Abstract

We grew several thulium- (Tm-) doped La2Be2O5 crystals and determined the concentration of the incorporated Tm using proton-induced x-ray emission. Polarized absorption and emission spectra of Tm:La2Be2O5 were investigated, allowing the stimulated-emission cross section to be estimated with the reciprocity method and the Fuchtbauer–Ladenburg equation. We report lifetime measurements of each of the transitions from the 3F4 to 3H6 multiplet and relate them to the radiative lifetime. In view of these results we revisit the question of Tm:La2Be2O5 as a prospective laser material for laser emission at 1.8 μm in the presence of losses and determine the pumping threshold and slope efficiency for a typical resonator geometry.

© 1998 Optical Society of America

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  1. T. S. Kubo and T. J. Kane, “Diode-pumped lasers at five eye-safe wavelengths,” IEEE J. Quantum Electron. 28, 1033–1040 (1992).
    [CrossRef]
  2. A. A. Kaminskii, “Progress in praseodymium crystalline lasers emitting in the visible,” in Advanced Solid State Lasers, A. A. Pinto and T. Y. Fan, eds., Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 266–270.
  3. L. J. Atherton, S. A. Payne, and C. D. Brandle, “Oxide and fluoride laser crystals,” Ann. Rev. Mater. Sci. 23, 453–502 (1993).
    [CrossRef]
  4. J. D. Kmetec, T. S. Kubo, and T. J. Kane, “Laser performance of diode pumped thulium-doped Y3Al5O12,(Y, Lu)3Al5O12,Lu3Al5O12, crystals,” Opt. Lett. 19, 186–188 (1994).
    [CrossRef]
  5. C. Hauglie-Hanssen and N. Djeu, “Further investigations of a 2 μm Tm:YVO4 Laser,” IEEE J. Quantum Electron. 30, 275–279 (1994).
    [CrossRef]
  6. X. X. Chang, P. Hong, M. Bass, and B. H. T. Chai, “Blue upconversion with excitation into Yb- and Tm-codoped fluoride crystals,” Phys. Rev. B 51, 9298–9301 (1988).
  7. T. Y. Fan, G. Huber, R. L. Byer, and P. Mitzscherlich, “Spectroscopy and diode laser-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
    [CrossRef]
  8. N. P. Barnes, E. D. Filer, F. L. Naranjo, W. J. Rodriguez, and M. R. Kokta, “Spectroscopic and laser properties of Ho, Tm:LuAG,” Opt. Lett. 18, 708–710 (1993).
    [CrossRef] [PubMed]
  9. G. J. Koch, J. P. Deyst, and M. E. Storm, “Single frequency lasing of monolithic Ho, Tm:YLF,” Opt. Lett. 18, 1235–1237 (1993).
    [CrossRef] [PubMed]
  10. R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
    [CrossRef]
  11. J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.
  12. S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
    [CrossRef]
  13. C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
    [CrossRef]
  14. L. A. Harris and H. Y. Yakel, “The crystal structure of La2Be2O5,” Acta Crystallogr. Sec. B 24, 672–682 (1968).
    [CrossRef]
  15. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
    [CrossRef]
  16. B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925–930 (1982).
    [CrossRef]
  17. W. Koechner, Solid-State Laser Engineering (Springer, New York, 1986), p. 17.
  18. S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
    [CrossRef]
  19. S. A. Payne, J. A. Caird, L. L. Chase, L. K. Smith, N. D. Nielsen, and W. F. Krupke, “Spectroscopy and gain mea surements of Nd3+ in SrF2 and other fluoride-structure hosts,” J. Opt. Soc. Am. B 8, 726–740 (1991).
    [CrossRef]
  20. W. E. Martin and D. Milam, “Gain saturation in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 1155–1163 (1982).
    [CrossRef]
  21. L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
    [CrossRef]
  22. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
    [CrossRef]
  23. G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
    [CrossRef]
  24. W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+,Nd3+,Sm3+,Dy3+,Ho3+,Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
    [CrossRef]
  25. W. F. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
    [CrossRef]
  26. W. Koechner, Solid-State Laser Engineering (Springer, New York, 1995), p. 34.
  27. M. J. P. Payne, Defence Research Agency (M), UK, has grown Er3Al5O12, i.e., replaced Y3+ ions completely with Er3+ ions.
  28. J. S. Griffith, The Theory of Transition Metal Ions (University Press, Cambridge, 1961).
  29. Lifetime calculated using the analyses of Judd and Ofelt (see Refs. 22 and 23).
  30. B. Henderson and G. F. Imbusch, Optical Spectroscopy of Inorganic Solids (Clarendon, Oxford, 1989), p. 250.
  31. T. Y. Fan and R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. QE-23, 605–612 (1987).
  32. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 473–483.
  33. R. I. Tricket, “Thulium:YAG laser for microsurgical tissue welding,” Bachelor of Technology Honours Thesis (Macquarie University, North Ryde, NSW, Australia, 1993).
  34. J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
    [CrossRef]

