Abstract

We report on a novel high-sensitivity method to characterize and improve mode matching into optical cavities. This method is based on heterodyne detection of cylindrical transverse cavity modes. A specially designed annular-segmented photodiode is used to measure the amplitude of nonresonant modes reflected by the cavity. Our measurements allow us to optimize cavity mode matching to nearly 99.98% and will play an important diagnostic role in gravitational-wave detectors.

© 2000 Optical Society of America

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References

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  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]
  2. D. Z. Anderson, Appl. Opt. 23, 2944 (1984).
    [CrossRef]
  3. N. M. Sampas and D. Z. Anderson, Appl. Opt. 29, 394 (1990).
    [CrossRef] [PubMed]
  4. Y. Hefetz, N. Mavalvala, and D. Sigg, J. Opt. Soc. Am. B 14, 1597 (1997).
    [CrossRef]
  5. N. Mavalvala, D. Sigg, and D. Shoemaker, Appl. Opt. 37, 7743 (1998).
    [CrossRef]
  6. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, Appl. Opt. 33, 5041 (1994).
    [CrossRef] [PubMed]
  7. A. Abramovici and the LIGO group, Science 256, 325 (1992).
    [CrossRef] [PubMed]
  8. B. Caron and the VIRGO group, Class. Quantum Gravity 14, 1461 (1997).
  9. W. Winkler, K. Danzmann, A. Ruediger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
    [CrossRef] [PubMed]
  10. D. E. McClelland, J. B. Camp, J. Mason, W. Kells, and S. E. Whitcomb, Opt. Lett. 24, 1014 (1999).
    [CrossRef]
  11. B. Willke, N. Uehara, E. K. Gustafson, R. L. Byer, P. J. King, S. U. Steel, and R. L. Savage, Opt. Lett. 23, 1704 (1998).
    [CrossRef]
  12. N. Mavalvala, “Alignment issues in Laser Interferometric Gravitational-Wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1997).
  13. A. Siegman, Lasers (University Science, Sausalito, Calif., 1986).
  14. D. Shaddock, Department of Physics, Australian National University, Acton ACT 0200, Australia (personal communication, 1999).
  15. B. Willke, Institut für Atom- und Molekühlphysik, Callinstrasse 38, D-30167 Hannover, Germany (personal communication, 1999).

1999 (1)

1998 (2)

1997 (2)

Y. Hefetz, N. Mavalvala, and D. Sigg, J. Opt. Soc. Am. B 14, 1597 (1997).
[CrossRef]

B. Caron and the VIRGO group, Class. Quantum Gravity 14, 1461 (1997).

1994 (1)

1992 (1)

A. Abramovici and the LIGO group, Science 256, 325 (1992).
[CrossRef] [PubMed]

1991 (1)

W. Winkler, K. Danzmann, A. Ruediger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
[CrossRef] [PubMed]

1990 (1)

1984 (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]

Abramovici, A.

A. Abramovici and the LIGO group, Science 256, 325 (1992).
[CrossRef] [PubMed]

Anderson, D. Z.

Byer, R. L.

Camp, J. B.

Caron, B.

B. Caron and the VIRGO group, Class. Quantum Gravity 14, 1461 (1997).

Danzmann, K.

W. Winkler, K. Danzmann, A. Ruediger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
[CrossRef] [PubMed]

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]

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]

Hefetz, Y.

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]

Kells, W.

King, P. J.

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]

Mason, J.

Mavalvala, N.

N. Mavalvala, D. Sigg, and D. Shoemaker, Appl. Opt. 37, 7743 (1998).
[CrossRef]

Y. Hefetz, N. Mavalvala, and D. Sigg, J. Opt. Soc. Am. B 14, 1597 (1997).
[CrossRef]

N. Mavalvala, “Alignment issues in Laser Interferometric Gravitational-Wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1997).

McClelland, D. E.

Meers, B. J.

Morrison, E.

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]

Robertson, D. I.

Ruediger, A.

W. Winkler, K. Danzmann, A. Ruediger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
[CrossRef] [PubMed]

Sampas, N. M.

Savage, R. L.

Schilling, R.

W. Winkler, K. Danzmann, A. Ruediger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
[CrossRef] [PubMed]

Shaddock, D.

D. Shaddock, Department of Physics, Australian National University, Acton ACT 0200, Australia (personal communication, 1999).

Shoemaker, D.

Siegman, A.

A. Siegman, Lasers (University Science, Sausalito, Calif., 1986).

Sigg, D.

Steel, S. U.

Uehara, N.

Ward, H.

E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, Appl. Opt. 33, 5041 (1994).
[CrossRef] [PubMed]

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]

Whitcomb, S. E.

Willke, B.

B. Willke, N. Uehara, E. K. Gustafson, R. L. Byer, P. J. King, S. U. Steel, and R. L. Savage, Opt. Lett. 23, 1704 (1998).
[CrossRef]

B. Willke, Institut für Atom- und Molekühlphysik, Callinstrasse 38, D-30167 Hannover, Germany (personal communication, 1999).

Winkler, W.

W. Winkler, K. Danzmann, A. Ruediger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
[CrossRef] [PubMed]

Appl. Opt. (4)

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]

Class. Quantum Gravity (1)

B. Caron and the VIRGO group, Class. Quantum Gravity 14, 1461 (1997).

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. A (1)

W. Winkler, K. Danzmann, A. Ruediger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
[CrossRef] [PubMed]

Science (1)

A. Abramovici and the LIGO group, Science 256, 325 (1992).
[CrossRef] [PubMed]

Other (4)

N. Mavalvala, “Alignment issues in Laser Interferometric Gravitational-Wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1997).

A. Siegman, Lasers (University Science, Sausalito, Calif., 1986).

D. Shaddock, Department of Physics, Australian National University, Acton ACT 0200, Australia (personal communication, 1999).

B. Willke, Institut für Atom- und Molekühlphysik, Callinstrasse 38, D-30167 Hannover, Germany (personal communication, 1999).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for measuring mode matching showing the incoming field, the EOM, lenses L1 and L2 for mode matching, wave plate λ/4, polarizer Pol, the cavity, two beam splitters BS, photodiode PD for length control, and the two BPD’s. The Gouy-phase telescopes (L4, L5) and (L6, L7) match the Gouy phases and the size of the beams to the detectors. Inset, geometry of the BPD’s and the fundamental and higher-order field eigenmodes. Stab., signal used to stabilize the frequency of the laser onto the eigenfrequency of the cavity.

Fig. 2
Fig. 2

Experimental (filled circles) and theoretical (lines) demodulated signals for various combinations of lens positions. The demodulated signals are scaled to be proportional to the real part (D2) and the imaginary part (D1) of the amplitude b of the laser field in the second-order Hermite–Gaussian eigenmode of the cavity.

Equations (5)

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

U00=Uˆ00-bUˆ20+Uˆ02,
b=δw2wˆ+iδz2zˆR,
SsinΩtImrFPA1Uˆ002-A0Uˆ002+b*1-rFPA1Uˆ00Uˆ20*+Uˆ02*-A0Uˆ00Uˆ20*+Uˆ02*,
D1=A11-rFPImbδz,
D2=A21-rFPRebδw,

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