Abstract

An analytical model of cw quasi-three-level lasers that includes the influence of energy-transfer upconversion (ETU) has been developed. The results of the general output modeling were applied to a laser with Gaussian beams, and rigorous numerical calculations have been made to study the influence of ETU on threshold, output power, spatial distribution of population-inversion density, and fractional thermal loading. The model was applied to a laser operating at 946 nm in Nd:YAG, where the dependence of laser-beam size on laser performance was investigated in particular. A simple model for the degradation of laser-beam quality from a transversally varying saturated gain is proposed that is in good agreement with measurements of the laser in a plane-plane cavity.

© 2004 Optical Society of America

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    [CrossRef] [PubMed]
  5. Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
    [CrossRef]
  6. T. Chuang, H. R. Verdún, “Energy-transfer up-conversion and excited-state absorption of laser-radiation in Nd:YLF laser crystals,” IEEE J. Quantum Electron. 32, 79–91 (1996).
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    [CrossRef]
  8. M. Pollnau, P. J. Hardman, W. A. Clarkson, D. C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4,” Opt. Commun. 147, 203–211 (1998).
    [CrossRef]
  9. M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
    [CrossRef]
  10. P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  14. Y. F. Chen, Y. P. Lan, S. C. Wang, “Influence of energy-transfer upconversion on the performance of high-power diode-end-pumped cw lasers,” IEEE J. Quantum Electron. 36, 615–619 (2000).
    [CrossRef]
  15. Y. F. Chen, “Pump-to-mode size ratio dependence of thermal loading in diode-end-pumped solid-state lasers,” J. Opt. Soc. Am. B 17, 1835–1840 (2000).
    [CrossRef]
  16. S. Bjurshagen, D. Evekull, R. Koch, “Efficient generation of blue light by frequency doubling of a Nd:YAG laser operating on 4F3/2 → 4I9/2 transitions,” Appl. Phys. B 76, 135–141 (2003).
    [CrossRef]
  17. K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653–659 (1979).
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  18. P. F. Moulton, “An investigation of the Co:MgF, laser system,” IEEE J. Quantum Electron. 21, 1582–1595 (1985).
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  19. W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-VerlagBerlin, 1999).
    [CrossRef]
  20. S. Singh, R. G. Smith, L. G. Van Uitert, “Stimulated-emission cross section and fluorescent quantum efficiency of Nd3+ in yttrium aluminum garnet at room temperature,” Phys. Rev. B 10, 2566–2572 (1974).
    [CrossRef]
  21. C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
    [CrossRef]
  22. J. Frauchiger, P. Albers, H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
    [CrossRef]
  23. S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
    [CrossRef]
  24. A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1068 (1992).
    [CrossRef]
  25. R. Wynne, J. L. Daneu, T. Y. Fan, “Thermal coefficients of the expansion and refractive index in YAG,” Appl. Opt. 38, 3282–3284 (1999).
    [CrossRef]
  26. T. Y. Fan, J. L. Daneu, “Thermal coefficients of the optical path length and refractive index in YAG,” Appl. Opt. 37, 1635–1637 (1998).
    [CrossRef]
  27. D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
    [CrossRef]
  28. A. E. Siegman, “Analysis of laser beam quality degradation caused by quartic phase aberrations,” Appl. Opt. 32, 5893–5901 (1993).
    [CrossRef] [PubMed]
  29. N. Hodgson, H. Weber, Optical Resonators (Springer-Verlag, Berlin, 1996).
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  31. T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. 19, 554–556 (1994).
    [CrossRef] [PubMed]
  32. W.A. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D 34, 2381–2395 (2001).
    [CrossRef]

2003 (2)

C. Czeranowsky, E. Heumann, G. Huber, “All-solid-state continuous-wave frequency-doubled Nd:YAG-BiBO laser with 2.8-W output power at 473 nm,” Opt. Lett. 28, 432–434 (2003).
[CrossRef] [PubMed]

