Abstract

Thermal lens measurements were made by means of a high-accuracy phase shift interferometer that combines a λ/1000 sensitivity and 10 µm transverse resolution. The effect of random small-scale modulation in thermally induced phase distortion predicted earlier was proved experimentally. The statistical parameters of modulation were measured depending on heating power for two different ceramic samples. The experimental data agree well with results of numerical simulation.

© 2008 Optical Society of America

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References

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  1. K. Ueda, "Ceramic lasers for IFE power plant," in Proceedings of International Conference on Lasers, Applications, and Technologies, St. Petersburg, p. LWG2 (2005).
  2. E. A. Khazanov, "Thermally induced birefringence in Nd:YAG ceramics," Opt. Lett. 27, 716-718 (2002).
    [CrossRef]
  3. M. A. Kagan and E. A. Khazanov, "Compensation for thermally induced birefringence in polycrystalline ceramic active elements," Quantum Electron. 33, 876-882 (2003).
    [CrossRef]
  4. I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
    [CrossRef] [PubMed]
  5. I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, "Properties of a thermal lens in laser ceramics," Quantum Electron. 37, 633-638 (2007).
    [CrossRef]
  6. I. L. Snetkov, A. A. Soloviev, and E. A. Khazanov, "Investigation of a thermal lens in thin disks of laser ceramics," Quantum Electron. (to be published).
  7. V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, "High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements," Appl. Opt. 45, 4092-4101 (2006).
    [CrossRef] [PubMed]
  8. A. A. Soloviev, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, "Compensation for thermally induced aberrations in optical elements by means of additional heating by CO2 laser radiation," Quantum Electron. 36, 939-945 (2006).
    [CrossRef]
  9. P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
    [CrossRef]
  10. O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
    [CrossRef]
  11. CaF2 Product Information Sheet (Corning Incorporated, 2003). http://www.corning.com/docs/specialtymaterials/pisheets/H0607_CaF2_Product_Sheet.pdf
  12. L. N. Soms and A. A. Tarasov, "Thermal deformation in color-center laser active elements. 1. Theoty," Sov. J. Quantum Electron. 9, 1506-1508 (1979).
    [CrossRef]
  13. Data Sheet for Calcium Fluoride (SCHOTT Lithotec, 2006). http://www.us.schott.com/lithotec/english/download/caf2_june_2006_final_us.pdf
  14. J. H. Burnett, "Stress-optical coefficients of 157 nm materials," Sematech 157 nm Tech. Data Rev., (Maryland, 2001) http://www.sematech.org/meetings/archives/litho/157/20011212/POSTER-Burnett-Metrology.pdf

2007 (3)

I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, "Properties of a thermal lens in laser ceramics," Quantum Electron. 37, 633-638 (2007).
[CrossRef]

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

2006 (2)

V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, "High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements," Appl. Opt. 45, 4092-4101 (2006).
[CrossRef] [PubMed]

A. A. Soloviev, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, "Compensation for thermally induced aberrations in optical elements by means of additional heating by CO2 laser radiation," Quantum Electron. 36, 939-945 (2006).
[CrossRef]

2005 (1)

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
[CrossRef] [PubMed]

2003 (1)

M. A. Kagan and E. A. Khazanov, "Compensation for thermally induced birefringence in polycrystalline ceramic active elements," Quantum Electron. 33, 876-882 (2003).
[CrossRef]

2002 (1)

1979 (1)

L. N. Soms and A. A. Tarasov, "Thermal deformation in color-center laser active elements. 1. Theoty," Sov. J. Quantum Electron. 9, 1506-1508 (1979).
[CrossRef]

Aung, Y. L.

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
[CrossRef] [PubMed]

Basiev, T.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Basiev, T. T.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

Dukel'ski, K.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Dukel'skii, K. V.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

Fedorov, P.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Fedorov, P. P.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

Ikesue, A.

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
[CrossRef] [PubMed]

Kagan, M. A.

M. A. Kagan and E. A. Khazanov, "Compensation for thermally induced birefringence in polycrystalline ceramic active elements," Quantum Electron. 33, 876-882 (2003).
[CrossRef]

Kamenetsky, E. E.

Khazanov, E. A.

