Abstract

Thermally induced beam distortions in laser ceramics with arbitrary grain size have been investigated. A model for the spatial spectral density of dielectric permeability variations was suggested. The average scattered intensity was calculated using the small disturbances method (theory of Rayleigh–Debye scattering). The direction pattern of the scattered field and the extinction coefficient have been obtained. The scattered power and the depolarization ratio fit with the corresponding values obtained in the geometric optics approximation in the range of its validity.

© 2012 Optical Society of America

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2011 (3)

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
[CrossRef]

R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
[CrossRef]

A. G. Vyatkin and E. A. Khazanov, “Thermally induced scattering of radiation in laser ceramics with arbitrary grain size,” Proc. SPIE 7994, 79940B (2011).

2010 (1)

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

2009 (1)

A. G. Vyatkin, and E. A. Khazanov, “Nonlinear thermally induced distortions of a laser beam in a cryogenic disk amplifier,” Quantum Electron. 39, 814–820 (2009).
[CrossRef]

2008 (1)

C. Jacinto, A. Benayas, T. Catunda, J. García-Soĺ, A. A. Kaminskii, and D. Jaque, “Microstructuration induced differences in the thermo-optical and luminescence properties of Nd:YAG fine grain ceramics and crystals,” J. Chem. Phys. 129, 104705 (2008).
[CrossRef]

2007 (5)

J.-F. Bisson, H. Yagi, T. Yanagitani, A. A. Kaminskii, Y. N. Barabanenkov, and K.-I. Ueda, “Influence of the grain boundaries on the heat transfer in laser ceramics,” Opt. Rev. 14, 1–13(2007).
[CrossRef]

A. A. Kaminskii, “Laser crystals and ceramics: recent advances,” Laser Photon. Rev. 1, 93–177 (2007).
[CrossRef]

S. Lee, D. Choi, C.-J. Kim, and J. Zhou, “Highly efficient diode side-pumped Nd:YAG ceramic laser with 210 W output power,” Opt. Laser Technol. 39, 705–709 (2007).
[CrossRef]

I. B. Mukhin, O. V. Palashov, I. L. Snetkov, and E. A. Khazanov, “Thermally induced wavefront distortions in laser ceramics,” Proc. SPIE 6610, 66100N (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]

2006 (2)

D. Kracht, D. Freiburg, R. Wilhelm, M. Frede, and C. Fallnich, “Core-doped Ceramic Nd:YAG Laser,” Opt. Express 14, 2690–2694 (2006).
[CrossRef]

A. Ikesue, Y. L. Aung, T. Taira, T. Kamimura, K. Yoshida, and G. L. Messing, “Progress in ceramic lasers,” Annu. Rev. Mater. Res. 36, 397–429 (2006).
[CrossRef]

2005 (2)

Y. Qi, X. Zhu, Q. Lou, J. Ji, J. Dong, and Y. Wei, “Nd:YAG ceramic laser obtained high slope-efficiency of 62% in high power applications,” Opt. Express 13, 8725–8729 (2005).
[CrossRef]

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, and I. A. Ivanov, “Influence of the orientation of a crystal on thermal polarization effects in high-power solid-state lasers,” JETP Lett. 81, 90–94 (2005).
[CrossRef]

2003 (3)

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

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

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

2002 (2)

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics—a new generation of solid state laser and optical materials,” J. Alloys Compd. 341, 220–225 (2002).
[CrossRef]

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

2001 (4)

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

V. Lupei, A. Lupei, N. Pavel, T. Taira, I. Shoji, and A. Ikesue, “Laser emission under resonant pump in the emitting level of concentrated Nd:YAG ceramics,” Appl. Phys. Lett. 79, 590–592 (2001).
[CrossRef]

V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
[CrossRef]

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

2000 (3)

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941(2000).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

1995 (2)

A. Ikesue, I. Furusato, and K. Kamata, “Fabrication of polycrystalline, transparent YAG ceramics by a solid-state reaction method,” J. Ceram. Am. Soc. 78, 225–228 (1995).
[CrossRef]

A. Ikesue, T. Kinoshita, K. Kamata, and K. Yoshida, “Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers,” J. Ceram. Am. Soc. 78, 1033–1040 (1995).
[CrossRef]

1983 (1)

R. V. Jones, “Light scattering in ceramics,” Proc. SPIE 362, 2–8 (1983).
[CrossRef]

1979 (1)

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

1971 (1)

1966 (1)

Aggarwal, I.

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
[CrossRef]

Akchurin, M. Sh.

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

Akiyama, Y.

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics—a new generation of solid state laser and optical materials,” J. Alloys Compd. 341, 220–225 (2002).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Alshits, V. I.

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

Aung, Y. L.