S. Bjurshagen, D. Evekull, R. Koch, “Efficient generation of blue light by frequency doubling of a Nd:YAG laser operating on 4F3/2 → 4I9/2 transitions,” Appl. Phys. B 76, 135–141 (2003).
[CrossRef]

2001 (1)

W.A. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D 34, 2381–2395 (2001).
[CrossRef]

2000 (3)

1999 (2)

P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
[CrossRef]

R. Wynne, J. L. Daneu, T. Y. Fan, “Thermal coefficients of the expansion and refractive index in YAG,” Appl. Opt. 38, 3282–3284 (1999).
[CrossRef]

1998 (5)

T. Y. Fan, J. L. Daneu, “Thermal coefficients of the optical path length and refractive index in YAG,” Appl. Opt. 37, 1635–1637 (1998).
[CrossRef]

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

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, W. A. Clarkson, D. C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4,” Opt. Commun. 147, 203–211 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
[CrossRef]

1997 (1)

1996 (1)

T. Chuang, H. R. Verdún, “Energy-transfer up-conversion and excited-state absorption of laser-radiation in Nd:YLF laser crystals,” IEEE J. Quantum Electron. 32, 79–91 (1996).
[CrossRef]

1995 (1)

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

1994 (2)

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. 19, 554–556 (1994).
[CrossRef] [PubMed]

1993 (1)

1992 (3)

J. Frauchiger, P. Albers, H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1068 (1992).
[CrossRef]

1988 (1)

1987 (3)

1985 (1)

P. F. Moulton, “An investigation of the Co:MgF, laser system,” IEEE J. Quantum Electron. 21, 1582–1595 (1985).
[CrossRef]

1979 (1)

K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653–659 (1979).
[CrossRef]

1974 (1)

S. Singh, R. G. Smith, L. G. Van Uitert, “Stimulated-emission cross section and fluorescent quantum efficiency of Nd3+ in yttrium aluminum garnet at room temperature,” Phys. Rev. B 10, 2566–2572 (1974).
[CrossRef]

Albers, P.

J. Frauchiger, P. Albers, H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

Bjurshagen, S.

S. Bjurshagen, D. Evekull, R. Koch, “Efficient generation of blue light by frequency doubling of a Nd:YAG laser operating on 4F3/2 → 4I9/2 transitions,” Appl. Phys. B 76, 135–141 (2003).
[CrossRef]

Bon, M.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Bonner, C. L.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

Bowers, M. S.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

Brown, D. C.

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

Byer, R.

Byer, R. L.

T. Taira, W. M. Tulloch, R. L. Byer, “Modeling of quasi-three-level lasers and operation of cw Yb:YAG lasers,” Appl. Opt. 36, 1867–1874 (1997).
[CrossRef] [PubMed]

T. Y. Fan, R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. 23, 605–612 (1987).
[CrossRef]

Chen, Y. F.

Y. F. Chen, Y. P. Lan, S. C. Wang, “Influence of energy-transfer upconversion on the performance of high-power diode-end-pumped cw lasers,” IEEE J. Quantum Electron. 36, 615–619 (2000).
[CrossRef]

Y. F. Chen, “Pump-to-mode size ratio dependence of thermal loading in diode-end-pumped solid-state lasers,” J. Opt. Soc. Am. B 17, 1835–1840 (2000).
[CrossRef]

Chuang, T.

T. Chuang, H. R. Verdún, “Energy-transfer up-conversion and excited-state absorption of laser-radiation in Nd:YLF laser crystals,” IEEE J. Quantum Electron. 32, 79–91 (1996).
[CrossRef]

Clarkson, W. A.

P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, W. A. Clarkson, D. C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4,” Opt. Commun. 147, 203–211 (1998).
[CrossRef]

Clarkson, W.A.

W.A. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D 34, 2381–2395 (2001).
[CrossRef]

Cousins, A. K.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1068 (1992).
[CrossRef]

Czeranowsky, C.

Daneu, J. L.

Descroix, E.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Evekull, D.

