Abstract

A collinear photothermal detection bench is described that makes use of a position-modulated heating source instead of the classic power-modulated source. This new modulation scheme increases by almost a factor 2 the sensitivity of a standard mirage bench. This bench is then used to measure the absorption coefficient of OH-free synthetic fused silica at 1064 nm in the parts per 106 range, which, combined with spectrophotometric measurements, confirms that the dominant absorption source is the OH content.

© 2003 Optical Society of America

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References

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  1. W. Winkler, K. Danzmann, A. Rüdiger, R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
    [CrossRef] [PubMed]
  2. K. A. Strain, J. Hough, N. A. Robertson, K. Skeldon, “Measurement of the absorptance of fused silica at λ = 514.5 nm,” Opt. Commun. 117, 385–388 (1995).
    [CrossRef]
  3. P. Y. Baurès, C. N. Man, “Measurements of optical absorption at 1.06 μm in low-loss materials,” Opt. Mat. 2, 241–247 (1993).
    [CrossRef]
  4. T. C. Rich, D. A. Pinnow, “Optical absorption in fused silica and fused quartz at 1.06 μm,” Appl. Opt. 12, 2234 (1973).
    [CrossRef]
  5. W. B. Jackson, N. M. Amer, A. C. Boccara, D. Fournier, “Photothermal deflection spectroscopy and detection,” Appl. Opt. 20, 1333–1344 (1981).
    [CrossRef] [PubMed]
  6. O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
    [CrossRef]
  7. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., E. D. A. Jeffrey, ed. (Academic, London, 1994).
  8. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), p. 130.

1996 (1)

O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[CrossRef]

1995 (1)

K. A. Strain, J. Hough, N. A. Robertson, K. Skeldon, “Measurement of the absorptance of fused silica at λ = 514.5 nm,” Opt. Commun. 117, 385–388 (1995).
[CrossRef]

1993 (1)

P. Y. Baurès, C. N. Man, “Measurements of optical absorption at 1.06 μm in low-loss materials,” Opt. Mat. 2, 241–247 (1993).
[CrossRef]

1991 (1)

W. Winkler, K. Danzmann, A. Rüdiger, R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[CrossRef] [PubMed]

1981 (1)

1973 (1)

Amer, N. M.

Baurès, P. Y.

P. Y. Baurès, C. N. Man, “Measurements of optical absorption at 1.06 μm in low-loss materials,” Opt. Mat. 2, 241–247 (1993).
[CrossRef]

Boccara, A. C.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), p. 130.

Danzmann, K.

W. Winkler, K. Danzmann, A. Rüdiger, R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[CrossRef] [PubMed]

Fabian, H.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[CrossRef]

Fournier, D.

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., E. D. A. Jeffrey, ed. (Academic, London, 1994).

Grzesik, U.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[CrossRef]

Haken, U.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[CrossRef]

Heitmann, W.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[CrossRef]

Hough, J.

K. A. Strain, J. Hough, N. A. Robertson, K. Skeldon, “Measurement of the absorptance of fused silica at λ = 514.5 nm,” Opt. Commun. 117, 385–388 (1995).
[CrossRef]

Humbach, O.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[CrossRef]

Jackson, W. B.

Man, C. N.

P. Y. Baurès, C. N. Man, “Measurements of optical absorption at 1.06 μm in low-loss materials,” Opt. Mat. 2, 241–247 (1993).
[CrossRef]

Pinnow, D. A.

Rich, T. C.

Robertson, N. A.

K. A. Strain, J. Hough, N. A. Robertson, K. Skeldon, “Measurement of the absorptance of fused silica at λ = 514.5 nm,” Opt. Commun. 117, 385–388 (1995).
[CrossRef]

Rüdiger, A.

W. Winkler, K. Danzmann, A. Rüdiger, R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[CrossRef] [PubMed]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., E. D. A. Jeffrey, ed. (Academic, London, 1994).

Schilling, R.

W. Winkler, K. Danzmann, A. Rüdiger, R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[CrossRef] [PubMed]

Skeldon, K.

K. A. Strain, J. Hough, N. A. Robertson, K. Skeldon, “Measurement of the absorptance of fused silica at λ = 514.5 nm,” Opt. Commun. 117, 385–388 (1995).
[CrossRef]

Strain, K. A.

