Abstract

Wavefront distortion in optical components induced by thermal lensing may affect performance and stability of optical systems, such as high-power lasers, and is also the base of several photothermal techniques. This distortion is a result of complex photoelastic effects that characterize the degradation and the propagation of the beam. A simple analytical solution is obtained only for low absorbing materials, with the assumption that the stresses obey either thin-disk or long-rod type distributions. In a previous work, part of this limitation was overcome, in which a unified model was proposed for the optical path change for weakly absorbing materials, regardless of its thickness. In this work, we developed a generalized theoretical model for the optical path change that is related to the temperature profile in a relatively simple manner for all classes of absorbing optical materials. The modeling is based on the solution of the thermoelastic equation and provides time-dependent expressions for the temperature, surface displacement, and stresses. This generalized model could have a significant impact on designing laser systems and has direct application in photothermal techniques, which correlate optical path change to thermal, optical, and mechanical properties of solid materials.

© 2012 Optical Society of America

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  1. C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
    [CrossRef]
  2. W. Winkler, K. Danzmann, A. Rüdiger, and R. Schilling, “Heating bu optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022–7036(1991).
    [CrossRef]
  3. M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
    [CrossRef]
  4. C. A. Klein, “Optical distortion coefficients of high-power laser windows,” Opt. Eng. 29, 343–350 (1990).
    [CrossRef]
  5. C. A. Klein, “Describing beam-aberration effects induced by laser-light transmitting components: a short account of Raytheon’s contribution,” Proc. SPIE 4376, 24–34 (2001).
    [CrossRef]
  6. C. A. Klein, “Analytical stress modeling of high-energy laser windows: application to fusion-cast calcium fluoride windows,” J. Appl. Phys. 98, 043103 (2005).
    [CrossRef]
  7. L. B. Glebov, “Intrinsic laser-induced breakdown of silicate glasses,” Proc. SPIE 4679, 321–331 (2002).
    [CrossRef]
  8. Y. Peng, Z. Sheng, H. Zhang, and X. Fan, “Influence of thermal deformations of the output windows of high-power laser systems on beam characteristics,” Appl. Opt. 43, 6465–6472 (2004).
    [CrossRef]
  9. W. Koechner and M. Bass, Solid-State Lasers: A Graduate Text (Springer, 2003).
  10. J. Shen, M. L. Baesso, and R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
    [CrossRef]
  11. N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
    [CrossRef]
  12. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, P. R. B. Pedreira, L. C. Malacarne, A. C. Bento, and M. L. Baesso, “Top-hat cw-laser-induced time-resolved modemismatched thermal lens spectroscopy for quantitative analysis of low-absorption materials,” Opt. Lett. 33, 1464–1466 (2008).
    [CrossRef]
  13. L. C. Malacarne, N. G. C. Astrath, and M. L. Baesso, “Unified theoretical model for calculating laser-induced wavefront distortion in optical materials,” J. Opt. Soc. Am. B 29, 1772–1777 (2012).
    [CrossRef]
  14. L. C. Malacarne, N. G. C. Astrath, G. V. B. Lukasievcz, E. K. Lenzi, M. L. Baesso, and S. E. Bialkowski, “Time-resolved thermal lens and thermal mirror spectroscopy with sample fluid heat coupling: a complete model for material characterization,” Appl. Spectrosc. 65, 99–104 (2011).
    [CrossRef]
  15. S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
    [CrossRef]
  16. W. Nowacki, Thermoelasticity (Pergamon, 1982), Vol. 3, p. 11.
  17. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon, 1959), Vol. 1, p. 78.
  18. C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
    [CrossRef]
  19. A. A. Kuzmin, D. E. Silin, A. A. Shaykin, I. E. Kozhevatov, and E. A. Khazanov, “Simple method of measurement of phase distortions in laser amplifiers,” J. Opt. Soc. Am. B 29, 1152–1156 (2012).
    [CrossRef]
  20. N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
    [CrossRef]

2012

2011

2008

2007

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

2006

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
[CrossRef]

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

2005

C. A. Klein, “Analytical stress modeling of high-energy laser windows: application to fusion-cast calcium fluoride windows,” J. Appl. Phys. 98, 043103 (2005).
[CrossRef]

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

2004

2002

L. B. Glebov, “Intrinsic laser-induced breakdown of silicate glasses,” Proc. SPIE 4679, 321–331 (2002).
[CrossRef]

2001

C. A. Klein, “Describing beam-aberration effects induced by laser-light transmitting components: a short account of Raytheon’s contribution,” Proc. SPIE 4376, 24–34 (2001).
[CrossRef]

1994

J. Shen, M. L. Baesso, and R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

1991

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

1990

C. A. Klein, “Optical distortion coefficients of high-power laser windows,” Opt. Eng. 29, 343–350 (1990).
[CrossRef]

1971

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

Anjos, V.