A. Ikesue, Y. L. Aung, T. Taira, T. Kamimura, K. Yoshida, and G. L. Messing, “Progress in ceramic lasers,” Annu. Rev. Mater. Res. 36, 397–429 (2006).
[CrossRef]

Bagayev, S. N.

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

Baker, C.

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
[CrossRef]

Balda, R.

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

Barabanenkov, Y. N.

J.-F. Bisson, H. Yagi, T. Yanagitani, A. A. Kaminskii, Y. N. Barabanenkov, and K.-I. Ueda, “Influence of the grain boundaries on the heat transfer in laser ceramics,” Opt. Rev. 14, 1–13(2007).
[CrossRef]

Benayas, A.

C. Jacinto, A. Benayas, T. Catunda, J. García-Soĺ, A. A. Kaminskii, and D. Jaque, “Microstructuration induced differences in the thermo-optical and luminescence properties of Nd:YAG fine grain ceramics and crystals,” J. Chem. Phys. 129, 104705 (2008).
[CrossRef]

Bhachu, B. S.

B. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” in Advanced Solid-State Photonics, OSA Technical Digest Series (Optical Society of America, 2008), paper WC5.

Bisson, J.-F.

J.-F. Bisson, H. Yagi, T. Yanagitani, A. A. Kaminskii, Y. N. Barabanenkov, and K.-I. Ueda, “Influence of the grain boundaries on the heat transfer in laser ceramics,” Opt. Rev. 14, 1–13(2007).
[CrossRef]

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

Bo, Y.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Burshtein, Z.

R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
[CrossRef]

Castillo, V. K.

M. Dubinskii, L. D. Merkle, G. A. Newburgh, J. R. Goff, V. K. Castillo, and G. J. Quarles, “Laser studies of 8% Nd:YAG ceramic gain material,” in Advanced Solid-State Photonics (TOPS), C. Denman and I. Sorokina, eds., Vol. 98 of OSA Trends in Optics and Photonics (Optical Society of America, 2005), paper 47. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2005-47 .

Catunda, T.

C. Jacinto, A. Benayas, T. Catunda, J. García-Soĺ, A. A. Kaminskii, and D. Jaque, “Microstructuration induced differences in the thermo-optical and luminescence properties of Nd:YAG fine grain ceramics and crystals,” J. Chem. Phys. 129, 104705 (2008).
[CrossRef]

Choi, D.

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R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
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V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
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R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
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A. Ikesue, T. Kinoshita, K. Kamata, and K. Yoshida, “Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers,” J. Ceram. Am. Soc. 78, 1033–1040 (1995).
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A. Ikesue, I. Furusato, and K. Kamata, “Fabrication of polycrystalline, transparent YAG ceramics by a solid-state reaction method,” J. Ceram. Am. Soc. 78, 225–228 (1995).
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A. Ikesue, Y. L. Aung, T. Taira, T. Kamimura, K. Yoshida, and G. L. Messing, “Progress in ceramic lasers,” Annu. Rev. Mater. Res. 36, 397–429 (2006).
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C. Jacinto, A. Benayas, T. Catunda, J. García-Soĺ, A. A. Kaminskii, and D. Jaque, “Microstructuration induced differences in the thermo-optical and luminescence properties of Nd:YAG fine grain ceramics and crystals,” J. Chem. Phys. 129, 104705 (2008).
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J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
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J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
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J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
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J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

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E. A. Khazanov, “Thermally induced birefringence in Nd:YAG ceramics,” Opt. Lett. 27, 716–718 (2002).
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Kim, C.-J.

S. Lee, D. Choi, C.-J. Kim, and J. Zhou, “Highly efficient diode side-pumped Nd:YAG ceramic laser with 210 W output power,” Opt. Laser Technol. 39, 705–709 (2007).
[CrossRef]

Kim, W.

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
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A. Ikesue, T. Kinoshita, K. Kamata, and K. Yoshida, “Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers,” J. Ceram. Am. Soc. 78, 1033–1040 (1995).
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J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

Kurimura, S.

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941(2000).
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Lee, S.

S. Lee, D. Choi, C.-J. Kim, and J. Zhou, “Highly efficient diode side-pumped Nd:YAG ceramic laser with 210 W output power,” Opt. Laser Technol. 39, 705–709 (2007).
[CrossRef]

Letts, S. A.

B. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” in Advanced Solid-State Photonics, OSA Technical Digest Series (Optical Society of America, 2008), paper WC5.

Li, C.

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

Li, C. Y.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Liu, W. B.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Lobad, A.

W. P. Latham, A. Lobad, T. C. Newell, and D. Stalnaker, “6.5 kW, Yb:YAG ceramic thin disk laser,” in Proceedings of the International Symposium on High Power Laser Ablation, C. R. Phipps, ed. (AIP, 2010), p. 758.