I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, "Properties of a thermal lens in laser ceramics," Quantum Electron. 37, 633-638 (2007).
[CrossRef]

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, "High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements," Appl. Opt. 45, 4092-4101 (2006).
[CrossRef] [PubMed]

A. A. Soloviev, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, "Compensation for thermally induced aberrations in optical elements by means of additional heating by CO2 laser radiation," Quantum Electron. 36, 939-945 (2006).
[CrossRef]

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
[CrossRef] [PubMed]

M. A. Kagan and E. A. Khazanov, "Compensation for thermally induced birefringence in polycrystalline ceramic active elements," Quantum Electron. 33, 876-882 (2003).
[CrossRef]

E. A. Khazanov, "Thermally induced birefringence in Nd:YAG ceramics," Opt. Lett. 27, 716-718 (2002).
[CrossRef]

I. L. Snetkov, A. A. Soloviev, and E. A. Khazanov, "Investigation of a thermal lens in thin disks of laser ceramics," Quantum Electron. (to be published).

Kozhevatov, I. E.

A. A. Soloviev, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, "Compensation for thermally induced aberrations in optical elements by means of additional heating by CO2 laser radiation," Quantum Electron. 36, 939-945 (2006).
[CrossRef]

V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, "High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements," Appl. Opt. 45, 4092-4101 (2006).
[CrossRef] [PubMed]

Mironov, I.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Mironov, I. A.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

Mukhin, I. B.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, "Properties of a thermal lens in laser ceramics," Quantum Electron. 37, 633-638 (2007).
[CrossRef]

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
[CrossRef] [PubMed]

Osiko, V.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Osiko, V. V.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

Palashov, O. V.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, "Properties of a thermal lens in laser ceramics," Quantum Electron. 37, 633-638 (2007).
[CrossRef]

V. V. Zelenogorsky, A. A. Solovyov, I. E. Kozhevatov, E. E. Kamenetsky, E. A. Rudenchik, O. V. Palashov, D. E. Silin, and E. A. Khazanov, "High-precision methods and devices for in situ measurements of thermally induced aberrations in optical elements," Appl. Opt. 45, 4092-4101 (2006).
[CrossRef] [PubMed]

A. A. Soloviev, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, "Compensation for thermally induced aberrations in optical elements by means of additional heating by CO2 laser radiation," Quantum Electron. 36, 939-945 (2006).
[CrossRef]

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
[CrossRef] [PubMed]

Popov, P.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Rudenchik, E. A.

Silin, D. E.

Smirnov, A.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Smirnov, A. N.

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

Smolyanski, P.

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Snetkov, I. L.

I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, "Properties of a thermal lens in laser ceramics," Quantum Electron. 37, 633-638 (2007).
[CrossRef]

I. L. Snetkov, A. A. Soloviev, and E. A. Khazanov, "Investigation of a thermal lens in thin disks of laser ceramics," Quantum Electron. (to be published).

Soloviev, A. A.

A. A. Soloviev, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, "Compensation for thermally induced aberrations in optical elements by means of additional heating by CO2 laser radiation," Quantum Electron. 36, 939-945 (2006).
[CrossRef]

I. L. Snetkov, A. A. Soloviev, and E. A. Khazanov, "Investigation of a thermal lens in thin disks of laser ceramics," Quantum Electron. (to be published).

Solovyov, A. A.

Soms, L. N.

L. N. Soms and A. A. Tarasov, "Thermal deformation in color-center laser active elements. 1. Theoty," Sov. J. Quantum Electron. 9, 1506-1508 (1979).
[CrossRef]

Tarasov, A. A.

L. N. Soms and A. A. Tarasov, "Thermal deformation in color-center laser active elements. 1. Theoty," Sov. J. Quantum Electron. 9, 1506-1508 (1979).
[CrossRef]

Zelenogorsky, V. V.

Appl. Opt. (1)

Doklady Phys. (1)

P. Popov, K.  Dukel'ski, I.  Mironov, A.  Smirnov, P.  Smolyanski, P.  Fedorov, V.  Osiko, T. Basiev, "Thermal Conductivity of CaF2 Optical Ceramic," Doklady Phys. 52, 7-9 (2007).
[CrossRef]

Opt. Express. (1)

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. Ikesue, and Y. L. Aung, "Experimental study of thermally induced depolarization in Nd:YAG ceramics," Opt. Express. 13, 5983-5987 (2005).
[CrossRef] [PubMed]

Opt. Lett. (1)

Quantum Electron. (5)

M. A. Kagan and E. A. Khazanov, "Compensation for thermally induced birefringence in polycrystalline ceramic active elements," Quantum Electron. 33, 876-882 (2003).
[CrossRef]

O. V. Palashov, E. A. Khazanov, I. B. Mukhin, I. A. Mironov, A. N. Smirnov, K. V. Dukel'skii, P. P. Fedorov, V. V. Osiko, and T. T. Basiev, "Comparison of the optical parametersof a CaF2 single crystal and optical ceramics," Quantum Electron. 37, 27-28 (2007).
[CrossRef]

I. L. Snetkov, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, "Properties of a thermal lens in laser ceramics," Quantum Electron. 37, 633-638 (2007).
[CrossRef]

I. L. Snetkov, A. A. Soloviev, and E. A. Khazanov, "Investigation of a thermal lens in thin disks of laser ceramics," Quantum Electron. (to be published).

