Abstract

A matrix method for tensor transformations in Voigt notation known from the elasticity calculations has been applied to elasto-optical calculations. Using invariant tensor-to-matrix mapping, the second- and fourth-rank Cartesian tensor transformations and basic operations can be performed by means of matrix multiplication. This approach brings what we believe is a new method of correct tensorial operations in Voigt notation, replacing a well-known approach that allocated specific constants to some matrix elements to even up the difference between the tensor transformations and $6 \times 6$ matrix operations. This general approach also simplifies the use of elasto-optical calculations for an arbitrary crystal class in an arbitrary orientation.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. P. Mason, M. Divoky, K. Ertel, J. Pilar, T. Butcher, M. Hanus, S. Banerjee, J. Phillips, J. Smith, M. De Vido, A. Lucianetti, C. Hernandez-Gomez, C. Edwards, T. Mocek, and J. Collier, “Kilowatt average power 100 J-level diode pumped solid state laser,” Optica 4, 438–439 (2017).
    [Crossref]
  2. B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
    [Crossref]
  3. J. F. Nye, Physical Properties of Crystals (Oxford University, 2011).
  4. Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effects in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95–101 (1995).
    [Crossref]
  5. D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
    [Crossref]
  6. M. Ostermeyer, D. Mudge, P. J. Veitch, and J. Munch, “Thermally induced birefringence in Nd:YAG slab lasers,” Appl. Opt. 45, 5368–5376 (2006).
    [Crossref]
  7. Y. Chen, B. Chen, M. K. R. Patel, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers–I,” IEEE J. Quantum Electron. 40, 909–916 (2004).
    [Crossref]
  8. H. Yang, G. Feng, and S. Zhou, “Thermal effects in high-power Nd:YAG disk-type solid state laser,” Opt. Laser Technol. 43, 1006–1015 (2011).
    [Crossref]
  9. O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
    [Crossref]
  10. L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
    [Crossref]
  11. M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
    [Crossref]
  12. K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
    [Crossref]
  13. J. C. Nadeau and M. Ferrari, “Invariant tensor-to-matrix mappings for evaluation of tensorial expressions,” J. Elasticity 52, 43–61 (1998).
    [Crossref]
  14. L. J. Walpole, “Fourth-rank tensors of the thirty-two crystal classes: multiplication tables,” Proc. R. Soc. Lond. A 391, 149–179 (1984).
    [Crossref]
  15. A. Authier, ed. International Tables for Crystallography (2006), Vol. D.
  16. T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1982).
  17. W. Koechner and D. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
    [Crossref]

2019 (1)

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

2018 (1)

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

2017 (1)

2014 (1)

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

2013 (1)

O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
[Crossref]

2011 (2)

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

H. Yang, G. Feng, and S. Zhou, “Thermal effects in high-power Nd:YAG disk-type solid state laser,” Opt. Laser Technol. 43, 1006–1015 (2011).
[Crossref]

2006 (1)

2004 (1)

Y. Chen, B. Chen, M. K. R. Patel, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers–I,” IEEE J. Quantum Electron. 40, 909–916 (2004).
[Crossref]

1998 (2)

D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
[Crossref]

J. C. Nadeau and M. Ferrari, “Invariant tensor-to-matrix mappings for evaluation of tensorial expressions,” J. Elasticity 52, 43–61 (1998).
[Crossref]

1995 (1)

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effects in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95–101 (1995).
[Crossref]

1984 (1)

L. J. Walpole, “Fourth-rank tensors of the thirty-two crystal classes: multiplication tables,” Proc. R. Soc. Lond. A 391, 149–179 (1984).
[Crossref]

1970 (1)

W. Koechner and D. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[Crossref]

Banerjee, S.

Bass, M.

Y. Chen, B. Chen, M. K. R. Patel, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers–I,” IEEE J. Quantum Electron. 40, 909–916 (2004).
[Crossref]

Besbes, M.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Brown, D. C.

D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
[Crossref]

Butcher, T.

Camy, P.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Chen, B.

Y. Chen, B. Chen, M. K. R. Patel, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers–I,” IEEE J. Quantum Electron. 40, 909–916 (2004).
[Crossref]

Chen, J.

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

Chen, Y.