Lou, Q.

Lu, J.

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics—a new generation of solid state laser and optical materials,” J. Alloys Compd. 341, 220–225 (2002).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Lu, J. H.

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

Lu, J. R.

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

Lumer, Y.

R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
[CrossRef]

Lupei, A.

V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
[CrossRef]

V. Lupei, A. Lupei, N. Pavel, T. Taira, I. Shoji, and A. Ikesue, “Laser emission under resonant pump in the emitting level of concentrated Nd:YAG ceramics,” Appl. Phys. Lett. 79, 590–592 (2001).
[CrossRef]

Lupei, V.

V. Lupei, A. Lupei, N. Pavel, T. Taira, I. Shoji, and A. Ikesue, “Laser emission under resonant pump in the emitting level of concentrated Nd:YAG ceramics,” Appl. Phys. Lett. 79, 590–592 (2001).
[CrossRef]

V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
[CrossRef]

Mandl, A.

A. Mandl, and D. E. Klimek, “Textron’s J-HPSSL 100 kW ThinZag® laser program,” in Conference on Laser Electro-Optics: Applications, OSA Technical Digest (Optical Society of America, 2010), paper JThH2.

Meir, A.

R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
[CrossRef]

Merkle, L. D.

M. Dubinskii, L. D. Merkle, G. A. Newburgh, J. R. Goff, V. K. Castillo, and G. J. Quarles, “Laser studies of 8% Nd:YAG ceramic gain material,” in Advanced Solid-State Photonics (TOPS), C. Denman and I. Sorokina, eds., Vol. 98 of OSA Trends in Optics and Photonics (Optical Society of America, 2005), paper 47. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2005-47 .

Messing, G. L.

A. Ikesue, Y. L. Aung, T. Taira, T. Kamimura, K. Yoshida, and G. L. Messing, “Progress in ceramic lasers,” Annu. Rev. Mater. Res. 36, 397–429 (2006).
[CrossRef]

Misawa, K.

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

Moshe, I.

R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
[CrossRef]

Mukhin, I. B.

I. B. Mukhin, O. V. Palashov, I. L. Snetkov, and E. A. Khazanov, “Thermally induced wavefront distortions in laser ceramics,” Proc. SPIE 6610, 66100N (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, and I. A. Ivanov, “Influence of the orientation of a crystal on thermal polarization effects in high-power solid-state lasers,” JETP Lett. 81, 90–94 (2005).
[CrossRef]

Murai, T.

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Musha, M.

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

Nakayama, S.

A. Ikesue, T. Yoda, S. Nakayama, and K. Yoshida, “Fabrication and laser performance of polycrystal and single crystal Nd:YAG by advanced ceramic processing,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (Optical Society of America, 2004), paper CTuT2. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2004-CTuT2 .

Newburgh, G. A.

M. Dubinskii, L. D. Merkle, G. A. Newburgh, J. R. Goff, V. K. Castillo, and G. J. Quarles, “Laser studies of 8% Nd:YAG ceramic gain material,” in Advanced Solid-State Photonics (TOPS), C. Denman and I. Sorokina, eds., Vol. 98 of OSA Trends in Optics and Photonics (Optical Society of America, 2005), paper 47. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2005-47 .

Newell, T. C.

W. P. Latham, A. Lobad, T. C. Newell, and D. Stalnaker, “6.5 kW, Yb:YAG ceramic thin disk laser,” in Proceedings of the International Symposium on High Power Laser Ablation, C. R. Phipps, ed. (AIP, 2010), p. 758.

Palashov, O. V.

I. B. Mukhin, O. V. Palashov, I. L. Snetkov, and E. A. Khazanov, “Thermally induced wavefront distortions in laser ceramics,” Proc. SPIE 6610, 66100N (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, and I. A. Ivanov, “Influence of the orientation of a crystal on thermal polarization effects in high-power solid-state lasers,” JETP Lett. 81, 90–94 (2005).
[CrossRef]

Pan, Y. B.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Parks, C. W.

B. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” in Advanced Solid-State Photonics, OSA Technical Digest Series (Optical Society of America, 2008), paper WC5.

Pavel, N.

V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
[CrossRef]

V. Lupei, A. Lupei, N. Pavel, T. Taira, I. Shoji, and A. Ikesue, “Laser emission under resonant pump in the emitting level of concentrated Nd:YAG ceramics,” Appl. Phys. Lett. 79, 590–592 (2001).
[CrossRef]

Peng, Q. J.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Petrov, T. S.

Prabhu, M.

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

Qi, Y.

Quarles, G. J.