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Astrath, F. B. G.

Astrath, N. G. C.

Baesso, M. L.

L. C. Malacarne, N. G. C. Astrath, and M. L. Baesso, “Unified theoretical model for calculating laser-induced wavefront distortion in optical materials,” J. Opt. Soc. Am. B 29, 1772–1777 (2012).
[CrossRef]

L. C. Malacarne, N. G. C. Astrath, G. V. B. Lukasievcz, E. K. Lenzi, M. L. Baesso, and S. E. Bialkowski, “Time-resolved thermal lens and thermal mirror spectroscopy with sample fluid heat coupling: a complete model for material characterization,” Appl. Spectrosc. 65, 99–104 (2011).
[CrossRef]

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, P. R. B. Pedreira, L. C. Malacarne, A. C. Bento, and M. L. Baesso, “Top-hat cw-laser-induced time-resolved modemismatched thermal lens spectroscopy for quantitative analysis of low-absorption materials,” Opt. Lett. 33, 1464–1466 (2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

J. Shen, M. L. Baesso, and R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

Balembois, F.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
[CrossRef]

Barton, M. A.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Bass, M.

W. Koechner and M. Bass, Solid-State Lasers: A Graduate Text (Springer, 2003).

Bell, M. J. V.

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Bento, A. C.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, P. R. B. Pedreira, L. C. Malacarne, A. C. Bento, and M. L. Baesso, “Top-hat cw-laser-induced time-resolved modemismatched thermal lens spectroscopy for quantitative analysis of low-absorption materials,” Opt. Lett. 33, 1464–1466 (2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Bialkowski, S. E.

Billingsley, G.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Blair, D. G.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Brooks, A.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Carslaw, H. S.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon, 1959), Vol. 1, p. 78.

Catunda, T.

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Chenais, S.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
[CrossRef]

Danzmann, K.

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

Degallaix, J.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Druon, F.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
[CrossRef]

Fan, X.

Fan, Y.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Forget, S.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
[CrossRef]

Gandra, F. G.

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Georges, P.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
[CrossRef]

Glebov, L. B.

L. B. Glebov, “Intrinsic laser-induced breakdown of silicate glasses,” Proc. SPIE 4679, 321–331 (2002).
[CrossRef]

Gray, M. B.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Hosken, D. J.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Jacinto, C.

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Jaeger, J. C.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon, 1959), Vol. 1, p. 78.

Ju, L.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Khazanov, E. A.

Klein, C. A.

C. A. Klein, “Analytical stress modeling of high-energy laser windows: application to fusion-cast calcium fluoride windows,” J. Appl. Phys. 98, 043103 (2005).
[CrossRef]

C. A. Klein, “Describing beam-aberration effects induced by laser-light transmitting components: a short account of Raytheon’s contribution,” Proc. SPIE 4376, 24–34 (2001).
[CrossRef]

C. A. Klein, “Optical distortion coefficients of high-power laser windows,” Opt. Eng. 29, 343–350 (1990).
[CrossRef]

Koechner, W.

W. Koechner and M. Bass, Solid-State Lasers: A Graduate Text (Springer, 2003).

Kozhevatov, I. E.

Kuzmin, A. A.

Lenzi, E. K.

Lima, S. M.

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Lukasievcz, G. V. B.

Malacarne, L. C.

McClelland, D. E.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Medina, A. N.

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Mow Lowry, C. M.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Mudge, D.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Munch, J.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Myers, J. D.

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

Myers, M. J.

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

Nowacki, W.

W. Nowacki, Thermoelasticity (Pergamon, 1982), Vol. 3, p. 11.

Nunes, L. A. O.

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

Oliveira, S. L.

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

Pedreira, P. R. B.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, P. R. B. Pedreira, L. C. Malacarne, A. C. Bento, and M. L. Baesso, “Top-hat cw-laser-induced time-resolved modemismatched thermal lens spectroscopy for quantitative analysis of low-absorption materials,” Opt. Lett. 33, 1464–1466 (2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

Peng, Y.

Rohling, J. H.

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

Rüdiger, A.

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

Schilling, R.

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

Shaykin, A. A.

Shen, J.