1994 (2)

J. D. Kmetec, T. S. Kubo, and T. J. Kane, “Laser performance of diode pumped thulium-doped Y3Al5O12,(Y, Lu)3Al5O12,Lu3Al5O12, crystals,” Opt. Lett. 19, 186–188 (1994).
[CrossRef]

C. Hauglie-Hanssen and N. Djeu, “Further investigations of a 2 μm Tm:YVO4 Laser,” IEEE J. Quantum Electron. 30, 275–279 (1994).
[CrossRef]

1993 (4)

L. J. Atherton, S. A. Payne, and C. D. Brandle, “Oxide and fluoride laser crystals,” Ann. Rev. Mater. Sci. 23, 453–502 (1993).
[CrossRef]

N. P. Barnes, E. D. Filer, F. L. Naranjo, W. J. Rodriguez, and M. R. Kokta, “Spectroscopic and laser properties of Ho, Tm:LuAG,” Opt. Lett. 18, 708–710 (1993).
[CrossRef] [PubMed]

G. J. Koch, J. P. Deyst, and M. E. Storm, “Single frequency lasing of monolithic Ho, Tm:YLF,” Opt. Lett. 18, 1235–1237 (1993).
[CrossRef] [PubMed]

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

1992 (2)

T. S. Kubo and T. J. Kane, “Diode-pumped lasers at five eye-safe wavelengths,” IEEE J. Quantum Electron. 28, 1033–1040 (1992).
[CrossRef]

S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
[CrossRef]

1991 (1)

1990 (1)

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

1989 (1)

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

1988 (3)

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
[CrossRef]

X. X. Chang, P. Hong, M. Bass, and B. H. T. Chai, “Blue upconversion with excitation into Yb- and Tm-codoped fluoride crystals,” Phys. Rev. B 51, 9298–9301 (1988).

T. Y. Fan, G. Huber, R. L. Byer, and P. Mitzscherlich, “Spectroscopy and diode laser-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

1987 (1)

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

1982 (2)

B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925–930 (1982).
[CrossRef]

W. E. Martin and D. Milam, “Gain saturation in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 1155–1163 (1982).
[CrossRef]

1975 (1)

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

1974 (1)

W. F. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
[CrossRef]

1968 (2)

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+,Nd3+,Sm3+,Dy3+,Ho3+,Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

L. A. Harris and H. Y. Yakel, “The crystal structure of La2Be2O5,” Acta Crystallogr. Sec. B 24, 672–682 (1968).
[CrossRef]

1964 (1)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[CrossRef]

1962 (2)

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
[CrossRef]

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
[CrossRef]

Atherton, L. J.

L. J. Atherton, S. A. Payne, and C. D. Brandle, “Oxide and fluoride laser crystals,” Ann. Rev. Mater. Sci. 23, 453–502 (1993).
[CrossRef]

Aull, B. F.

B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925–930 (1982).
[CrossRef]

Barnes, N. P.

Bass, M.

X. X. Chang, P. Hong, M. Bass, and B. H. T. Chai, “Blue upconversion with excitation into Yb- and Tm-codoped fluoride crystals,” Phys. Rev. B 51, 9298–9301 (1988).

Begley, R. F.

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Brandle, C. D.

L. J. Atherton, S. A. Payne, and C. D. Brandle, “Oxide and fluoride laser crystals,” Ann. Rev. Mater. Sci. 23, 453–502 (1993).
[CrossRef]

Byer, R. L.

T. Y. Fan, G. Huber, R. L. Byer, and P. Mitzscherlich, “Spectroscopy and diode laser-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

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

Caird, J. A.