M. Dubinskii, L. D. Merkle, G. A. Newburgh, J. R. Goff, V. K. Castillo, and G. J. Quarles, “Laser studies of 8% Nd:YAG ceramic gain material,” in Advanced Solid-State Photonics (TOPS), C. Denman and I. Sorokina, eds., Vol. 98 of OSA Trends in Optics and Photonics (Optical Society of America, 2005), paper 47. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2005-47 .

Quelle, F. W.

Rice, D. K.

Rotter, M. D.

B. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” in Advanced Solid-State Photonics, OSA Technical Digest Series (Optical Society of America, 2008), paper WC5.

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskiy, Vvedeniye v statisticheskuyu radiofiziku, Tom 2 [Introduction to Statistical Radiophysics, Vol. 2 (Nauka, 1978).

Sadowski, B.

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
[CrossRef]

Sanghera, J.

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
[CrossRef]

Sato, Y.

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941(2000).
[CrossRef]

Shaw, B.

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
[CrossRef]

Shimony, Y.

R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
[CrossRef]

Shirakawa, A.

Shirikawa, A.

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

Shoji, I.

V. Lupei, A. Lupei, N. Pavel, T. Taira, I. Shoji, and A. Ikesue, “Laser emission under resonant pump in the emitting level of concentrated Nd:YAG ceramics,” Appl. Phys. Lett. 79, 590–592 (2001).
[CrossRef]

V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941(2000).
[CrossRef]

Snetkov, I. L.

I. B. Mukhin, O. V. Palashov, I. L. Snetkov, and E. A. Khazanov, “Thermally induced wavefront distortions in laser ceramics,” Proc. SPIE 6610, 66100N (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]

Soms, L. N.

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

Song, J.

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

Soules, T. F.

B. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” in Advanced Solid-State Photonics, OSA Technical Digest Series (Optical Society of America, 2008), paper WC5.

Stalnaker, D.

W. P. Latham, A. Lobad, T. C. Newell, and D. Stalnaker, “6.5 kW, Yb:YAG ceramic thin disk laser,” in Proceedings of the International Symposium on High Power Laser Ablation, C. R. Phipps, ed. (AIP, 2010), p. 758.

Stubbs, D. P.

H. M. Kahan, D. P. Stubbs, and R. V. Jones, “The potentialities of fine grained ceramics for optical and acoustical applications,” in Optical and Acoustical Micro-Electronics, J. Fox ed. (Polytechnic, 1975), pp. 185–204.

Taira, T.

A. Ikesue, Y. L. Aung, T. Taira, T. Kamimura, K. Yoshida, and G. L. Messing, “Progress in ceramic lasers,” Annu. Rev. Mater. Res. 36, 397–429 (2006).
[CrossRef]

V. Lupei, A. Lupei, N. Pavel, T. Taira, I. Shoji, and A. Ikesue, “Laser emission under resonant pump in the emitting level of concentrated Nd:YAG ceramics,” Appl. Phys. Lett. 79, 590–592 (2001).
[CrossRef]

V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941(2000).
[CrossRef]

T. Taira, A. Ikesue, and K. Yoshida, “Diode pumped Nd:YAG ceramics lasers,” in Advanced Solid State Lasers, W. Bosenberg and M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998), paper CS4.

Takaichi, K.

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Tarasov, A. A.

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

Tatarskiy, V. I.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskiy, Vvedeniye v statisticheskuyu radiofiziku, Tom 2 [Introduction to Statistical Radiophysics, Vol. 2 (Nauka, 1978).

Tian, C. Y.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Timoshenko, S.

S. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, 1951).

Ueda, K.

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics—a new generation of solid state laser and optical materials,” J. Alloys Compd. 341, 220–225 (2002).
[CrossRef]

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

Ueda, K.-I.

J.-F. Bisson, H. Yagi, T. Yanagitani, A. A. Kaminskii, Y. N. Barabanenkov, and K.-I. Ueda, “Influence of the grain boundaries on the heat transfer in laser ceramics,” Opt. Rev. 14, 1–13(2007).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Uematsu, T.

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Villalobos, G.

J. Sanghera, B. Shaw, W. Kim, G. Villalobos, C. Baker, J. Frantz, M. Hunt, B. Sadowski, and I. Aggarwal, “Ceramic laser materials,” Proc. SPIE 7912, 79121Q (2011).
[CrossRef]

Vyatkin, A. G.

A. G. Vyatkin and E. A. Khazanov, “Thermally induced scattering of radiation in laser ceramics with arbitrary grain size,” Proc. SPIE 7994, 79940B (2011).

A. G. Vyatkin, and E. A. Khazanov, “Nonlinear thermally induced distortions of a laser beam in a cryogenic disk amplifier,” Quantum Electron. 39, 814–820 (2009).
[CrossRef]

Wang, B. S.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Wei, Y.

Wilhelm, R.

