Abstract

We have constructed a model that will be useful in designing Nd: phosphate glass lasers that are heated when run repetitively, continuously, or in the burst mode. The model predicts the temperature dependence of the gain coefficient and the extractable stored energy density. Changes in the populations of the upper and lower laser levels are described by Boltzmann distributions. The generalized Einstein relations are used to relate the stimulated-emission and absorption cross sections. Variations of the cross sections with temperature have been inferred from measurements of the threshold energies of a flash-lamp-pumped rod oscillator, over the range 288 to 365 K. With only a single input of the gain coefficient at one temperature, our model predicts the gain coefficient and the extractable stored energy density at other temperatures.

© 1992 Optical Society of America

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  1. J. L. Emmett, W. F. Krupke, W. R. Sooy, “The potential of high-average power solid state lasers,” UCRL-53571 (Lawrence Livermore National Laboratory, Livermore, Calif., 1984).
  2. W. F. Krupke, “Solid state laser driver for an ICF reactor,” Fusion Technol. 15, 377 (1989).
  3. S. B. Sutton, G. F. Albrecht, H. F. Robey, “Heat removal and optical distortion in a gas cooled disk amplifier,” J. Am. Inst. Aeronaut Astronaut. (to be published).
  4. G. F. Albrecht, S. B. Sutton, H. F. Robey, B. L. Freitas, “Flow, heat transfer and wafefast distortion in a gas cooled disk amplifier,” in High Power and Solid State Lasers II, G. Dube, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1040, 37 (1989).
    [CrossRef]
  5. H. F. Robey, G. F. Albrecht, B. L. Freitas, “Flow conditioning for improved optical propagation of beams through regions bounded by surfaces of high solidity,” J. Appl. Phys. 69, 1915 (1991).
    [CrossRef]
  6. G. F. Albrecht, H. F. Robey, A. C. Erlandson, “Optical properties of turbulent channel flow,” Appl. Opt. 29, 3079 (1990).
    [CrossRef] [PubMed]
  7. V. A. Alekseeva, I. F. Balashov, S. I. Khankov, “Temperature dependence of the gain coefficient of phosphate-neodymium glass,” Sov. J. Opt. Technol. 49, 739 (1982).
  8. V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
    [CrossRef]
  9. V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
    [CrossRef]
  10. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. A 136, 954 (1969).
  11. C. Brecker, L. A. Riseberg, M. J. Weber, “Line-narrowed fluorescence spectra and site-dependent transition probabilities of Nd3+ in oxide and fluoride glasses,” Phys. Rev. B 18, 5799 (1978).
    [CrossRef]
  12. S. E. Stokowski, R. A. Saroyan, M. J. Weber, “Nd-doped laser glass spectroscopic and physical properties,” M-095 (Lawrence Livermore National Laboratory, Livermore, Calif., 1978).
  13. J. M. Pellegrino, W. M. Yen, M. J. Weber, “Composition dependence of Nd homogenous linewidth in glasses,” J. Appl. Phys. 51, 6332 (1980).
    [CrossRef]
  14. Multiphonon decay rates for excited rare-earth ions are generally predicted by an exponential gap law. See L. A. Riseberg, M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 91; C. B. Layne, W. H. Lowdermilk, M. J. Weber, “Nonradiative relaxation of rare-earth ions in silicate laser glass,” IEEE J. Quantum Electron. QE-11, 798 (1975).
    [CrossRef]
  15. Recently the multiphonon decay rates for excited Nd3+ions were found to exceed the rates predicted by the exponential gap law (see Refs. 14 and 15) by as many as 3 orders of magnitude. See L. L. Chase, Lawrence Livermore National Laboratory, Livermore, Calif. (personal communication) and Refs. 16 and 17.
  16. T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
    [CrossRef]
  17. T. T. Basiev, A. Y. Dergachev, Y. V. Orlovski, S. Georgeschu, A. Lupei, “Nonradiative multiphonon relaxation and energy transfer from the strongly quenched high-lying levels on Nd3+ ions in laser crystals,” in Digest of the Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989).
  18. J. R. Thornton, W. D. Fountain, G. W. Flint, T. G. Crow, “Properties of neodymium laser materials,” Appl. Opt. 8, 1087 (1969).
    [CrossRef] [PubMed]
  19. D. W. Hall, R. A. Haas, W. R. Krupke, M. J. Weber, “Spectral and polarization hole burning in neodymium glass lasers,” IEEE J. Quantum Electron. QE-19, 1716 (1983).
  20. M. M. Mann, L. G. DeShazer, “Energy levels and spectral broadening of neodymium ions in laser glass,” J. Appl. Phys. 41, 2951 (1970).
    [CrossRef]
  21. D. Findlay, R. A. Clay, “Model predicting the temperature dependence of the gain coefficient and the extractable stored energy density in Nd:phosphorus glass lasers,” Phys. Lett. 20, 277 (1966).
    [CrossRef]
  22. S. Timoshenko, J. M. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951), p. 400.
  23. J. A. Glaze, S. Guch, J. B. Trenholme, “Parasitic suppression in large-aperture Nd:glass disk laser amplifiers,” Appl. Opt. 13, 2808 (1974).
    [CrossRef] [PubMed]
  24. L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
    [CrossRef]
  25. J. A. Caird, A. J. Ramponi, P. R. Staver, “Quantun efficiency and excited-state relaxation dynamics in neodymium-doped phosphate glasses,” J. Opt. Soc. Am. B 8, 1391 (1991).
    [CrossRef]
  26. W. E. Martin, D. Milam, “Gain saturation in Nd:doped laser materials,” IEEE J. Quantum Electron. QE-18, 1155 (1982).
    [CrossRef]
  27. L. M. Frantz, J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346, (1963).
    [CrossRef]
  28. A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981).

