Abstract

We present a method for measuring absorption at the 1 × 10-5 cm-1 level in high-quality optical materials. Using a Shack-Hartmann wave-front detector, thermal lensing in these materials may be measured. Then, the absorption coefficient may be estimated by fitting the observed deformation to a thermal lensing model based on the temperature dependences of the refractive index and the thermal expansion coefficient. For a particular sample of fused silica, the absorption coefficient was determined to be 1.8 ± 0.4 × 10-5 cm-1. Obtaining this result requires a resolution in the optical path length better than ±0.1 nm.

© 2003 Optical Society of America

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  1. A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
    [CrossRef] [PubMed]
  2. K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
    [CrossRef]
  3. D. E. McClelland, J. B. Camp, J. Mason, W. Kells, S. E. Whitcomb, “Arm cavity resonant sideband control for laser interferometric gravitational wave detectors,” Opt. Lett. 24, 1014–1016 (1999).
    [CrossRef]
  4. Claude Boccara, Laboratoire d’Optique Physique, Paris, France (private communication, 1998).
  5. D. Bunimovich, E. Belotserkovsky, L. Nagli, A. Katzir, “Measurements of absorption coefficients using noncontact fiber-optic laser calorimetry,” Appl. Opt. 34, 743–745 (1995).
    [CrossRef] [PubMed]
  6. D. Bunimovich, L. Nagli, A. Katzir, “Absorption measurements of mixed silver halide crystals and fibers by laser calorimetry,” Appl. Opt. 33, 117–119 (1994).
    [CrossRef] [PubMed]
  7. D. R. Neal, D. J. Armstrong, W. T. Turner, “Wavefront sensors for control and processing monitoring in optics manufacture,” in Laser as Tool for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 211–220 (1997).
    [CrossRef]
  8. J. D. Mansell, J. Hennawi, E. K. Gustafson, “Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensor,” Appl. Opt. 40, 366–374 (2001).
    [CrossRef]
  9. CLAS2D Operation Manual, Revision 1.50a (WaveFront Sciences, Inc., Albuquerque, N. Mex., 1999), p. 69.
  10. Quartz Glass for Optics, Optical Properties (Heraeus, Hanau, Germany, 1994).
  11. See for example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976), chaps. 2 and 3.
  12. Darren Armstrong, WaveFront Sciences, Inc., 14810 Central Avenue NW, Albuquerque, N. Mex. 87123-3905 (private communication, 1998).
  13. R. Beausoleil, Edward L. Ginzton Laboratory, Stanford University, Stanford, Calif. 94305 (private communication, 2000).

2001 (1)

1999 (1)

1995 (1)

1994 (2)

D. Bunimovich, L. Nagli, A. Katzir, “Absorption measurements of mixed silver halide crystals and fibers by laser calorimetry,” Appl. Opt. 33, 117–119 (1994).
[CrossRef] [PubMed]

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

1992 (1)

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Abramovici, A.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Althouse, W.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Armstrong, D. J.

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wavefront sensors for control and processing monitoring in optics manufacture,” in Laser as Tool for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 211–220 (1997).
[CrossRef]

Armstrong, Darren

Darren Armstrong, WaveFront Sciences, Inc., 14810 Central Avenue NW, Albuquerque, N. Mex. 87123-3905 (private communication, 1998).

Beausoleil, R.

R. Beausoleil, Edward L. Ginzton Laboratory, Stanford University, Stanford, Calif. 94305 (private communication, 2000).

Belotserkovsky, E.

Boccara, Claude

Claude Boccara, Laboratoire d’Optique Physique, Paris, France (private communication, 1998).

Bunimovich, D.

Camp, J. B.

Danzmann, K.

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Drever, R. W. P.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Gursel, Y.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Gustafson, E. K.

Hennawi, J.

Katzir, A.

Kawamura, S.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Kells, W.

Mansell, J. D.

Mason, J.

McClelland, D. E.