Xu, J.

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

Xu, Z. Y.

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

Yagi, H.

J.-F. Bisson, H. Yagi, T. Yanagitani, A. A. Kaminskii, Y. N. Barabanenkov, and K.-I. Ueda, “Influence of the grain boundaries on the heat transfer in laser ceramics,” Opt. Rev. 14, 1–13(2007).
[CrossRef]

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics—a new generation of solid state laser and optical materials,” J. Alloys Compd. 341, 220–225 (2002).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Yamamoto, B. M.

B. M. Yamamoto, B. S. Bhachu, K. P. Cutter, S. N. Fochs, S. A. Letts, C. W. Parks, M. D. Rotter, and T. F. Soules, “The use of large transparent ceramics in a high powered, diode pumped solid-state laser,” in Advanced Solid-State Photonics, OSA Technical Digest Series (Optical Society of America, 2008), paper WC5.

Yanagitani, T.

J.-F. Bisson, H. Yagi, T. Yanagitani, A. A. Kaminskii, Y. N. Barabanenkov, and K.-I. Ueda, “Influence of the grain boundaries on the heat transfer in laser ceramics,” Opt. Rev. 14, 1–13(2007).
[CrossRef]

A. Shirakawa, K. Takaichi, H. Yagi, J.-F. Bisson, J. Lu, M. Musha, K. Ueda, T. Yanagitani, T. S. Petrov, and A. A. Kaminskii, “Diode-pumped mode-locked Yb3+:Y2O3 ceramic laser,” Opt. Express 11, 2911–2916 (2003).
[CrossRef]

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics—a new generation of solid state laser and optical materials,” J. Alloys Compd. 341, 220–225 (2002).
[CrossRef]

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

Yoda, T.

A. Ikesue, T. Yoda, S. Nakayama, and K. Yoshida, “Fabrication and laser performance of polycrystal and single crystal Nd:YAG by advanced ceramic processing,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (Optical Society of America, 2004), paper CTuT2. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2004-CTuT2 .

Yoshida, K.

A. Ikesue, Y. L. Aung, T. Taira, T. Kamimura, K. Yoshida, and G. L. Messing, “Progress in ceramic lasers,” Annu. Rev. Mater. Res. 36, 397–429 (2006).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941(2000).
[CrossRef]

A. Ikesue, T. Kinoshita, K. Kamata, and K. Yoshida, “Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers,” J. Ceram. Am. Soc. 78, 1033–1040 (1995).
[CrossRef]

T. Taira, A. Ikesue, and K. Yoshida, “Diode pumped Nd:YAG ceramics lasers,” in Advanced Solid State Lasers, W. Bosenberg and M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998), paper CS4.

A. Ikesue, T. Yoda, S. Nakayama, and K. Yoshida, “Fabrication and laser performance of polycrystal and single crystal Nd:YAG by advanced ceramic processing,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (Optical Society of America, 2004), paper CTuT2. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2004-CTuT2 .

Zhou, J.

S. Lee, D. Choi, C.-J. Kim, and J. Zhou, “Highly efficient diode side-pumped Nd:YAG ceramic laser with 210 W output power,” Opt. Laser Technol. 39, 705–709 (2007).
[CrossRef]

Zhu, X.

Annu. Rev. Mater. Res. (1)

A. Ikesue, Y. L. Aung, T. Taira, T. Kamimura, K. Yoshida, and G. L. Messing, “Progress in ceramic lasers,” Annu. Rev. Mater. Res. 36, 397–429 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

J. Lu, J. Song, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, and A. Kudryashov, “High-power Nd:Y3Al5O12 ceramic laser,” Appl. Phys. 39, 1048–1050 (2000).

Appl. Phys. B (1)

J. Lu, M. Prabhu, J. Song, C. Li, J. Xu, K. Ueda, A. A. Kaminskii, H. Yagi, and T. Yanagitani, “Optical properties and highly efficient laser oscillation of Nd:YAG ceramic,” Appl. Phys. B 71, 469–473 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, and A. Kudryashov, “72 W Nd:Y3Al5O12 ceramic laser,” Appl. Phys. Lett. 78, 3586–3588 (2001).
[CrossRef]

I. Shoji, S. Kurimura, Y. Sato, T. Taira, A. Ikesue, and K. Yoshida, “Optical properties and laser characteristics of highly Nd3+-doped Y3Al5O12 ceramics,” Appl. Phys. Lett. 77, 939–941(2000).
[CrossRef]

V. Lupei, A. Lupei, N. Pavel, T. Taira, I. Shoji, and A. Ikesue, “Laser emission under resonant pump in the emitting level of concentrated Nd:YAG ceramics,” Appl. Phys. Lett. 79, 590–592 (2001).
[CrossRef]