Y. Chen, B. Chen, M. K. R. Patel, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers–I,” IEEE J. Quantum Electron. 40, 909–916 (2004).
[Crossref]

Collier, J.

De Vido, M.

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

P. Mason, M. Divoky, K. Ertel, J. Pilar, T. Butcher, M. Hanus, S. Banerjee, J. Phillips, J. Smith, M. De Vido, A. Lucianetti, C. Hernandez-Gomez, C. Edwards, T. Mocek, and J. Collier, “Kilowatt average power 100 J-level diode pumped solid state laser,” Optica 4, 438–439 (2017).
[Crossref]

Divoky, M.

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

P. Mason, M. Divoky, K. Ertel, J. Pilar, T. Butcher, M. Hanus, S. Banerjee, J. Phillips, J. Smith, M. De Vido, A. Lucianetti, C. Hernandez-Gomez, C. Edwards, T. Mocek, and J. Collier, “Kilowatt average power 100 J-level diode pumped solid state laser,” Optica 4, 438–439 (2017).
[Crossref]

O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
[Crossref]

Dong, S.

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effects in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95–101 (1995).
[Crossref]

Doualan, J.-L.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Druon, F.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Edwards, C.

Ertel, K.

Feng, G.

H. Yang, G. Feng, and S. Zhou, “Thermal effects in high-power Nd:YAG disk-type solid state laser,” Opt. Laser Technol. 43, 1006–1015 (2011).
[Crossref]

Ferrari, M.

J. C. Nadeau and M. Ferrari, “Invariant tensor-to-matrix mappings for evaluation of tensorial expressions,” J. Elasticity 52, 43–61 (1998).
[Crossref]

Genevrier, K.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Georges, P.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Guo, S.

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

Hanus, M.

Hernandez-Gomez, C.

Klimo, O.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Koechner, W.

W. Koechner and D. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[Crossref]

Korn, G.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

LeGarrec, B.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Leng, J.

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

Liu, L.

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

Liu, Z.

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

Lu, Q.

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

Lü, Q.

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effects in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95–101 (1995).
[Crossref]

Lucianetti, A.

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

P. Mason, M. Divoky, K. Ertel, J. Pilar, T. Butcher, M. Hanus, S. Banerjee, J. Phillips, J. Smith, M. De Vido, A. Lucianetti, C. Hernandez-Gomez, C. Edwards, T. Mocek, and J. Collier, “Kilowatt average power 100 J-level diode pumped solid state laser,” Optica 4, 438–439 (2017).
[Crossref]

O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
[Crossref]

Margarone, D.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Mason, P.

Mocek, T.

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

P. Mason, M. Divoky, K. Ertel, J. Pilar, T. Butcher, M. Hanus, S. Banerjee, J. Phillips, J. Smith, M. De Vido, A. Lucianetti, C. Hernandez-Gomez, C. Edwards, T. Mocek, and J. Collier, “Kilowatt average power 100 J-level diode pumped solid state laser,” Optica 4, 438–439 (2017).
[Crossref]

O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
[Crossref]

Moncorgé, R.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Mudge, D.

Munch, J.

Nadeau, J. C.

J. C. Nadeau and M. Ferrari, “Invariant tensor-to-matrix mappings for evaluation of tensorial expressions,” J. Elasticity 52, 43–61 (1998).
[Crossref]

Narasimhamurty, T. S.

T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1982).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford University, 2011).

Ostermeyer, M.

Papadopoulos, D. N.

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

Patel, M. K. R.

Y. Chen, B. Chen, M. K. R. Patel, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers–I,” IEEE J. Quantum Electron. 40, 909–916 (2004).
[Crossref]

Phillips, J.

Pilar, J.

Precek, M.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Rice, D.

W. Koechner and D. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[Crossref]

Rus, B.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Sawicka, M.

O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
[Crossref]

Sawicka-Chyla, M.

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

Sebban, S.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Slezak, O.

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
[Crossref]

Smith, J.

Veitch, P. J.

Walpole, L. J.

L. J. Walpole, “Fourth-rank tensors of the thirty-two crystal classes: multiplication tables,” Proc. R. Soc. Lond. A 391, 149–179 (1984).
[Crossref]

Weber, S.

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Wittrock, U.

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effects in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95–101 (1995).
[Crossref]

Xu, X.