S. Bjurshagen, D. Evekull, R. Koch, “Efficient generation of blue light by frequency doubling of a Nd:YAG laser operating on 4F3/2 → 4I9/2 transitions,” Appl. Phys. B 76, 135–141 (2003).
[CrossRef]

Fan, T. Y.

Ferrand, B.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

Frauchiger, J.

J. Frauchiger, P. Albers, H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

Friel, G. J.

P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
[CrossRef]

Garnier, N.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Gruber, R.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Guy, S.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

Guyot, Y.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Hanna, D. C.

P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
[CrossRef]

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, W. A. Clarkson, D. C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4,” Opt. Commun. 147, 203–211 (1998).
[CrossRef]

Hardman, P. J.

P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, W. A. Clarkson, D. C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4,” Opt. Commun. 147, 203–211 (1998).
[CrossRef]

Heumann, E.

Hodgson, N.

N. Hodgson, H. Weber, Optical Resonators (Springer-Verlag, Berlin, 1996).

Huber, G.

Kern, M. A.

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
[CrossRef]

Koch, R.

S. Bjurshagen, D. Evekull, R. Koch, “Efficient generation of blue light by frequency doubling of a Nd:YAG laser operating on 4F3/2 → 4I9/2 transitions,” Appl. Phys. B 76, 135–141 (2003).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-VerlagBerlin, 1999).
[CrossRef]

Kubodera, K.

K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653–659 (1979).
[CrossRef]

Lan, Y. P.

Y. F. Chen, Y. P. Lan, S. C. Wang, “Influence of energy-transfer upconversion on the performance of high-power diode-end-pumped cw lasers,” IEEE J. Quantum Electron. 36, 615–619 (2000).
[CrossRef]

Laporte, P.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Length, W.

Manan, H.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Merazzi, S.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Moncorgé, R.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Moulton, P. F.

P. F. Moulton, “An investigation of the Co:MgF, laser system,” IEEE J. Quantum Electron. 21, 1582–1595 (1985).
[CrossRef]

Otsuka, K.

K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653–659 (1979).
[CrossRef]

Peuser, P.

Pfistner, C.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Pollnau, M.

P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, W. A. Clarkson, D. C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4,” Opt. Commun. 147, 203–211 (1998).
[CrossRef]

Risk, W. P.

Rivoire, J. Y.

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

Seamans, J. F.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

Shepherd, D. P.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

Siegman, A. E.

Singh, S.

S. Singh, R. G. Smith, L. G. Van Uitert, “Stimulated-emission cross section and fluorescent quantum efficiency of Nd3+ in yttrium aluminum garnet at room temperature,” Phys. Rev. B 10, 2566–2572 (1974).
[CrossRef]

Smith, R. G.

S. Singh, R. G. Smith, L. G. Van Uitert, “Stimulated-emission cross section and fluorescent quantum efficiency of Nd3+ in yttrium aluminum garnet at room temperature,” Phys. Rev. B 10, 2566–2572 (1974).
[CrossRef]

Taira, T.

Tidwell, S. C.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

Tropper, A. C.

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

Tulloch, W. M.

Van Uitert, L. G.

S. Singh, R. G. Smith, L. G. Van Uitert, “Stimulated-emission cross section and fluorescent quantum efficiency of Nd3+ in yttrium aluminum garnet at room temperature,” Phys. Rev. B 10, 2566–2572 (1974).
[CrossRef]

Verdún, H. R.

T. Chuang, H. R. Verdún, “Energy-transfer up-conversion and excited-state absorption of laser-radiation in Nd:YLF laser crystals,” IEEE J. Quantum Electron. 32, 79–91 (1996).
[CrossRef]

Wang, S. C.

Y. F. Chen, Y. P. Lan, S. C. Wang, “Influence of energy-transfer upconversion on the performance of high-power diode-end-pumped cw lasers,” IEEE J. Quantum Electron. 36, 615–619 (2000).
[CrossRef]

Weber, H.

N. Hodgson, H. Weber, Optical Resonators (Springer-Verlag, Berlin, 1996).

Weber, H. P.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

J. Frauchiger, P. Albers, H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

Weber, R.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Wynne, R.