Crystallogr. Rep. (1)

A. A. Kaminski, M. Sh. Akchurin, V. I. Alshits, K. Ueda, K. Takaichi, J. Lu, T. Uematsu, M. Musha, A. Shirikawa, V. Gabler, H. J. Eichler, H. Yagi, T. Yanagitani, S. N. Bagayev, J. Fernandez, and R. Balda, “New data on the physical properties of Y3Al5O12-based nanocrystalline laser ceramics,” Crystallogr. Rep. 48, 515–519 (2003).
[CrossRef]

J. Alloys Compd. (1)

J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, and A. A. Kaminskii, “Neodymium doped yttrium aluminum garnet (Y3Al5O12) nanocrystalline ceramics—a new generation of solid state laser and optical materials,” J. Alloys Compd. 341, 220–225 (2002).
[CrossRef]

J. Ceram. Am. Soc. (2)

A. Ikesue, I. Furusato, and K. Kamata, “Fabrication of polycrystalline, transparent YAG ceramics by a solid-state reaction method,” J. Ceram. Am. Soc. 78, 225–228 (1995).
[CrossRef]

A. Ikesue, T. Kinoshita, K. Kamata, and K. Yoshida, “Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers,” J. Ceram. Am. Soc. 78, 1033–1040 (1995).
[CrossRef]

J. Chem. Phys. (1)

C. Jacinto, A. Benayas, T. Catunda, J. García-Soĺ, A. A. Kaminskii, and D. Jaque, “Microstructuration induced differences in the thermo-optical and luminescence properties of Nd:YAG fine grain ceramics and crystals,” J. Chem. Phys. 129, 104705 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

JETP Lett. (1)

I. B. Mukhin, O. V. Palashov, E. A. Khazanov, and I. A. Ivanov, “Influence of the orientation of a crystal on thermal polarization effects in high-power solid-state lasers,” JETP Lett. 81, 90–94 (2005).
[CrossRef]

Jpn. J. Appl. Phys. part 2-letters (1)

J. R. Lu, J. H. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Nd3+:Y2O3 ceramic laser,” Jpn. J. Appl. Phys. part 2-letters 40, L1277–L1279 (2001).
[CrossRef]

Laser Photon. Rev. (1)

A. A. Kaminskii, “Laser crystals and ceramics: recent advances,” Laser Photon. Rev. 1, 93–177 (2007).
[CrossRef]

Opt. Commun. (2)

C. Y. Li, Y. Bo, B. S. Wang, C. Y. Tian, Q. J. Peng, D. F. Cui, Z. Y. Xu, W. B. Liu, X. Q. Feng, and Y. B. Pan, “A kilowatt level diode-side-pumped QCW Nd:YAG ceramic laser,” Opt. Commun. 283, 5145–5148 (2010).
[CrossRef]

V. Lupei, T. Taira, A. Lupei, N. Pavel, I. Shoji, and A. Ikesue, “Spectroscopy and laser emission under hot band resonant pump in highly doped Nd:YAG ceramics,” Opt. Commun. 195, 225–232 (2001).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (1)

S. Lee, D. Choi, C.-J. Kim, and J. Zhou, “Highly efficient diode side-pumped Nd:YAG ceramic laser with 210 W output power,” Opt. Laser Technol. 39, 705–709 (2007).
[CrossRef]

Opt. Lett. (1)

Opt. Mater. (1)

R. Feldman, Y. Golan, Z. Burshtein, S. Jackel, I. Moshe, A. Meir, Y. Lumer, and Y. Shimony, “Strengthening of poly-crystalline (ceramic) Nd:YAG elements for high-power laser applications,” Opt. Mater. 33, 695–701 (2011).
[CrossRef]

Opt. Rev. (1)

J.-F. Bisson, H. Yagi, T. Yanagitani, A. A. Kaminskii, Y. N. Barabanenkov, and K.-I. Ueda, “Influence of the grain boundaries on the heat transfer in laser ceramics,” Opt. Rev. 14, 1–13(2007).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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T. Taira, A. Ikesue, and K. Yoshida, “Diode pumped Nd:YAG ceramics lasers,” in Advanced Solid State Lasers, W. Bosenberg and M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998), paper CS4.

J. Lu, T. Murai, K. Takaichi, T. Uematsu, K.-I. Ueda, Y. Akiyama, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “1.46 kW CW Nd:YAG ceramic laser,” presented at the Advanced Solid-State Lasers, Quebec, Canada, 3–6 February 2002.

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Figures (4)

Fig. 1.
Fig. 1.

Ceramic element and the incident electric field.

Fig. 2.
Fig. 2.

(a) Spectrum Φ0 as a function of ζ. (b) Direction patterns of the average scattered intensity (isotropic approximation) in the xz (top half) and yz (bottom half) planes as functions of ψ (in degrees) for single scale spherical grains.