Carnall, W. T.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+,Nd3+,Sm3+,Dy3+,Ho3+,Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Case, L. L.

S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
[CrossRef]

Cashmore, D.

J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.

Chai, B. H. T.

X. X. Chang, P. Hong, M. Bass, and B. H. T. Chai, “Blue upconversion with excitation into Yb- and Tm-codoped fluoride crystals,” Phys. Rev. B 51, 9298–9301 (1988).

Chang, X. X.

X. X. Chang, P. Hong, M. Bass, and B. H. T. Chai, “Blue upconversion with excitation into Yb- and Tm-codoped fluoride crystals,” Phys. Rev. B 51, 9298–9301 (1988).

Chase, L. L.

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

S. A. Payne, J. A. Caird, L. L. Chase, L. K. Smith, N. D. Nielsen, and W. F. Krupke, “Spectroscopy and gain mea surements of Nd3+ in SrF2 and other fluoride-structure hosts,” J. Opt. Soc. Am. B 8, 726–740 (1991).
[CrossRef]

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
[CrossRef]

Clayton, E.

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

Cline, C. F.

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Cousens, D. R.

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

Deloach, L. D.

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

Deyst, J. P.

Djeu, N.

C. Hauglie-Hanssen and N. Djeu, “Further investigations of a 2 μm Tm:YVO4 Laser,” IEEE J. Quantum Electron. 30, 275–279 (1994).
[CrossRef]

Dutoit, M.

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Esterowitz, L.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Fan, T. Y.

T. Y. Fan, G. Huber, R. L. Byer, and P. Mitzscherlich, “Spectroscopy and diode laser-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

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

Fields, P. R.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+,Nd3+,Sm3+,Dy3+,Ho3+,Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Filer, E. D.

Fueloep, K.

J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.

Griffin, W. L.

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

Griffith, J. S.

J. S. Griffith, The Theory of Transition Metal Ions (University Press, Cambridge, 1961).

Gruber, J. B.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Harget, P. J.

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Harris, L. A.

L. A. Harris and H. Y. Yakel, “The crystal structure of La2Be2O5,” Acta Crystallogr. Sec. B 24, 672–682 (1968).
[CrossRef]

Hauglie-Hanssen, C.

C. Hauglie-Hanssen and N. Djeu, “Further investigations of a 2 μm Tm:YVO4 Laser,” IEEE J. Quantum Electron. 30, 275–279 (1994).
[CrossRef]

Henderson, B.

B. Henderson and G. F. Imbusch, Optical Spectroscopy of Inorganic Solids (Clarendon, Oxford, 1989), p. 250.

Hills, M. E.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Hong, P.

X. X. Chang, P. Hong, M. Bass, and B. H. T. Chai, “Blue upconversion with excitation into Yb- and Tm-codoped fluoride crystals,” Phys. Rev. B 51, 9298–9301 (1988).

Horsburgh, M. A.

J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.

Huber, G.

T. Y. Fan, G. Huber, R. L. Byer, and P. Mitzscherlich, “Spectroscopy and diode laser-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

Imbusch, G. F.

B. Henderson and G. F. Imbusch, Optical Spectroscopy of Inorganic Solids (Clarendon, Oxford, 1989), p. 250.

Jenssen, H. P.

B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925–930 (1982).
[CrossRef]

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Judd, B. R.

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, “Progress in praseodymium crystalline lasers emitting in the visible,” in Advanced Solid State Lasers, A. A. Pinto and T. Y. Fan, eds., Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 266–270.

Kane, T. J.

J. D. Kmetec, T. S. Kubo, and T. J. Kane, “Laser performance of diode pumped thulium-doped Y3Al5O12,(Y, Lu)3Al5O12,Lu3Al5O12, crystals,” Opt. Lett. 19, 186–188 (1994).
[CrossRef]

T. S. Kubo and T. J. Kane, “Diode-pumped lasers at five eye-safe wavelengths,” IEEE J. Quantum Electron. 28, 1033–1040 (1992).
[CrossRef]

Kintz, G. J.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Kmetec, J. D.

Koch, G. J.

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer, New York, 1995), p. 34.

W. Koechner, Solid-State Laser Engineering (Springer, New York, 1986), p. 17.

Kokta, M. R.

Krupke, W. F.