N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, P. R. B. Pedreira, L. C. Malacarne, A. C. Bento, and M. L. Baesso, “Top-hat cw-laser-induced time-resolved modemismatched thermal lens spectroscopy for quantitative analysis of low-absorption materials,” Opt. Lett. 33, 1464–1466 (2008).
[CrossRef]

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

J. Shen, M. L. Baesso, and R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

Sheng, Z.

Silin, D. E.

Slagmolen, B. J. J.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Snook, R. D.

J. Shen, M. L. Baesso, and R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

Sparks, M.

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

Veitch, P. J.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Winkler, W.

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

Zhang, H.

Zhao, C.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Zhou, J.

Appl. Opt.

Appl. Phys. Lett.

N. G. C. Astrath, L. C. Malacarne, P. R. B. Pedreira, A. C. Bento, M. L. Baesso, and J. Shen, “Time-resolved thermal mirror for nanoscale surface displacement detection in low absorbing solids,” Appl. Phys. Lett. 91, 191908 (2007).
[CrossRef]

Appl. Spectrosc.

J. Appl. Phys.

J. Shen, M. L. Baesso, and R. D. Snook, “Three-dimensional model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry and time-resolved measurements of thin-film samples,” J. Appl. Phys. 75, 3738–3748 (1994).
[CrossRef]

C. A. Klein, “Analytical stress modeling of high-energy laser windows: application to fusion-cast calcium fluoride windows,” J. Appl. Phys. 98, 043103 (2005).
[CrossRef]

M. Sparks, “Optical distortion by heated windows in high-power laser systems,” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Eng.

C. A. Klein, “Optical distortion coefficients of high-power laser windows,” Opt. Eng. 29, 343–350 (1990).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. B

N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20 K,” Phys. Rev. B 71, 214202 (2005).
[CrossRef]

C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: Application to Nd3+-doped glasses,” Phys. Rev. B 73, 125107 (2006).
[CrossRef]

Phys. Rev. Lett.

C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. Mow Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, “Compensation of strong thermal lensing in high-optical-power Cavities,” Phys. Rev. Lett. 96, 231101 (2006).
[CrossRef]

Proc. SPIE

C. A. Klein, “Describing beam-aberration effects induced by laser-light transmitting components: a short account of Raytheon’s contribution,” Proc. SPIE 4376, 24–34 (2001).
[CrossRef]

L. B. Glebov, “Intrinsic laser-induced breakdown of silicate glasses,” Proc. SPIE 4679, 321–331 (2002).
[CrossRef]

Prog. Quantum Electron.

S. Chenais, F. Druon, S. Forget, F. Balembois, and P. Georges, “On thermal effects in solid-state lasers: the case of ytterbium-doped materials,” Prog. Quantum Electron. 30, 89–153(2006).
[CrossRef]

Other

W. Nowacki, Thermoelasticity (Pergamon, 1982), Vol. 3, p. 11.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon, 1959), Vol. 1, p. 78.

W. Koechner and M. Bass, Solid-State Lasers: A Graduate Text (Springer, 2003).

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Figures (1)

Fig. 1.
Fig. 1.

Scaled optical path S(0,t)/(Q0l0) calculated with different approximations for Q98 glass with (a) l0=1, 2, 5 mm and β=50m1 and (b) l0=2mm and β=50, 150, 350m1. Inset shows S(0,0.2)/(Q0l0) versus β. The parameters used in the simulations are found in [18] with qq=1.5×1012Pa1.

Equations (39)