Zeller, P.

Appl. Opt. (4)

Appl. Phys. B (1)

S. Bjurshagen, D. Evekull, R. Koch, “Efficient generation of blue light by frequency doubling of a Nd:YAG laser operating on 4F3/2 → 4I9/2 transitions,” Appl. Phys. B 76, 135–141 (2003).
[CrossRef]

IEEE J. Quantum Electron. (11)

P. F. Moulton, “An investigation of the Co:MgF, laser system,” IEEE J. Quantum Electron. 21, 1582–1595 (1985).
[CrossRef]

Y. F. Chen, Y. P. Lan, S. C. Wang, “Influence of energy-transfer upconversion on the performance of high-power diode-end-pumped cw lasers,” IEEE J. Quantum Electron. 36, 615–619 (2000).
[CrossRef]

P. J. Hardman, W. A. Clarkson, G. J. Friel, M. Pollnau, D. C. Hanna, “Energy-transfer upconversion and thermal lensing in high-power end-pumped Nd:YLF laser crystals,” IEEE J. Quantum Electron. 35, 647–655 (1999).
[CrossRef]

T. Y. Fan, R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. 23, 605–612 (1987).
[CrossRef]

T. Chuang, H. R. Verdún, “Energy-transfer up-conversion and excited-state absorption of laser-radiation in Nd:YLF laser crystals,” IEEE J. Quantum Electron. 32, 79–91 (1996).
[CrossRef]

S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, B. Ferrand, “High-inversion densities in Nd:YAG: upconversion and bleaching,” IEEE J. Quantum Electron. 34, 900–909 (1998).
[CrossRef]

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

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

J. Frauchiger, P. Albers, H. P. Weber, “Modeling of thermal lensing and higher order ring mode oscillation in end-pumped cw Nd:YAG lasers,” IEEE J. Quantum Electron. 28, 1046–1056 (1992).
[CrossRef]

S. C. Tidwell, J. F. Seamans, M. S. Bowers, A. K. Cousins, “Scaling cw diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[CrossRef]

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1068 (1992).
[CrossRef]

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[CrossRef]

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W.A. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D 34, 2381–2395 (2001).
[CrossRef]

Opt. Commun. (1)

M. Pollnau, P. J. Hardman, W. A. Clarkson, D. C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4,” Opt. Commun. 147, 203–211 (1998).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (3)

S. Singh, R. G. Smith, L. G. Van Uitert, “Stimulated-emission cross section and fluorescent quantum efficiency of Nd3+ in yttrium aluminum garnet at room temperature,” Phys. Rev. B 10, 2566–2572 (1974).
[CrossRef]

Y. Guyot, H. Manan, J. Y. Rivoire, R. Moncorgé, N. Garnier, E. Descroix, M. Bon, P. Laporte, “Excited-state-absorption and upconversion studies of Nd3+-doped single crystals Y3Al5O12, YLiF4 and LaMgAL11O19,” Phys. Rev. B 51, 784–799 (1995).
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG,” Phys. Rev. B 58, 16,076–16,092 (1998).
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Figures (19)

Fig. 1
Fig. 1

Energy-level diagram of Nd:YAG.

Fig. 2
Fig. 2

Normalized threshold as a function of mode waist ratio a = w P /w L for four values of upconversion parameter U for a laser experiencing no reabsorption loss (B = 0).

Fig. 3
Fig. 3

Normalized threshold as a function of mode waist ratio a = w P /w L for four values of upconversion parameter U for a laser experiencing reabsorption loss (B = 1).

Fig. 4
Fig. 4

Normalized internal laser power as a function of mode waist ratio a = w P /w L for four values of upconversion parameter U for a laser experiencing no reabsorption loss (B = 0). F is the normalized pump power.

Fig. 5
Fig. 5

Normalized internal laser power as a function of mode waist ratio a = w P /w L for four values of upconversion parameter U for a laser experiencing reabsorption loss (B = 1). F is the normalized pump power.