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
[CrossRef]

S. A. Payne, J. A. Caird, L. L. Chase, L. K. Smith, N. D. Nielsen, and W. F. Krupke, “Spectroscopy and gain mea surements of Nd3+ in SrF2 and other fluoride-structure hosts,” J. Opt. Soc. Am. B 8, 726–740 (1991).
[CrossRef]

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
[CrossRef]

W. F. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
[CrossRef]

Kubo, T. S.

J. D. Kmetec, T. S. Kubo, and T. J. Kane, “Laser performance of diode pumped thulium-doped Y3Al5O12,(Y, Lu)3Al5O12,Lu3Al5O12, crystals,” Opt. Lett. 19, 186–188 (1994).
[CrossRef]

T. S. Kubo and T. J. Kane, “Diode-pumped lasers at five eye-safe wavelengths,” IEEE J. Quantum Electron. 28, 1033–1040 (1992).
[CrossRef]

Kway, W. L.

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
[CrossRef]

La France, T. S.

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Macfarlane, R. M.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Martin, W. E.

W. E. Martin and D. Milam, “Gain saturation in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 1155–1163 (1982).
[CrossRef]

McCumber, D. E.

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[CrossRef]

Milam, D.

W. E. Martin and D. Milam, “Gain saturation in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 1155–1163 (1982).
[CrossRef]

Mitzscherlich, P.

T. Y. Fan, G. Huber, R. L. Byer, and P. Mitzscherlich, “Spectroscopy and diode laser-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

Morris, R. C.

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Morrison, C. A.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Naranjo, F. L.

Newkirk, H. W.

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
[CrossRef]

Nielsen, N. D.

Ofelt, G. S.

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
[CrossRef]

Payne, M. J. P.

M. J. P. Payne, Defence Research Agency (M), UK, has grown Er3Al5O12, i.e., replaced Y3+ ions completely with Er3+ ions.

Payne, S. A.

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

L. J. Atherton, S. A. Payne, and C. D. Brandle, “Oxide and fluoride laser crystals,” Ann. Rev. Mater. Sci. 23, 453–502 (1993).
[CrossRef]

S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
[CrossRef]

S. A. Payne, J. A. Caird, L. L. Chase, L. K. Smith, N. D. Nielsen, and W. F. Krupke, “Spectroscopy and gain mea surements of Nd3+ in SrF2 and other fluoride-structure hosts,” J. Opt. Soc. Am. B 8, 726–740 (1991).
[CrossRef]

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
[CrossRef]

Picone, P. J.

J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.

Quarles, G. J.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Rajnak, K.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+,Nd3+,Sm3+,Dy3+,Ho3+,Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Richards, J.

J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.

Rodriguez, W. J.

Ryan, C. G.

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

Seymour, R. S.

J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.

Sie, S. H.

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 473–483.

Smith, L. K.

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
[CrossRef]

S. A. Payne, J. A. Caird, L. L. Chase, L. K. Smith, N. D. Nielsen, and W. F. Krupke, “Spectroscopy and gain mea surements of Nd3+ in SrF2 and other fluoride-structure hosts,” J. Opt. Soc. Am. B 8, 726–740 (1991).
[CrossRef]

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
[CrossRef]

Storm, M. E.

Suter, G. F.

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

Tricket, R. I.

R. I. Tricket, “Thulium:YAG laser for microsurgical tissue welding,” Bachelor of Technology Honours Thesis (Macquarie University, North Ryde, NSW, Australia, 1993).

Turner, G. A.

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

Webb, R.

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

Yakel, H. Y.

L. A. Harris and H. Y. Yakel, “The crystal structure of La2Be2O5,” Acta Crystallogr. Sec. B 24, 672–682 (1968).
[CrossRef]

Acta Crystallogr. Sec. B (1)

L. A. Harris and H. Y. Yakel, “The crystal structure of La2Be2O5,” Acta Crystallogr. Sec. B 24, 672–682 (1968).
[CrossRef]

Ann. Rev. Mater. Sci. (1)

L. J. Atherton, S. A. Payne, and C. D. Brandle, “Oxide and fluoride laser crystals,” Ann. Rev. Mater. Sci. 23, 453–502 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

R. C. Morris, C. F. Cline, R. F. Begley, M. Dutoit, P. J. Harget, H. P. Jenssen, T. S. La France, and R. Webb, “Lanthanum beryllate: a new rare-earth ion laser host,” Appl. Phys. Lett. 27, 444–445 (1975).
[CrossRef]