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

Yang, H.

H. Yang, G. Feng, and S. Zhou, “Thermal effects in high-power Nd:YAG disk-type solid state laser,” Opt. Laser Technol. 43, 1006–1015 (2011).
[Crossref]

Zhou, S.

H. Yang, G. Feng, and S. Zhou, “Thermal effects in high-power Nd:YAG disk-type solid state laser,” Opt. Laser Technol. 43, 1006–1015 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

K. Genevrier, D. N. Papadopoulos, M. Besbes, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Thermally-induced-anisotropy issues in oriented cubic laser crystals, the cryogenically cooled case,” Appl. Phys. B 124, 209 (2018).
[Crossref]

IEEE J. Quantum Electron. (5)

Y. Chen, B. Chen, M. K. R. Patel, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers–I,” IEEE J. Quantum Electron. 40, 909–916 (2004).
[Crossref]

O. Slezak, A. Lucianetti, M. Divoky, M. Sawicka, and T. Mocek, “Optimization of wavefront distortions and thermal-stress induced birefringence in a cryogenically-cooled multislab laser amplifier,” IEEE J. Quantum Electron. 49, 960–966 (2013).
[Crossref]

D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
[Crossref]

W. Koechner and D. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. 6, 557–566 (1970).
[Crossref]

M. Sawicka-Chyla, M. Divoky, O. Slezak, M. De Vido, A. Lucianetti, and T. Mocek, “Numerical analysis of thermal effects in a concept of a cryogenically cooled Yb: YAG multislab 10 J/100-Hz laser amplifier,” IEEE J. Quantum Electron. 55, 1–8 (2019).
[Crossref]

J. Elasticity (1)

J. C. Nadeau and M. Ferrari, “Invariant tensor-to-matrix mappings for evaluation of tensorial expressions,” J. Elasticity 52, 43–61 (1998).
[Crossref]

Opt. Laser Technol. (3)

L. Liu, S. Guo, Q. Lu, X. Xu, J. Leng, J. Chen, and Z. Liu, “Stress-induced depolarization loss in a YAG zigzag slab,” Opt. Laser Technol. 43, 622–629 (2011).
[Crossref]

H. Yang, G. Feng, and S. Zhou, “Thermal effects in high-power Nd:YAG disk-type solid state laser,” Opt. Laser Technol. 43, 1006–1015 (2011).
[Crossref]

Q. Lü, U. Wittrock, and S. Dong, “Photoelastic effects in Nd:YAG rod and slab lasers,” Opt. Laser Technol. 27, 95–101 (1995).
[Crossref]

Optica (1)

Proc. R. Soc. Lond. A (1)

L. J. Walpole, “Fourth-rank tensors of the thirty-two crystal classes: multiplication tables,” Proc. R. Soc. Lond. A 391, 149–179 (1984).
[Crossref]

Proc. SPIE (1)

B. LeGarrec, S. Sebban, D. Margarone, M. Precek, S. Weber, O. Klimo, G. Korn, and B. Rus, “ELI-Beamlines: Extreme light infrastructure science and technology with ultra-intense lasers,” Proc. SPIE 8962, 89620I (2014).
[Crossref]

Other (3)

J. F. Nye, Physical Properties of Crystals (Oxford University, 2011).

A. Authier, ed. International Tables for Crystallography (2006), Vol. D.

T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1982).

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Tables (3)

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Table 1. Notation Overview

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Table 2. Transformation of the Basic Tensor Operations

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Table 3. Symmetry Constraints on the Optical Indicatrix

Equations (72)