Fig. 3.
Fig. 3.

(a) Direction patterns of the average scattered intensity in the xz (top half) and yz (bottom half) planes as functions of ψ (in degrees) for the single scale spherical grains. (b) Dependence of scattered power fraction Q, the characteristic spatial angle of the direction pattern, and 1χ on the grain size. See notes in Section 5 and Appendix A. The vertical line is a guide for the eye.

Fig. 4.
Fig. 4.

Scheme for compensation of depolarization with two elements (gray) and a 90° rotator.

Equations (50)

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

ΔBrr+ΔBφφ=F0(r)+F1Σ(r)+(A1cos2φγ+B1sin2φγ)Δ(r)/2,ΔBrrΔBφφ=(A1cos2φγ+B1sin2φγ)Σ(r)+[A2+B3+(A2B3)cos4φγ+(A3+B2)sin4φγ]Δ(r)/2,2ΔBrφ=(B1cos2φγA1sin2φγ)Σ(r)+[B2A3+(B2+A3)cos4φγ+(B3A2)sin4φγ]Δ(r)/2,
F0(r)=(πaaaa+πaabb)(σrr+σφφ)+2πaabbσzz,Σ(r)=πS(σrr+σφφ2σzz)/2,Δ(r)=πS(σrrσφφ).
F1=2(1ξ)[a3(α,β)+b3(α,β)1],A1=(1ξ)a1(α,β),A2=ξ+(1ξ)a3(α,β),A3=(1ξ)c1(α,β),B1=(1ξ)b1(α,β),B2=(1ξ)c1(α,β),B3=ξ+(1ξ)b3(α,β),
a1=[sin22α(1cos4β)sin22β]/2,a3=[1(sin22α)/4]sin4β+cos22αcos2β,b1=1/4·sinβsin2βsin4α,b3=sin22αcos2β,c1=sin4αcosβ(1+cos2β)/4
ε=ε0+εT+ε1,
E1(rR)=k024πVexp[ik0|rRrS|I0(rR,rS)]|rRrS|ε1(rS)[E0(rS)n(rRrS)(n(rRrS)·E0(rS))]d3rS,I0(r,r)=01f[x+(xx)τ,y+(yy)τ,z+(zz)τ]dτ,f(r)=ε0+εT(r),
S1(rR)=S0π2k041sin2ψRcos2φRrR2n(rR)VfE2(rS)Φε[q(rR,rS)|rS]d3rS,
Φε(κ|r)=18π3VBε(ρ|r)exp(iκρ)d3ρ
h(rS)=π2k040πsinψRdψR02π(1sin2ψRcos2φR)Φε[q(rR,rS)|rS]dφR,
Q=VfE2(rS)h(rS)d3rS2π0RfE2(rS)rSdrS.
Φ0(κ)=12π2κ0P(ρ)sin(κρ)ρdρ
Φ0(κ)=l03π2[1+(κl0)2]2,
Φ0(κ)=3dl3π2ζ4(cosζ22ζsinζ2)2,
S1(rR)=S0π2k041sin2ψRcos2φRrR2Φ0[q0(rR)]n(rR)VfE2(rS)K(rS)d3rS.
h(rS)=4π2k04K(rS)(IΦ12IΦ2),IΦ1=01τΦ0[2k0f(rS)τ]dτ,IΦ2=01(τ3τ5)Φ0[2k0f(rS)τ]dτ.
IΦ1=3dl32π2I1,IΦ2=3dl32π2I2,I1=132[1Λ2+1Λ4(sin2ΛΛ1)1cos2Λ2Λ6],I2=132Λ4[3(sinΛΛ)23+sin2ΛΛ+2(1Λ2)02Λ1cosττdτ].
εij=(ε0+εT)δij+εAij+ε1ij,
E0r(rS)=A0fE(rS)cosφSexp[ik0zI0A(rS,rSzSz0)+iΦ(rS)],E0φ(rS)=A0fE(rS)sinφSexp[ik0zI0A(rS,rSzSz0)iΦ(rS)],E0z(rS)0,
S1(rR)=S0π2k04n(rR)rR2Φ0[q0(rR)]VfE2(rS)KΣ(rS)d3rS,