IEEE J. Quantum Electron. (10)

S. A. Payne, L. L. Case, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+,Tm3+, and Ho3+,” IEEE J. Quantum Electron. QE-28, 2619–2630 (1992).
[CrossRef]

B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 925–930 (1982).
[CrossRef]

T. S. Kubo and T. J. Kane, “Diode-pumped lasers at five eye-safe wavelengths,” IEEE J. Quantum Electron. 28, 1033–1040 (1992).
[CrossRef]

C. Hauglie-Hanssen and N. Djeu, “Further investigations of a 2 μm Tm:YVO4 Laser,” IEEE J. Quantum Electron. 30, 275–279 (1994).
[CrossRef]

T. Y. Fan, G. Huber, R. L. Byer, and P. Mitzscherlich, “Spectroscopy and diode laser-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quantum Electron. 24, 2243–2252 (1988).
[CrossRef]

W. E. Martin and D. Milam, “Gain saturation in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. QE-18, 1155–1163 (1982).
[CrossRef]

L. D. Deloach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications,” IEEE J. Quantum Electron. 29, 1179–1191 (1993).
[CrossRef]

W. F. Krupke, “Induced-emission cross sections in neodymium laser glasses,” IEEE J. Quantum Electron. QE-10, 450–457 (1974).
[CrossRef]

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

J. Chem. Phys. (2)

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
[CrossRef]

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+,Nd3+,Sm3+,Dy3+,Ho3+,Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nucl. Instrum. Methods Phys. Res. B (1)

C. G. Ryan, D. R. Cousens, S. H. Sie, W. L. Griffin, G. F. Suter, and E. Clayton, “Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe,” Nucl. Instrum. Methods Phys. Res. B 47, 55–71 (1990).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (2)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[CrossRef]

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
[CrossRef]

Phys. Rev. B (2)

J. B. Gruber, M. E. Hills, R. M. Macfarlane, C. A. Morrison, G. A. Turner, G. J. Quarles, G. J. Kintz, and L. Esterowitz, “Spectra and energy levels of Tm3+:Y3Al5O12,” Phys. Rev. B 40, 9464–9478 (1989).
[CrossRef]

X. X. Chang, P. Hong, M. Bass, and B. H. T. Chai, “Blue upconversion with excitation into Yb- and Tm-codoped fluoride crystals,” Phys. Rev. B 51, 9298–9301 (1988).

Other (10)

A. A. Kaminskii, “Progress in praseodymium crystalline lasers emitting in the visible,” in Advanced Solid State Lasers, A. A. Pinto and T. Y. Fan, eds., Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), pp. 266–270.

W. Koechner, Solid-State Laser Engineering (Springer, New York, 1986), p. 17.

J. Richards, K. Fueloep, R. S. Seymour, D. Cashmore, P. J. Picone, and M. A. Horsburgh, “Nd:BeL laser at 1365 nm,” in Advanced Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 5 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 119–123.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 473–483.

R. I. Tricket, “Thulium:YAG laser for microsurgical tissue welding,” Bachelor of Technology Honours Thesis (Macquarie University, North Ryde, NSW, Australia, 1993).

W. Koechner, Solid-State Laser Engineering (Springer, New York, 1995), p. 34.

M. J. P. Payne, Defence Research Agency (M), UK, has grown Er3Al5O12, i.e., replaced Y3+ ions completely with Er3+ ions.

J. S. Griffith, The Theory of Transition Metal Ions (University Press, Cambridge, 1961).

Lifetime calculated using the analyses of Judd and Ofelt (see Refs. 22 and 23).

B. Henderson and G. F. Imbusch, Optical Spectroscopy of Inorganic Solids (Clarendon, Oxford, 1989), p. 250.

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Figures (12)

Fig. 1
Fig. 1

Unpolarized absorption spectrum for 0.2% Tm:BeL in the region of wavelengths available for pumping by diode lasers at 685 and 785 nm.

Fig. 2
Fig. 2

Measured Tm content in the crystal versus actual Tm content in the mix. The Tm content in the crystal (by weight percent) is measured by the PIXE method. The spread of data points shows the variation of Tm concentration among the samples and along the cross section of each sample.

