers, L.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Stevenson, A. J.

Sun, K. X.

K. X. Sun, Bull. Am. Phys. Soc. 42, 1106 (1997).

Sun, K.-X.

K.-X. Sun, E. K. Gustafson, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1359 (1997).
[CrossRef]

K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, Phys. Rev. Lett. 76, 3053 (1996).
[CrossRef] [PubMed]

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Tu, M. P.

C. N. Man, D. Shoemaker, M. P. Tu, and D. Dewey, Phys. Lett. 148, 8 (1990).
[CrossRef]

Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Weiss, R.

Whitcomb, S. E.

M. W. Regehr, F. J. Raab, and S. E. Whitcomb, Opt. Lett. 20, 1507 (1995).
[CrossRef] [PubMed]

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Wiess, R.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Zucker, M. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Bull. Am. Phys. Soc.

K. X. Sun, Bull. Am. Phys. Soc. 42, 1106 (1997).

MIT Res. Lab. Electron. Q. Rep.

R. Weiss, MIT Res. Lab. Electron. Q. Rep. 105, 54 (1972).

Opt. Lett.

Phys. Lett.

C. N. Man, D. Shoemaker, M. P. Tu, and D. Dewey, Phys. Lett. 148, 8 (1990).
[CrossRef]

Phys. Rev. Lett.

K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, Phys. Rev. Lett. 76, 3053 (1996).
[CrossRef] [PubMed]

Science

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Wiess, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Other

S. Ezekiel and H. J. Arditty, eds., Fiber-Optic Rotation Sensors (Springer-Verlag, Berlin, 1982).
[CrossRef]

J. Giaime, “Studies of laser interferometer design and a vibration isolation system for interferometric gravitational wave detectors,” Ph.D dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1995).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup and the polarization states at several positions in the system: LASER, 300-mW Nd:YAG laser; ISO, Faraday isolator. PM, PM1, electro-optic phase modulators; AM1, electro-optic amplitude modulators; HW, HW1, half-wave plates; QW1, quarter-wave plate; M1, M2, arm mirrors; BS, beam splitter; PBS, polarizing beam splitter; OX, transmission polarization axis of the polarizing beam splitter; DET1, DET2, detectors for polarization projections  1 and 2, respectively; DIFF, difference port of a rf hybrid junction; MIX: double-balanced rf mixer as a demodulator; OSC, rf oscillator at 96  MHz; PS, rf phase shifter; AMP, rf amplifier. Polarization states at locations (A)–(E) are drawn below the experimental setup.

Fig. 2
Fig. 2

Spectral density of the difference photocurrent converted to differential phase. The vertical scale is 12.5  dB/division for electrical power and 6.25  dB/division for differential optical phase. The calibration peak at 1  kHz is for a measured 18-nm mirror displacement corresponding to a 9.97-µrad differential optical phase signal. The IF resolution bandwidth is 18.7  Hz. (a) Balanced detection, demonstrating the low-frequency signal extraction and common mode rejection of laser- and mirror-tilt-induced amplitude noise. (b) Spectrum taken when one of the detectors was blocked to disable balanced detection. As much as 20  dB of excess amplitude noise is evident from 0 to 3  kHz and at peaks at 2, 4, 6, and 8  kHz. (c) Differential phase measurement with frequency and phase modulation applied to the input laser (see text for details). The signal extraction and the noise floor, and thus the phase sensitivity, were not affected by laser frequency modulation.

Equations (2)

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Eoutm=tm2 expiϕccw-rm2 expiϕcwEinm,
I1-I2=η1Eouts+Eoutp/2 2-η2×Eouts-Eoutp/22=2ηReEoutpEouts*,

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