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s ijkl = s ijlk ,
s ijkl = s jikl ,
i j α = { i , i = j 9 ( i + j ) , i j .
s ijkl = s klij .
[ σ 11 , σ 22 , σ 33 , σ 23 , σ 31 , σ 12 ] T [ σ 1 , σ 2 , σ 3 , σ 4 , σ 5 , σ 6 ] T .
I ijkl = 1 2 [ δ ik δ j l + δ i l δ j k ] .
[ I ] = diag [ 1 , 1 , 1 , 1 2 , 1 2 , 1 2 ]
[ I ] 1 = diag [ 1 , 1 , 1 , 2 , 2 , 2 ] .
x i = a ij x j ,
c ij = a ik a j l c k l
c ijkl = a i m a j n a k o a l p c m n o p
{ c } = [ A ] { c }
[ c ] = [ A ] [ c ] [ A ] T ,
[ A ] = [ a 11 2 a 12 2 a 13 2 2 a 12 a 13 2 a 13 a 11 2 a 11 a 12 a 21 2 a 22 2 a 23 2 2 a 22 a 23 2 a 23 a 21 2 a 21 a 22 a 31 2 a 32 2 a 33 2 2 a 32 a 33 2 a 31 a 33 2 a 31 a 32 a 21 a 31 a 22 a 32 a 23 a 33 a 23 a 32 + a 33 a 22 a 21 a 33 + a 31 a 23 a 22 a 31 + a 32 a 21 a 31 a 11 a 32 a 12 a 33 a 13 a 33 a 12 + a 13 a 32 a 13 a 31 + a 11 a 33 a 32 a 11 + a 12 a 31 a 11 a 21 a 12 a 22 a 13 a 23 a 13 a 22 + a 23 a 12 a 11 a 23 + a 21 a 13 a 12 a 21 + a 11 a 22 ] .
c m n o p = a p l a o k a n j a m i c ijkl .
[ A ] 1 = [ I ] [ A ] T [ I ] 1 .
σ ij = c ijkl ε k l { σ } = [ c ] [ I ] 1 { ε } ,
ε ij = s ijkl σ k l { ε } = [ s ] [ I ] 1 { σ } .
{ σ } = [ c ] [ I ] 1 [ s ] [ I ] 1 { σ } .
σ ^ { σ } ¯ = { σ } ,
ε ^ { ε } ¯ = [ I ] 1 { ε } ,
c ¯ [ c ] ¯ = [ c ] ,
s ¯ [ s ] ¯ = [ I ] 1 [ s ] [ I ] 1 ,
[ s ] = [ c 1 ] = [ I ] [ c ] 1 [ I ] .
s i i j j = c 11 + c 12 ( c 11 c 12 ) ( c 11 + 2 c 12 ) , i = j ,
s i i j j = c 12 ( c 11 c 12 ) ( c 11 + 2 c 12 ) , i j ,
s i j i j , s i j j i = 1 4 c 44 , i j ,
[ c ] = [ A ] [ c ] [ A ] T ,
D i = ϵ ij E j .
η ik ϵ k j = ϵ ik η k j = δ ij .
ϵ ij x i x j = 1 ,
η ij x i x j = 1 ,
x 1 2 n 1 2 + x 2 2 n 2 2 + x 3 2 n 3 2 = 1 ,
n i 2 = ϵ i i = 1 η i i .
n i = 1 Λ i .
η ij 0 = η 0 δ ij , η 0 = [ n ( T ) ] 2 ,
η ij 0 = diag [ η , η , η ] , η , = [ n , ( T ) ] 2 ,
η ij 0 = diag [ η 1 , η 2 , η 3 ] , η i = [ n i ( T ) ] 2 .
Δ η ij = p ijkl ε k l = π ijkl σ k l ,
π ijkl = p ijmn s mnkl .
η ij = η ij 0 + Δ η ij = η ij 0 + π ijkl σ k l .
[ π ] = [ p ] [ I ] 1 [ s ] .
[ π ] = [ p ] [ c ] 1 [ I ] .
[ π ] = [ A ] [ π ] [ A ] T = [ A ] [ p ] [ c ] 1 [ I ] [ A ] T .
{ Δ η } = [ π ] [ I ] 1 { σ } = [ A ] [ p ] [ c ] 1 [ I ] [ A ] T [ I ] 1 { σ } ,
[ π ] ¯ = [ A ] [ p ] [ c ] 1 [ I ] [ A ] T [ I ] 1 .