K. A. Strain, J. Hough, N. A. Robertson, K. Skeldon, “Measurement of the absorptance of fused silica at λ = 514.5 nm,” Opt. Commun. 117, 385–388 (1995).
[CrossRef]

Winkler, W.

W. Winkler, K. Danzmann, A. Rüdiger, R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), p. 130.

Appl. Opt. (2)

J. Non-Cryst. Solids (1)

O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann, “Analysis of OH absorption bands in synthetic silica,” J. Non-Cryst. Solids 203, 19–26 (1996).
[CrossRef]

Opt. Commun. (1)

K. A. Strain, J. Hough, N. A. Robertson, K. Skeldon, “Measurement of the absorptance of fused silica at λ = 514.5 nm,” Opt. Commun. 117, 385–388 (1995).
[CrossRef]

Opt. Mat. (1)

P. Y. Baurès, C. N. Man, “Measurements of optical absorption at 1.06 μm in low-loss materials,” Opt. Mat. 2, 241–247 (1993).
[CrossRef]

Phys. Rev. A (1)

W. Winkler, K. Danzmann, A. Rüdiger, R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036 (1991).
[CrossRef] [PubMed]

Other (2)

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., E. D. A. Jeffrey, ed. (Academic, London, 1994).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), p. 130.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the collinear mirage setup. To modulate the pump beam, either a mechanical chopper is inserted between the two mirrors of the periscope or the second periscope mirror is tilted by use of a piezo-motorized mirror holder. The 24-W Nd:YAG pump beam is focused inside the sample by an f = 200 mm lens (L1). The 1-mW He-Ne probe beam is focused by an f = 80 mm lens (L2). An interference filter (F) and a mirror protect the two-quadrant detector (D) from spurious light.

Fig. 2
Fig. 2

(a) Theoretical and (b) experimental mirage signal amplitude (solid curves) chopped-pump beam and (dashed curves) position-modulated pump beam.

Fig. 3
Fig. 3

Typical mirage signal recorded with (a) a position-modulated and (b) a chopped pump beam. The sample absorption is α = 0.6 ppm/cm. The absorption is calculated by comparison of these data to those for the same measurement performed with a reference sample.

Fig. 4
Fig. 4

Absorption coefficient versus OH content in various Suprasil 311 and Suprasil 311SV samples.

Fig. 5
Fig. 5

Geometry of the beams inside the samples projected on the xOy, xOz, and yOz planes. The average distance between the probe beam and the oscillating pump beam is x, x 0 is the amplitude of the pump beam oscillations, and β is the angle between the two beams.

Equations (49)