Fig. 6
Fig. 6

Radial distribution of the normalized population-inversion density (integrated over z) under lasing conditions for F = 200, S = 200, B = 1, and four values of U. Units on the vertical axis are arbitrary but consistent from figure to figure. The laser field profile is indicated by a dashed curve.

Fig. 7
Fig. 7

Radial distribution of F ETU (integrated and taken as a mean over z) under lasing conditions for F = 200, S = 200, B = 1, and three values of U. The pump field profile is indicated by the dashed-dotted line and is shown constant for all figures.

Fig. 8
Fig. 8

Calculated output power including the influence of ETU at 946 nm versus laser-mode radius w L for four pump powers P P .

Fig. 9
Fig. 9

Radial distribution of the population-inversion density (integrated and taken as a mean over z) under lasing conditions for 20.6 W of pump power and three values of laser-mode radius w L .

Fig. 10
Fig. 10

Radial distribution of fractional thermal loading ξ (integrated and taken as a mean over z) under lasing conditions for 20.6 W of pump power and three values of laser-mode radius w L .

Fig. 11
Fig. 11

Radial distribution of heat-source density Q (integrated and taken as a mean over z) under lasing conditions for 20.6 W of pump power and three values of laser-mode radius w L . The absorbed pump power is 16.0 W, and the total generated heat is 5.7 W for w L = 50 μm, 3.4 W for w L = 100 μm, and 3.1 W for w L = 200 μm.

Fig. 12
Fig. 12

Temperature distributions in the Nd:YAG crystal at 20.6 W of pump power: (a) T max = 361 K; (b) T max = 327 K; (c) T max = 334 K.

Fig. 13
Fig. 13

OPD (solid curves) versus radial coordinate r at 20.6-W pump power and three values of laser mode radius w L . Dashed lines, polynomial fits OPD(r) = OPD(0) -r 2/2f th + C 4 r 4, where f th = 21 mm for w L = 50 μm, f th = 40 mm for w L = 100 μm, and f th = 30 mm for w L = 200 μm.

Fig. 14
Fig. 14

Calculated focal length f th of the thermal lens including ETU under lasing conditions at 946 nm versus laser-mode radius w L for four pump powers PP .

Fig. 15
Fig. 15

Calculated beam radius of fundamental laser mode w L,00 resulting from the thermal lens including ETU versus laser-mode radius w L for four pump powers P P .

Fig. 16
Fig. 16

Calculated beam-quality factor M 2 of the laser beam at 946 nm versus laser-mode radius w L for four pump powers P P . Solid curves, degradation in beam quality from saturated gain effects; dashed curves, degradation in beam quality from thermally induced quartic phase aberrations.

Fig. 17
Fig. 17

Output power at 946 nm versus input power: circles, measured power; solid curve, calculated power including ETU; dashed curve, calculated power not including ETU.

Fig. 18
Fig. 18

Dioptric power D th of the thermal lens under lasing conditions at 946 nm versus input power: circles, measured values; solid curve, calculated values including ETU; dashed curve, calculated values not including ETU.

Fig. 19
Fig. 19

Beam-quality factor M 2 of the laser beam at 946 nm versus input power: circles, measured values; solid curve, calculated values including ETU; dashed curve, calculated values not including ETU.

Equations (51)