{ Δ η } = [ π ] ¯ { σ } ,
p ¯ [ p ] ¯ = [ p ] ,
π ¯ [ π ] ¯ = [ π ] [ I ] 1 .
{ η } = { η 0 } + { Δ η } = { η 0 } + [ π ] ¯ { σ } .
{ η 0 } = [ A ] { η 0 } ,
{ Δ η } = [ π ] [ I ] 1 { σ } = [ π ] [ A ] T [ I ] 1 { σ } = [ p ] [ I ] 1 [ s ] [ A ] T [ I ] 1 { σ } = [ p ] [ c ] 1 [ I ] [ A ] T [ I ] 1 { σ }
{ Δ η } = [ A ] [ p ] [ c ] 1 [ I ] [ A ] T [ I ] 1 { σ } ,
π 1111 = π 2222 = 1 2 Δ 1 [ ( p 1111 + p 1122 ) c 3333 2 p 1133 c 1133 ] + 1 2 Δ 2 [ ( p 1111 p 1122 ) c 2323 2 p 1123 c 1123 ] ,
π 1122 = π 2211 = 1 2 Δ 1 [ ( p 1111 + p 1122 ) c 3333 2 p 1133 c 1133 ] 1 2 Δ 2 [ ( p 1111 p 1122 ) c 2323 2 p 1123 c 1123 ] ,
π 1133 = π 2233 = 1 Δ 1 [ p 1133 ( c 1111 + c 1122 ) ( p 1111 + p 1122 ) c 1133 ] ,
π 1123 = π 1132 = π 2223 = π 2232 = π 1213 = π 2113 = π 1231 = π 2131 = 1 2 Δ 2 [ p 1123 ( c 1111 c 1122 ) ( p 1111 p 1122 ) c 1123 ] ,
π 3311 = π 3322 = 1 Δ 1 [ p 3311 c 3333 p 3333 c 1133 ] ,
π 3333 = 1 Δ 1 [ p 3333 ( c 1111 + c 1122 ) 2 p 3311 c 1133 ] ,
π 2311 = π 3211 = π 2322 = π 3222 = π 1312 = π 3112 = π 1321 = π 3121 = 1 Δ 2 [ p 2311 c 2323 p 2323 c 1123 ] ,
π 2323 = π 3223 = π 2332 = π 3232 = π 1313 = π 3113 = π 1331 = π 3131 = 1 2 Δ 2 [ p 2323 ( c 1111 c 1122 ) 2 p 2311 c 1123 ] ,
π 1212 = π 2112 = π 1221 = π 2121 = 1 2 [ π 1111 π 1122 ] ,
Δ 1 c 3333 ( c 1111 + c 1122 ) 2 c 1133 2 ,
Δ 2 c 2323 ( c 1111 c 1122 ) 2 c 1123 2 .
[ π ] ¯ = [ p ] ¯ [ s ] ¯ = [ p ] [ c ] 1 .
[ π ] = [ π ] ¯ [ I ] = [ p ] [ c ] 1 [ I ] .
[ π ] = [ p ] [ I ] 1 [ s ] = [ p ] [ I ] 1 [ I ] [ c ] 1 [ I ] = [ p ] [ c ] 1 [ I ] .
a 110 = [ 1 2 1 2 0 0 0 1 1 2 1 2 0 ] , a 111 = [ 1 6 2 6 1 6 1 2 0 1 2 1 3 1 3 1 3 ] .
{ Δ η } = [ p ] [ I ] 1 { ε } .
[ p [ 110 ] ] = [ A [ 110 ] ] [ p ] [ A [ 110 ] ] T [ I ] 1 ,
[ p 11 [ 110 ] p 12 [ 110 ] p 13 [ 110 ] 0 0 0 p 12 [ 110 ] p 22 [ 110 ] p 12 [ 110 ] 0 0 0 p 13 [ 110 ] p 12 [ 110 ] p 11 [ 110 ] 0 0 0 0 0 0 p 44 [ 110 ] 0 0 0 0 0 0 p 55 [ 110 ] 0 0 0 0 0 0 p 44 [ 110 ] ] ,
[ p 11 [ 111 ] p 12 [ 111 ] p 13 [ 111 ] 0 p 15 [ 111 ] 0 p 12 [ 111 ] p 11 [ 111 ] p 13 [ 111 ] 0 p 15 [ 111 ] 0 p 13 [ 111 ] p 13 [ 111 ] p 33 [ 111 ] 0 0 0 0 0 0 p 44 [ 111 ] 0 p 15 [ 111 ] 1 2 p 15 [ 111 ] 1 2 p 15 [ 111 ] 0 0 p 44 [ 111 ] 0 0 0 0 p 15 [ 111 ] 0 p 66 [ 111 ] ] ,