Abstract

We describe the first experimental demonstration of light recycling of a Michelson interferometer with Fabry–Perot cavities in the arms of the interferometer. Light recycling is a technique for efficiently using the light in long-baseline interferometers, such as those being proposed for the detection of gravitational radiation. An increase in the interferometer circulating power by a factor of 18 is observed, which is in good agreement with the expected gain given the losses in the system. Several phenomena associated with this configuration of coupled optical cavities are discussed.

© 1992 Optical Society of America

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References

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  1. D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
    [CrossRef]
  2. R. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, Les Houches 1982, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, 1983), pp. 321–338.
  3. J. Y. Vinet, B. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
    [CrossRef]
  4. B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
    [CrossRef]
  5. B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A 142, 465–470 (1989).
    [CrossRef]
  6. C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, External modulation technique for sensitive interferometric detection of displacements, Phys. Lett. A 148, 8–16 (1990).
    [CrossRef]
  7. K. A. Strain, B. J. Meers, “Experimental demonstration of dual recycling for interferometric gravitational-wave detectors,” Phys. Rev. Lett. 66, 1391–1394 (1991).
    [CrossRef] [PubMed]
  8. R. Vogt, “The U.S. LIGO project,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23 June 1991.
  9. R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” Mass. Inst. Technol. Res. Lab. Electron. Q. Rep. 105, 54–76 (1972).
  10. C. Townes, A. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955), p. 426, in the context of microwave spectroscopy; proposed in the present context by R. Drever, California Institute of Technology, Pasadena, Calif. 91125 (personal communication, 1986).
  11. D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
    [CrossRef]
  12. R. Schilling, L. Schnupp, Max-Planck Institut für Quantenoptik, Garching bei München, Germany (personal communication, 1986).
  13. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 524–530.

1991 (2)

K. A. Strain, B. J. Meers, “Experimental demonstration of dual recycling for interferometric gravitational-wave detectors,” Phys. Rev. Lett. 66, 1391–1394 (1991).
[CrossRef] [PubMed]

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
[CrossRef]

1990 (1)

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, External modulation technique for sensitive interferometric detection of displacements, Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

1989 (1)

B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A 142, 465–470 (1989).
[CrossRef]

1988 (3)

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

J. Y. Vinet, B. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
[CrossRef]

1972 (1)

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” Mass. Inst. Technol. Res. Lab. Electron. Q. Rep. 105, 54–76 (1972).

Brillet, A.

J. Y. Vinet, B. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

Christensen, N.

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
[CrossRef]

Dewey, D.

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, External modulation technique for sensitive interferometric detection of displacements, Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

Drever, R.

R. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, Les Houches 1982, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, 1983), pp. 321–338.

Fritschel, P.

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
[CrossRef]

Giaime, J.

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
[CrossRef]

Maischberger, K.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

Man, C. N.

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, External modulation technique for sensitive interferometric detection of displacements, Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

J. Y. Vinet, B. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

Meers, B.

J. Y. Vinet, B. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

Meers, B. J.

K. A. Strain, B. J. Meers, “Experimental demonstration of dual recycling for interferometric gravitational-wave detectors,” Phys. Rev. Lett. 66, 1391–1394 (1991).
[CrossRef] [PubMed]

B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A 142, 465–470 (1989).
[CrossRef]

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
[CrossRef]

Pham Tu, M.

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, External modulation technique for sensitive interferometric detection of displacements, Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

Rüdiger, A.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

Schawlow, A.

C. Townes, A. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955), p. 426, in the context of microwave spectroscopy; proposed in the present context by R. Drever, California Institute of Technology, Pasadena, Calif. 91125 (personal communication, 1986).

Schilling, R.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

R. Schilling, L. Schnupp, Max-Planck Institut für Quantenoptik, Garching bei München, Germany (personal communication, 1986).

Schnupp, L.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

R. Schilling, L. Schnupp, Max-Planck Institut für Quantenoptik, Garching bei München, Germany (personal communication, 1986).

Shoemaker, D.

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
[CrossRef]

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, External modulation technique for sensitive interferometric detection of displacements, Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 524–530.

Strain, K. A.

K. A. Strain, B. J. Meers, “Experimental demonstration of dual recycling for interferometric gravitational-wave detectors,” Phys. Rev. Lett. 66, 1391–1394 (1991).
[CrossRef] [PubMed]

Townes, C.

C. Townes, A. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955), p. 426, in the context of microwave spectroscopy; proposed in the present context by R. Drever, California Institute of Technology, Pasadena, Calif. 91125 (personal communication, 1986).