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θopt=2 0.597wf,
ω  D/w2,
ϕ=-1ndndTαP0κ1sin βDω12π gx,
gx=-8ixw3exp-2x2w2;
gx=i 8w3exp-2x2w2exp-x02w2p=0-1pIpx02w2-Ip+1x02w2x0I2p4x0xw2-2xI2p+14x0xw2+x0I2p+24x0xw2.
δP  VαVdcηprobeηpump Pprobe,
l2wsin β.
OHppm43×10-6 αcm-1
2T-iωD T+1κ Pω=0,
Θ2π-3/2 T exp ixλx+yλy+zλzdxdydz,
T=2π-3/2 Θ exp-ixλx+yλy+zλzdλxdλydλz.
Πω=2π-3/2 Pω exp ixλx+yλy+zλzdxdydz.
q2=λx2+λy2+λz2+iωD
-q2Θ+1κ Πω=0.
Pωx, y, z=αP02πw2exp-2y2w2exp-2w2x-x0 cos ωt2.
Pωx, y, z=α 2π P02πw2exp-2x2+y2w2.
Pωx, y, z=αP02πw2exp-2x2+y2w2×exp-x02w2exp4x0xw2cosωt×exp-x02w2cos2ωt.
exp4x0xw2cosωt=J0-i 4x0xw2+2 p=1 ipJp-i 4x0xw2×cospωt,exp-x02w2cos2ωt=J0i x02w2+2 p=1 ipJpi x02w2×cos2pωt,
exp4x0xw2cosωt=I04x0xw2+2 p=1 Ip4x0xw2cospωt,exp-x02w2cos2ωt=I0x02w2+2 p=1-1pIpx02w2×cos2pωt.
2I0x02w2I14x0xw2-2I1x02w2I14x0xw2,-2I1x02w2I34x0xw2+2I2x02w2I34x0xw2,+2I2x02w2I54x0xw2-2I3x02w2I54x0xw2 .
Γpx02w2=Ipx02w2-Ip+1x02w2,
2 p=0-1pΓpI2p+14x0xw2.
Πω=2παP0Φλxλyδλz,
Φλx=2 exp-x02w2p=0-1pΓpx02w2×F2πw2exp-2x2w2I2p+14x0xw2,
λy=F2πw2exp-2y2w2=12πexp-w2λy28,
ϕ=1ndndT-+Txds,
ϕ=1ndndT-+Tx, s sin βxds,
ϕ=1ndndT-+2π-3/2  -iλxθ exp-ixλx+yλy+zλzdλxdλydλzds,
θλx, λy=1κq22παP0Φλxλy
 Θ exp-izλzdλz=θλx, λy2π F-1δλz=θλx, λy.
ϕ=-indndTαP0κ12π-+ λxΦλxλyq2exp-ixλx+s sin βλydλxdλyds.
-+exp-is sin βλyds=2πsin β F-11=2πsin β δλy,
ϕ=-indndTαP0κ0sin β-+λxλx2+iω/D×Φλxexp-ixλxdλx.
0=12π.
ϕ=-1ndndTαP0κ1sin βDω12π×-+ λxΦλxexp-ixλxdλx.
- Φλxλx exp-iλxxdλx=2 exp-x02w2p=0-1pΓpx02w2×- F2πw2exp-2x2w2I2p+14x0xw2×λx exp-iλxxdλx.
f * gλ=12π- fλ-ξgξdξ.
F2πw2exp-2x2w2=λx,
- Φλxλx exp-iλxxdλx=2 exp-x02w2p=0-1pΓpx02w2×- * Ω2p+1λxλx exp-iλxxdλx,
Ω2p+1λx=FI2p+14x0xw2.
- * Ω2p+1λxλx exp-iλxxdλx=-12π- λx-αΩ2p+1αdα×λx exp-iλxxdλx=12π- Ω2p+1α- λx-αλx exp-iλxxdλxdα=12π- Ω2p+1α×- ξξ+αexp-iξ+αxdξdα=12π- Ω2p+1αexp-iαx×- ξξ+αexp-iξxdξdα,
- ξξ+αexp-iξxdξ=- ξξ exp-iξxdξ+α - ξexp-iξxdξ=-8ixw3exp-2x2w2+α 2wexp-2x2w2=2wexp-2x2w2-4ixw2+α.
- * Ω2p+1λxλx exp-iλxxdλx =12π2wexp-2x2w2-4ixw2×- Ω2p+1αexp-iαxdα+- Ω2p+1αα exp-iαxdα =12π2wexp-2x2w2-4ixw2×- Ω2p+1αexp-iαxdα+i ddx- Ω2p+1αexp-iαxdα,
- Ω2p+1αexp-iαxdα=2π F-1Ω2p+1=2πI2p+14x0xw2
dI2p+1zdz=12I2p+2z+I2pzddx I2p+14x0xw2=2x0w2I2p+24x0xw2+I2p4x0xw2,
- * Ωλxλx exp-iλxxdλx=i 4w3exp-2x2w2×x0I2p4x0xw2-2xI2p+14x0xw2+x0I2p+24x0xw2.
- Φλxλx exp-iλxxdλx=i 8w3exp-2x2w2exp-x02w2×p=0-1pΓpx02w2x0I2p4x0xw2-2xI2p+14x0xw2+x0I2p+24x0xw2.
ϕ=-1ndndTαP0κ1sin βDω12π gx,
gx=i 8w3exp-2x2w2exp-x02w2p=0-1pIpx02w2-Ip+1x02w2x0I2p4x0xw2-2xI2p+14x0xw2+x0I2p+24x0xw2.

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