Fig. 3
Fig. 3

Polarized ground-state absorption spectra at room temperature for the polarization vector E and the propagation vector k parallel to the crystallographic directions a, b, c. Curve (a) is for kc, Ea; curve (b) is for kc, Eb; curve (c) is for kb, Ec; curve (d) is for kb, Ea; curve (e) is for ka, Eb; curve (f) is for ka, Ec. All curves except curve (f) have been arbitrarily shifted along the y axis for clarity.

Fig. 4
Fig. 4

Polarized fluorescence spectra at room temperature for polarization vector E and propagation vector k parallel to crystallographic directions a, b, c. Curve (a) is for kc, Ea; curve (b) is for kc, Eb; curve (c) is for kb, Ec; curve (d) is for kb, Ea; curve (e) is for ka, Eb; curve (f) is for ka, Ec. All curves except curve (f) have been arbitrarily shifted along the y axis for clarity.

Fig. 5
Fig. 5

Unpolarized absorption cross section at various temperatures. Curve (a) is at 300 K, curve (b) is at 190 K, curve (c) is at 100 K, and curve (d) is at 10 K. All curves except curve (d) have been shifted for clarity. X and P2P8 are identified in Fig. 7.

Fig. 6
Fig. 6

Unpolarized fluorescence spectra at various temperatures. Curve (a) is at 300 K, curve (b) is at 120 K, and curve (c) is at 10 K. X and R2R7 are identified in Fig. 7.

Fig. 7
Fig. 7

Stark-level components of the ground (3H6 multiplet) and excited (3F4 multiplet) states of the trivalent Tm ion in BeL; (a) and (b) denote the lower and upper laser levels, respectively. X and Ps are shown in absorption (Fig. 5), and X and Rs are shown in the emission (Fig. 6) spectra. X is the zero phonon line.

Fig. 8
Fig. 8

Variation of the 3F4-level emission decay time with temperature.

Fig. 9
Fig. 9

Emission cross section calculated (i) from Eq. (1) and (ii) from Eq. (3). Equation (1) is used to convert the absorption spectrum into a derived emission spectrum (b) by means of the zero-line energy of EZPL=5860 cm-1 and the partition function ratio Zl/Zu=1.61. The calculated radiative lifetime of τrad =3.2 ms is used in the Fuchtbauer–Ladensburg Eq. (3) to get curve (a).

Fig. 10
Fig. 10

Raman-spectra measurement performed on the Tm:BeL crystal with the Renishaw Raman-spectroscopy instrument excited by a He–He laser.

Fig. 11
Fig. 11

Absorbed pump-power threshold as a function of the round-trip cavity loss for a typical cavity geometry. Lines (a), (b), and (c) are for mode radii of 50 μm, 35 μm, and 20 μm, respectively, in Tm:BeL, whereas line (d) is for Tm:YAG for mode radius of 50 μm. The Tm concentrations in BeL and YAG were 0.2% and 4.0%, respectively.

Fig. 12
Fig. 12

Calculated output power as a function of absorbed pump power for (a) Tm:YAG and (b) Tm:BeL. Slope efficiency for Tm:YAG is 37% for 2% output coupling and 50-μm mode radius, whereas for the same output coupling and mode radius the slope efficiency for Tm:BeL is 50%.

Tables (2)

Tables Icon

Table 1 Comparison with Earlier Work of Parameters of Tm:BeL

Tables Icon

Table 2 Parameters for Determination of Threshold Power and Slope Efficiency

Equations (11)

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

σem(v)=σabs(v) ZlZu exp[(EZPL-hv)/kT].
Zl,u=idi exp(-Ei/kT).
σemα(v)=λ2gα(v)8πn2τrad,
gα(v)=3SαβSβ,
A(J, J)=64π4e23(2J+1)hλ¯3 n(n2+2)29×t=2,4,6Ωt|S, L, JU(t)S, L, J|2.
1τrad=JA(J, J).
τnrad1+1exp(ωph/kBT)-1-p,
P=τrad-1τrad-1+τnrad-1=0.147.
Ptha=πhνp2 fbηpτem (ω02+ωp2)δ2σem+faN0L,
Pthi=Ptha[1-exp(-αL)],
Iout=[(1-R1)+(1-R2)]PaPtha-1 hνp2σemτem.

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