A. A. Soloviev, I. E. Kozhevatov, O. V. Palashov, and E. A. Khazanov, "Compensation for thermally induced aberrations in optical elements by means of additional heating by CO2 laser radiation," Quantum Electron. 36, 939-945 (2006).
[CrossRef]

Sov. J. Quantum Electron. (1)

L. N. Soms and A. A. Tarasov, "Thermal deformation in color-center laser active elements. 1. Theoty," Sov. J. Quantum Electron. 9, 1506-1508 (1979).
[CrossRef]

Other (4)

Data Sheet for Calcium Fluoride (SCHOTT Lithotec, 2006). http://www.us.schott.com/lithotec/english/download/caf2_june_2006_final_us.pdf

J. H. Burnett, "Stress-optical coefficients of 157 nm materials," Sematech 157 nm Tech. Data Rev., (Maryland, 2001) http://www.sematech.org/meetings/archives/litho/157/20011212/POSTER-Burnett-Metrology.pdf

K. Ueda, "Ceramic lasers for IFE power plant," in Proceedings of International Conference on Lasers, Applications, and Technologies, St. Petersburg, p. LWG2 (2005).

CaF2 Product Information Sheet (Corning Incorporated, 2003). http://www.corning.com/docs/specialtymaterials/pisheets/H0607_CaF2_Product_Sheet.pdf

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Figures (8)

Fig. 1.
Fig. 1.

Scheme of experimental setup : 1 - CO2 laser, 2 -semitransparent salt wedge, 3 - power meter, 4–5 - spherical mirrors, 6 -chopper, 7 - alignment diode source, 8 - sample under study, 9–10 metallic mirrors, 11 - absorber, 12 - probe radiation source, 13 - speckle fission unit, 14 - CCD-camera, 15, 18, 19 - lenses, 16 -wave front conjugation unit, 17 - reference plate, 20 - semitransparent mirror, 21 - aperture

Fig. 2.
Fig. 2.

Possible variants of interferometric measurements. S1 and S2 are sample surfaces. Doubled incident beam is presented with red solid and blue dashed lines. The reflections of the probe beam are marked by the following characters: a - from the reference plate, b - from the front surface, c - from the rear surface.

Fig. 3.
Fig. 3.

Typical ‘cold’ profiles of the ceramic sample at bulk a) and surface b) measurements.

Fig. 4.
Fig. 4.

Crossections of typical ‘cold’ profiles of the ceramic sample at bulk a) and surface b) measurements with the parabolic fitting superpose.

Fig. 5.
Fig. 5.

The dependence of thermally induced thermolens in ceramics on heating power for bulk (solid line) and surface (dash line) measurements.

Fig. 6.
Fig. 6.

Differential phase distortions in single crystalline (a) and ceramic (b) element at bulk measurements.

Fig. 7.
Fig. 7.

The differences of distortions presented on the Fig. 6 from smooth 4-th degree approximations for single crystal (a) and for ceramics (b).

Fig. 8.
Fig. 8.

The dependence of experimental STD on 1/F of the corresponding thermolens. The linear approximation is plotted by a thin blue solid line for the single crystal, by red and green thin solid lines for the 3.5 mm-thick and 3 mm thick ceramic elements, respectively. The thick red solid line corresponds to numerical modeling. The approximating lines originate from point [0;0,6] that corresponds to measurement accuracy (λ/1000).

Equations (4)

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

Δ Ω = λ Δ x .
Δ Ω d λ 2 π ,
Δ L ( z ) = 0 l [ n 0 ( Δ S 1 ( z ) + Δ S 2 ( z ) ) + β T ( z ) + Δ n ( z ) ] dz ,
Δ L = 0 l [ ( n 0 1 ) Δ S 1 + n 0 Δ S 2 + β T ( z ) + Δ n ( z ) ] dz

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