Mizuno, J.

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Nagli, L.

Neal, D. R.

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wavefront sensors for control and processing monitoring in optics manufacture,” in Laser as Tool for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 211–220 (1997).
[CrossRef]

Nelson, P.

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Raab, F. J.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Rüdiger, A.

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Schilling, R.

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Shoemaker, D.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Sievers, L.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Spero, R. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Strain, K.

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Thorne, K.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Turner, W. T.

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wavefront sensors for control and processing monitoring in optics manufacture,” in Laser as Tool for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 211–220 (1997).
[CrossRef]

Vogt, R. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Weiss, R.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Whitcomb, S. E.

D. E. McClelland, J. B. Camp, J. Mason, W. Kells, S. E. Whitcomb, “Arm cavity resonant sideband control for laser interferometric gravitational wave detectors,” Opt. Lett. 24, 1014–1016 (1999).
[CrossRef]

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Winkler, W.

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Yariv, A.

See for example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976), chaps. 2 and 3.

Zucker, M. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Appl. Opt. (3)

Opt. Lett. (1)

Phys. Lett. A. (1)

K. Strain, K. Danzmann, J. Mizuno, P. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A. 194, 124–132 (1994).
[CrossRef]

Science (1)

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Other (7)

Claude Boccara, Laboratoire d’Optique Physique, Paris, France (private communication, 1998).

CLAS2D Operation Manual, Revision 1.50a (WaveFront Sciences, Inc., Albuquerque, N. Mex., 1999), p. 69.

Quartz Glass for Optics, Optical Properties (Heraeus, Hanau, Germany, 1994).

See for example, A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976), chaps. 2 and 3.

Darren Armstrong, WaveFront Sciences, Inc., 14810 Central Avenue NW, Albuquerque, N. Mex. 87123-3905 (private communication, 1998).

R. Beausoleil, Edward L. Ginzton Laboratory, Stanford University, Stanford, Calif. 94305 (private communication, 2000).

D. R. Neal, D. J. Armstrong, W. T. Turner, “Wavefront sensors for control and processing monitoring in optics manufacture,” in Laser as Tool for Manufacturing II, L. R. Migliore, R. D. Schaeffer, eds., Proc. SPIE2993, 211–220 (1997).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. Dichroic mirrors are highly reflective at 1.06 µm and partially transmissive at 633 nm. z = 0 is the waist location of the probe beam. z = zf = 4.62 m, and z = zobs = 4.84 m denote the locations of the sample and the image plane of the SHWD, respectively.

Fig. 2
Fig. 2

Schematic view of lenslet and detector arrays in the SHWD.

Fig. 3
Fig. 3

Schematic view of the relationship between the displacement of focal point on the detector plane (δ) and the change in the wavelength slope. The dashed curve represents the reference wavefront and the solid line represents the data wave front.

Fig. 4
Fig. 4

Sample 10-W and 0-W data.

Fig. 5
Fig. 5

The points are the averaged wave front at 10 W. The lower dotted curve shows the calculated wave front for an absorption coefficient of 1.2 × 10-5 cm-1; the upper dotted curve is for 2.2 × 10-5 cm-1.

Tables (1)

Tables Icon

Table 1 Numbers Used to Estimate the Absorption Coefficient

Equations (8)

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ΔTr=Pγl4πκi=0-1i2 r2w2iii!,
ΔOPL=0.07741 PγlκdndT+αn×rw2+0.4rw,
Robs10W=1Rf-1f1+Δz1Rf-1f+Δzλπwf222+λπwf221Rf-1f2+λπwf221Rf-1f1+Δz1Rf-1f+Δzλπwf22,
Robs0W=1Rf1+ΔzRf+Δzλπwf222+λπwf221Rf2+λπwf22 1Rf1+ΔzRf+Δzλπwf22.
ΔOPLobs1feff=1Robs0W-1Robs10W,
dndT1K
α1K
κWmK

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