Vinet, J. Y.

J. Y. Vinet, B. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

Vogt, R.

R. Vogt, “The U.S. LIGO project,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23 June 1991.

Weiss, R.

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
[CrossRef]

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” Mass. Inst. Technol. Res. Lab. Electron. Q. Rep. 105, 54–76 (1972).

Winkler, W.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

App. Opt. (1)

D. Shoemaker, P. Fritschel, J. Giaime, N. Christensen, R. Weiss, “Prototype Michelson interferometer with Fabry–Perot cavities,” App. Opt. 30, 3133–3138 (1991).
[CrossRef]

Mass. Inst. Technol. Res. Lab. Electron. Q. Rep. (1)

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” Mass. Inst. Technol. Res. Lab. Electron. Q. Rep. 105, 54–76 (1972).

Phys. Lett. A (2)

B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A 142, 465–470 (1989).
[CrossRef]

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, External modulation technique for sensitive interferometric detection of displacements, Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

Phys. Rev. D (3)

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423–432 (1988).
[CrossRef]

J. Y. Vinet, B. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
[CrossRef]

Phys. Rev. Lett. (1)

K. A. Strain, B. J. Meers, “Experimental demonstration of dual recycling for interferometric gravitational-wave detectors,” Phys. Rev. Lett. 66, 1391–1394 (1991).
[CrossRef] [PubMed]

Other (5)

R. Vogt, “The U.S. LIGO project,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23 June 1991.

R. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, Les Houches 1982, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, 1983), pp. 321–338.

C. Townes, A. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955), p. 426, in the context of microwave spectroscopy; proposed in the present context by R. Drever, California Institute of Technology, Pasadena, Calif. 91125 (personal communication, 1986).

R. Schilling, L. Schnupp, Max-Planck Institut für Quantenoptik, Garching bei München, Germany (personal communication, 1986).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 524–530.

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Figures (2)

Fig. 1
Fig. 1

(a) Optical elements of a recycled Michelson interferometer with Fabry–Perot cavities in the arms. (b) When the interferometer is operating at the dark fringe of the antisymmetric output, the two arms and beam splitter are modeled by one arm cavity, creating a three-mirror cavity. (c) The arm cavity is then modeled by a single mirror, having reflection and transmission coefficients of a Fabry–Perot cavity. The tilde denotes a complex quantity.

Fig. 2
Fig. 2

Experimental arrangement.

Tables (2)

Tables Icon

Table I Losses for the Recycled Simple Michelson Interferometer

Tables Icon

Table II Losses for the Recycled Fabry–Perot Arm Michelson Interferometer

Equations (10)

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ϕ noise = ( 2 h υ / η P ) 1 / 2 ,
P anti = 1 2 P 0 [ 1 C cos ( ϕ ¯ d ) ] ,
P int / P 0 = T 1 [ 1 ( R 1 R 2 ) 1 / 2 ] 2 = T 1 { 1 [ ( 1 A 1 T 1 ) ( 1 A 2 ) ] 1 / 2 } 2 ,
T 1 = ( 1 A 1 ) [ 1 R 2 ( 1 A 1 ) ] .
G rec max = P int max / P 0 = 1 A 2 + A 1 / ( 1 A 1 ) 1 A 2 + A 1 .
r ˜ cav ( θ ) = r 1 r 2 ( r 1 2 + t 1 2 ) exp i θ 1 r 1 r 2 exp i θ , t ˜ cav ( θ ) = t 1 t 2 exp i θ / 2 1 r 1 r 2 exp i θ ,
E rec / E 0 = t rec ( 1 r 1 r 2 exp i θ c ) 1 r 1 r 2 exp i θ c + r rec ( r 1 r 2 ( r 1 2 + t 1 2 ) exp i θ c ) exp i θ r ,
Δ υ rec Δ υ cav ( 1 R cav ) / 2 = Δ υ cav / 2 G rec ,
E T / E 0 = t rec t 1 t 2 exp i ( θ r + θ c ) / 2 1 + r rec r 1 exp i θ r r 1 r 2 exp i θ c r rec r 2 ( r 1 2 + t 1 2 ) exp i ( θ r + θ c ) .
θ c = tan 1 { r rec t 1 2 sin θ r r 1 [ 1 + r rec 2 ( r 1 2 + t 1 2 ) ] + r rec ( 2 r 1 2 + t 1 2 ) cos θ r } .

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