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S(r,t)=Sf(r,t)+b(r,0,t)b(r,l0,t)n(r,z,t)dz,
Sth(r,t)=nT0l0T(r,z,t)dz.
Sst+(r,t)=n0340l0[(q+q)(σrr+σϕϕ)+2qσzz]dz,
Sst(r,t)=n0340l0[(qq)(σrrσϕϕ)]dz.
Sex(r,t)=(n01)[uz(r,l0,t)uz(r,0,t)].
tT(r,z,t)D2T(r,z,t)=Q(r)Q(z)Q(t).
T(r,z,t)=2π00T(α,λ,t)cos(λz)J0(αr)αdαdλ.
T(α,λ,t)=Q(α)Q(λ)0tQ(τ)eD(α2+λ2)(tτ)dτ.
2Ψ(r,z,t)=1+ν1ναTT(r,z,t),
22ψ(r,z,t)=0,
uz=Ψz+112ν[2(1ν)22z2]ψ,σzz=E1+ν(2r2+1rr)Ψ+E1ν2ν2[(2ν)22z2]ψz,
σrr=E1+ν(2z2+1rr)Ψ+E1ν2ν2(ν22r2)ψz,
σϕϕ=E1+ν(2r2+2z2)Ψ+E1ν2ν2(ν21rr)ψz.
Ψ=1+νν1αT2π00T(α,λ,t)α2+λ2cos(λz)J0(αr)αdαdλ,
ψ=(1ν2ν2)(ν1)π/2αT00T(α,λ,t)(α2+λ2)J0(αr)×[q1+q2cos(l0λ)+q3λα1sin(l0λ)cosh(2l0α)2l02α21]dαdλ.
q1=zαcosh(2l0αzα)+α(z4l0ν)cosh(zα)4νcosh(l0αzα)sinh(l0α)+2l0(zl0)α2sinh(zα),
q2=α[z+l0(4ν1)]cosh(l0αzα)+(l0z)αcosh(l0α+zα)+2(l0zα2+ν)sinh(l0αzα)+2νsinh(l0α+zα),
q3=2l0αcosh(l0α)[zαcosh(zα)+(12ν)sinh(zα)]+2sinh(l0α)[α(z2l0ν)cosh(zα)(1+l0zα22ν)sinh(zα)].
σi=1l00l0σii(r,z,t)dz,
σz=ϱ00g1T(α,λ,t)α2+λ2αJ0(αr)dαdλ,
σr=ϱ00g2T(α,λ,t)α2+λ2J1(αr)rdαdλ,
σϕ=ϱ00g2T(α,λ,t)α2+λ2[αJ0(αr)J1(αr)r]dαdλ,
g1=1l0λ[l0α+sinh(l0α)]×{2αλ[cosh(l0α)1][1+cos(l0λ)]sin(l0λ)[l0α(α2+λ2)+(α2λ2)sinh(l0α)]},
g2=1l0λ[l0α+sinh(l0α)]×{2αλν[cosh(l0α)1][1+cos(l0λ)]sin(l0λ)[l0α(α2+λ2)+(α2+λ22λ2ν)sinh(l0α)]}.
Δu(r,t)=uz(r,l0,t)uz(r,0,t)=l0(1+ν)αT2π00q(α,λ)×T(α,λ,t)J0(αr)αdαdλ,
q(α,λ)=2αl0α(e2l0α+2l0αel0α1)(α2+λ2)×{(el0α1)2α[1+cos(l0λ)](1e2l0α)λsin(l0λ)}.
S(r,t)=2π00l0χ+(α,λ)T(α,λ,t)J0(rα)αdαdλ,
χ+(α,λ)=nTsin(l0λ)l0λ+ϑstp+(α,λ)+ϑexq(α,λ),
p+(α,λ)=1l0λ(α2+λ2)[l0α+sinh(l0α)]{2αλ(qν+qν+2q)[1+cos(l0λ)][cosh(l0α)1]sin(l0λ)[l0(q+3q)α(α2+λ2)]sin(l0λ)sinh(l0α)[(q+3q)α2+λ2(qq2qν2qν)]}.
Sst=2π00l0χ(α,λ)T(α,λ,t)J2(αr)αdαdλ,
χ(α,λ)=ϑst(qq)l0λ(α2+λ2)(l0α+sinh(l0α)){2αλν[1+cos(l0λ)][cosh(l0α)1]+sin(l0λ)[l0α(α2+λ2)+(α2+λ22λ2ν)sinh(l0α)]}.
S(r,t)=0l0χ(α)T(α,t)J0(rα)αdα,
χ(α)=nT+ϑex4h(α)l0α+ϑst[(q+3q)4[qν+q(2+ν)]h(α)l0α],
χ0=nT+n03EαT4(q+q)+(n01)(1+ν)αT,
χ=nT+n03EαT4(1ν)(q+3q).
S(r,t)=0l0χβ+(α)T(α,t)J0(rα)αdα,
χβ+(α)=nT1eβl0βl0+ϑstpβ+(α)+ϑexqβ(α),
pβ+(α)=el0α[l0α+sinh(l0α)]el0β2l0β(β2α2)×{2αβ(el0α1)2(el0β+1)(qν+q(ν+2))+β2(1e2l0α)(el0β1)[2ν(q+q)q+q]2αel0α(el0β1)(q+3q)[l0(α2β2)+αsinh(l0α)]},
qβ(α)=4el0β/2l0(β2α2)[l0α+sinh(l0α)]×[βsinh(l0α)sinh(l0β/2)2αcosh(l0β/2)sinh(l0α/2)2].

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