Abstract

Absorption of laser beam power in optical elements induces thermal gradients that may cause unwanted phase aberrations. In precision measurement applications, such as laser interferometric gravitational-wave detection, corrective measures that require mechanical contact with or attachments to the optics are precluded by noise considerations. We describe a radiative thermal corrector that can counteract thermal lensing and (or) thermoelastic deformation induced by coating and substrate absorption of collimated Gaussian beams. This radiative system can correct anticipated distortions to a high accuracy, at the cost of an increase in the average temperature of the optic. A quantitative analysis and parameter optimization is supported by results from a simplified proof-of-principle experiment, demonstrating the method’s feasibility for our intended application.

© 2004 Optical Society of America

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  1. A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
    [CrossRef] [PubMed]
  2. E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, “LIGO Scientific Collaboration (LSC) white paper on detector research and development,” (California Institute of Technology, Pasadena, Calif., 1999), http://www.ligo.caltech.edu/docs/T/T990080-00.pdf .
  3. W. Winkler, K. Danzmann, A. Rüdiger, and R. Schilling, Phys. Rev. A 44, 7022 (1991).
    [CrossRef] [PubMed]
  4. R. C. Lawrence, “Active wavefront correction in laser interferometric gravitational wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 2003), http://www.ligo.caltech.edu/docs/P/P030001-00.pdf .
  5. R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
    [CrossRef]
  6. P. Hello and J. Vinet, J. Phys. (France) 51, 1267 (1990).
  7. P. Hello and J. Vinet, J. Phys. (France) 51, 2243 (1990).
  8. H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
    [CrossRef]

2002

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
[CrossRef]

2000

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

1992

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

1991

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

1990

P. Hello and J. Vinet, J. Phys. (France) 51, 1267 (1990).

P. Hello and J. Vinet, J. Phys. (France) 51, 2243 (1990).

Abramovici, A.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Althouse, W.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Aufmuth, P.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Danzmann, K.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

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

Drever, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Fritschel, P.

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
[CrossRef]

Gürsel, Y.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Gustafson, E.

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, “LIGO Scientific Collaboration (LSC) white paper on detector research and development,” (California Institute of Technology, Pasadena, Calif., 1999), http://www.ligo.caltech.edu/docs/T/T990080-00.pdf .

Hello, P.

P. Hello and J. Vinet, J. Phys. (France) 51, 1267 (1990).

P. Hello and J. Vinet, J. Phys. (France) 51, 2243 (1990).

Kawamura, S.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Lawrence, R.

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
[CrossRef]

Lawrence, R. C.

R. C. Lawrence, “Active wavefront correction in laser interferometric gravitational wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 2003), http://www.ligo.caltech.edu/docs/P/P030001-00.pdf .

Lück, H.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Marfuta, P.

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
[CrossRef]

Müller, K.-O.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Raab, F.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Rüdiger, A.

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

Schilling, R.

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

Shoemaker, D.

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
[CrossRef]

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, “LIGO Scientific Collaboration (LSC) white paper on detector research and development,” (California Institute of Technology, Pasadena, Calif., 1999), http://www.ligo.caltech.edu/docs/T/T990080-00.pdf .

Sievers, L.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Spiro, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Strain, K.

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, “LIGO Scientific Collaboration (LSC) white paper on detector research and development,” (California Institute of Technology, Pasadena, Calif., 1999), http://www.ligo.caltech.edu/docs/T/T990080-00.pdf .

Thorne, K.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Vinet, J.

P. Hello and J. Vinet, J. Phys. (France) 51, 2243 (1990).

P. Hello and J. Vinet, J. Phys. (France) 51, 1267 (1990).

Vogt, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Weiss, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, “LIGO Scientific Collaboration (LSC) white paper on detector research and development,” (California Institute of Technology, Pasadena, Calif., 1999), http://www.ligo.caltech.edu/docs/T/T990080-00.pdf .

Whitcomb, S.

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Winkler, W.

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

Zucker, M.

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
[CrossRef]

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Class. Quantum Grav.

R. Lawrence, M. Zucker, P. Fritschel, P. Marfuta, and D. Shoemaker, Class. Quantum Grav. 19, 1803 (2002).
[CrossRef]

J. Phys. (France)

P. Hello and J. Vinet, J. Phys. (France) 51, 1267 (1990).

P. Hello and J. Vinet, J. Phys. (France) 51, 2243 (1990).

Opt. Commun.

H. Lück, K.-O. Müller, P. Aufmuth, and K. Danzmann, Opt. Commun. 175, 275 (2000).
[CrossRef]

Phys. Rev. A

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

Science

A. Abramovici, W. Althouse, R. Drever, Y. Gürsel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spiro, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Other

E. Gustafson, D. Shoemaker, K. Strain, and R. Weiss, “LIGO Scientific Collaboration (LSC) white paper on detector research and development,” (California Institute of Technology, Pasadena, Calif., 1999), http://www.ligo.caltech.edu/docs/T/T990080-00.pdf .

R. C. Lawrence, “Active wavefront correction in laser interferometric gravitational wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 2003), http://www.ligo.caltech.edu/docs/P/P030001-00.pdf .

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Figures (3)

Fig. 1
Fig. 1

Cross-sectional view of shielded heating ring thermal compensation of absorption-induced aberrations in a transmissive optical element.

Fig. 2
Fig. 2

Setup of the heating ring experiment. The probe examines the test optic in transmission, and the pump shines on the far optical surface.

Fig. 3
Fig. 3

Results of the shielded heating ring test. (a) Raw pump-induced optical path distortion due to 50 mW of 10.6µm pump power delivered in a Gaussian profile of 1.5-cm radius. (b) Residual optical path distortion after optimization of the heater current. The contour interval in both plots is 2 nm. The calculated scattered power from a 1.06µm-wavelength TEM00 Gaussian beam of 1.5-cm radius is given at the top of each diagram. (c) Points from both maps are replotted as a function of radial coordinate and superimposed on our model’s prediction (solid curve). The dashed curves show the envelope of the predicted result if the heating ring is an ellipse with eccentricity 0.2.

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