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dN4x, y, zdt=RrPx, y, z-N4x, y, z-N40τ-cσn ΔNx, y, zΦϕ0x, y, z-WN4x, y, z-N402=0,
ΔN-ΔN0=fa+fbN4-N40,
dΔNx, y, zdt=fa+fbRrPx, y, z-ΔNx, y, z-ΔN0τ-cσn×fa+fbΔNx, y, zΦϕ0x, y, z-Wfa+fbΔNx, y, z-ΔN02=0,
R=PPηahνP,
Φ=2lc*PoutchνLT,
crystal rPx, y, zdV=1.
cavity ϕ0x, y, zdV=1.
dΦdt=cσncrystal ΔNx, y, zΦϕ0x, y, zdV-Φτc=0,
ΔN=2τfRrP+2 cστn fNa0Φϕ01+cστn fΦϕ0+1+cστn fΦϕ02+4Wτ2RrP+4Wτ2cσn Na0Φϕ01/2-Na0,
ΔNth=2τfRthrP1+1+4Wτ2RthrP1/2-Na0.
2σlc*ncrystal ΔNx, y, zϕ0x, y, zdV=δ,
2σlc*ncrystal2τfRrPϕ0+2 cστn fNa0Φϕ201+cστn fΦϕ0+1+cστn fΦϕ02+4Wτ2RrP+4Wτ2cσn Na0Φϕ01/2dV=δ+δl,
Rth=δ+δl2στflc*× crystal2rPϕ01+1+4Wτ2RthrP1/2dV-1.
rPr, z=2αηaπwP2exp-2r2wP2exp-αz,
ϕ0r, z=2πwL2lc*exp-2r2wL2,
a=wPwL,
x=2r2wP2,
F=4τσRπwL2δ,
S=2cστΦπwL2lc*,
B=2Na0σlδ.
UP=8Wτ2αRηaπwP2,
UL=8Wτ2cσNa0ΦπwL2lc*.
F=1+B-2Ba2l00lfS exp-2a2x1+fS exp-a2x+1+fS exp-a2x2+UP exp-xexp-αz+UL exp-a2x1/2dzdx2f αηa00lexp-a2+1xexp-αz1+fS exp-a2x+1+fS exp-a2x2+UP exp-xexp-αz+UL exp-a2x1/2dzdx,
U=2Wτδfσl,
UP=αlηaa2 fUF,
UL=fUBS.
F=1+B2Ba2 l00lfS exp(2a2x)1+fS exp(a2x)+[(1+1fS exp(a2x)]2+αl/ηaa2×fUF exp(x)exp(αz)+fUBS exp(a2x)dzdx 2fαηa 00lexp[(a2+1)x]exp(αz)1+fS exp(a2x)+[(1+fS exp(a2x)]2+αl/ηaa2×fUF exp(x)exp(αz)+fUBS exp(a2x)dzdx
Fth=1+B2f αηa00lexp-a2+1xexp-αz1+1+αl/ηaa2×fUFth exp-xexp-αz1/2dzdx.
absorption=fRrPx, y, z-cσn fΔN0Φϕ0x, y, z,
emission=-ΔNx, y, z-ΔN0τ-cσn fΔNx, y, z-ΔN0Φϕ0x, y, z,
upconversion=-WfΔNx, y, z-ΔN02.
FETU=|upconversionabsorption|=1-|emissionabsorption|,
FETUx, y, z=1-ΔNx, y, z+Na0ΔNno ETUx, y, z+Na0,
ΔNno ETUx, y, z=τfRrPx, y, z+cστ/nfNa0Φϕ0x, y, z1+cστ/nfΦϕ0x, y, z-Na0.
FETUx, y, z=1-21+1+4Wτ2RrPx, y, z+4Wτ2cσn Na0Φϕ0x, y, z1+cστn fΦϕ0x, y, z21/2.
ξx, y, z=ξ01-FETUx, y, z+FETUx, y, z,
FETU,NLx, y, z=1-21+1+4Wτ2RrPx, y, z1/2.
wPz=wP01+λPMP2z-zP0πnwP0221/2,
αPP=33×PPW+69 m-1PP<7 W300 m-1PP7 W.
Qr, z=ξr, zPPηarPr, z.
-KTTr, z=-Qr, z,
KT=K0T0/T,
OPDr=0l χTTr, zdz,
χT=dndTT+Cαn-11+ναTT.
αTT=2.3511×10-8 T-2.4748×10-7 K-1,
dndTT=3.5210×10-8 T-1.8896×10-6 K-1.
OPDr-OPD0=-r22fth+C4r4,
Mr2=Mi22+Mq221/2,
Mq2=4πC4wL4λL2.
wL=wL,00ML2,
ML2=wL/wL,002,

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