KΣ=(Krrrrcos2φS+Krφrφsin2φS)[1sin2ψRcos2(φRφS)]+(Kφφφφsin2φS+Krφrφcos2φS)[1sin2ψRsin2(φRφS)]+(Krrφφ+Krφrφ)cos2Φsin2φSsin2ψRsin[2(φRφS)]/2+(Krzrzcos2φS+Kφzφzsin2φS)sin2ψR,
DΣ=SfE2KΣdSSfE2dS=Drrrr+Dφφφφ2[1sin2ψR2(1+cos2φR2)]+Drφrφ[1sin2ψR2(1cos2φR2)]+(Drrφφ+Drφrφ)cos2Φsin2ψR2cos2φR2+(Drzrz+Dφzφz)sin2ψR2,
KΣavg=KΣ1[1(sin2ψR)/2]+KΣ2sin2ψR,KΣ1=Krrrrcos2φS+Kφφφφsin2φS+Krφrφ,KΣ2=Krzrzcos2φS+Kφzφzsin2φS,
h(rS)=4π2k04[KΣ1(rS)(IΦ12IΦ2)+4KΣ2(rS)IΦ2].
KΣ1AVG=(Krrrr+Kφφφφ)/2+Krφrφ,KΣ2AVG=(Krzrz+Kφzφz)/2.
Krrrr=πS2ε04(ξ1)2[5(σφφσzz)2+4(σφφ+σzz2σrr)2]/525,Kφφφφ=πS2ε04(ξ1)2[5(σrrσzz)2+4(σrr+σzz2σφφ)2]/525,Krφrφ=ε04(ξ1)2[7Δ2(r)+4Σ2(r)]/420,Krrφφ=ε04(ξ1)2[31Δ2(r)+4Σ2(r)]/2100,Krzrz=πS2ε04(ξ1)2[7(σrrσzz)2+(σrr+σzz2σφφ)2]/420,Kφzφz=πS2ε04(ξ1)2[7(σφφσzz)2+(σφφ+σzz2σrr)2]/420,
KΣ1AVG=ε04(ξ1)2[19Δ2(r)+14Σ2(r)]/525,KΣ2AVG=ε04(ξ1)2[Δ2(r)+2Σ2(r)]/105.
σrr=σ0(u1)/πS,σzz=σ0(4u2)/πS,σφφ=σ0(3u1)/πS,σ0=p/(2k0n03L),p=αTEPΣk0n03πS8πκ(1ν),
σzz=0,p=αTEPΣk0n03πS8πκ.
DΣ6sin2ψR[1(cos2φR)/30],
DΣ6sin2ψR[1(cos2φR)/6].
Q=(Λp)2(dl/L)(ξ1)2(3I12I2)/35.
Q3p2(ξ1)2dl/(1120L)
Q(Λp)2(ξ1)2dl/(1890L).
S1D(rR)=S0π2k04z04πΦ0(q0)dΩfE2(rS)0LKΣ1D(rS)dzS,
KΣ1D=[(Krrrr+Kφφφφ)/4cosΔavgKrrφφ/2]sin22φS+Krφrφ[cos22φScos2(2ΦΔavg/2)+sin2(2ΦΔavg/2)],
Δavg=pXu2,X=3ξ+25,
KΣ1D=[(Krrrr+Kφφφφ)/2Krrφφ]sin22φS+Krφrφ{cos22φS[cos22Φ+cos2(Δavg2Φ)]+sin22Φ+sin2(Δavg2Φ)}.
QsingleD=3p2dl128L01(AAD+ADcosΔavg+3B2B2sinΔavgΔavg)du,QcompensD=3p2dl64L01(A+3B2B2sin2Δavg2Δavg)du,
A=12σ02ε04(Krrrr+Kφφφφ2Krrφφ),B=Krφrφσ02ε04,AD=Krrφφ2σ02ε04.
K=(Krrrr+Kφφφφ)/4+Krrφφ/2.
Q=3(Λp)2(dl/L)(ξ1)2(I12I2)/350
1χp2(ξ1)2(1+σd2)/(2800N),
l0=23dl,σd2=18.
1χ=3p2(ξ1)2dl/(11200L)
γsingle=14[1sin(pX/2)pX/2]+p232N01[(A+B2)cosΔavg+BB2sinΔavgΔavg]du,γcompens=p216N01(A+3B2B2sin2Δavg2Δavg)du,
γsingle=14[1sin(pX/2)pX/2]+3p2dl128L01[(A+B2)cosΔavg+BB2sinΔavgΔavg]du,γcompens=3p2dl64L01(A+3B2B2sin2Δavg2Δavg)du.
εij=(ε0+εT+ε1)δij+εAij.
Krrrr=Kφφφφ=Krrφφ=K,Krφrφ=0.
S1(rR)S1D(rR)=S0π2k04z04πΦ0(q0)dΩfE2(rS)0L[KΣ1(rS)KΣ1D(rS)]dzS,
QsingleQsingleD=3p2dl128L01[3(AAD)ADcosΔavg+B2(1+sinΔavgΔavg)]du,QcompensQcompensD=3p2dl64L01[3A4AD+B2(1+sin2Δavg2Δavg)]du.

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