1991 (2)

H. F. Robey, G. F. Albrecht, B. L. Freitas, “Flow conditioning for improved optical propagation of beams through regions bounded by surfaces of high solidity,” J. Appl. Phys. 69, 1915 (1991).
[CrossRef]

J. A. Caird, A. J. Ramponi, P. R. Staver, “Quantun efficiency and excited-state relaxation dynamics in neodymium-doped phosphate glasses,” J. Opt. Soc. Am. B 8, 1391 (1991).
[CrossRef]

1990 (1)

1989 (1)

W. F. Krupke, “Solid state laser driver for an ICF reactor,” Fusion Technol. 15, 377 (1989).

1987 (1)

T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
[CrossRef]

1986 (1)

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

1983 (1)

D. W. Hall, R. A. Haas, W. R. Krupke, M. J. Weber, “Spectral and polarization hole burning in neodymium glass lasers,” IEEE J. Quantum Electron. QE-19, 1716 (1983).

1982 (2)

V. A. Alekseeva, I. F. Balashov, S. I. Khankov, “Temperature dependence of the gain coefficient of phosphate-neodymium glass,” Sov. J. Opt. Technol. 49, 739 (1982).

W. E. Martin, D. Milam, “Gain saturation in Nd:doped laser materials,” IEEE J. Quantum Electron. QE-18, 1155 (1982).
[CrossRef]

1981 (1)

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

1980 (1)

J. M. Pellegrino, W. M. Yen, M. J. Weber, “Composition dependence of Nd homogenous linewidth in glasses,” J. Appl. Phys. 51, 6332 (1980).
[CrossRef]

1978 (1)

C. Brecker, L. A. Riseberg, M. J. Weber, “Line-narrowed fluorescence spectra and site-dependent transition probabilities of Nd3+ in oxide and fluoride glasses,” Phys. Rev. B 18, 5799 (1978).
[CrossRef]

1977 (1)

L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
[CrossRef]

1974 (1)

1970 (1)

M. M. Mann, L. G. DeShazer, “Energy levels and spectral broadening of neodymium ions in laser glass,” J. Appl. Phys. 41, 2951 (1970).
[CrossRef]

1969 (2)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. A 136, 954 (1969).

J. R. Thornton, W. D. Fountain, G. W. Flint, T. G. Crow, “Properties of neodymium laser materials,” Appl. Opt. 8, 1087 (1969).
[CrossRef] [PubMed]

1966 (1)

D. Findlay, R. A. Clay, “Model predicting the temperature dependence of the gain coefficient and the extractable stored energy density in Nd:phosphorus glass lasers,” Phys. Lett. 20, 277 (1966).
[CrossRef]

1963 (1)

L. M. Frantz, J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346, (1963).
[CrossRef]

Ageeva, L. E.

L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
[CrossRef]

Albrecht, G. F.

H. F. Robey, G. F. Albrecht, B. L. Freitas, “Flow conditioning for improved optical propagation of beams through regions bounded by surfaces of high solidity,” J. Appl. Phys. 69, 1915 (1991).
[CrossRef]

G. F. Albrecht, H. F. Robey, A. C. Erlandson, “Optical properties of turbulent channel flow,” Appl. Opt. 29, 3079 (1990).
[CrossRef] [PubMed]

S. B. Sutton, G. F. Albrecht, H. F. Robey, “Heat removal and optical distortion in a gas cooled disk amplifier,” J. Am. Inst. Aeronaut Astronaut. (to be published).

G. F. Albrecht, S. B. Sutton, H. F. Robey, B. L. Freitas, “Flow, heat transfer and wafefast distortion in a gas cooled disk amplifier,” in High Power and Solid State Lasers II, G. Dube, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1040, 37 (1989).
[CrossRef]

Alekseeva, V. A.

V. A. Alekseeva, I. F. Balashov, S. I. Khankov, “Temperature dependence of the gain coefficient of phosphate-neodymium glass,” Sov. J. Opt. Technol. 49, 739 (1982).

Balashov, I. F.

V. A. Alekseeva, I. F. Balashov, S. I. Khankov, “Temperature dependence of the gain coefficient of phosphate-neodymium glass,” Sov. J. Opt. Technol. 49, 739 (1982).

Basiev, T. T.

T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
[CrossRef]

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovski, S. Georgeschu, A. Lupei, “Nonradiative multiphonon relaxation and energy transfer from the strongly quenched high-lying levels on Nd3+ ions in laser crystals,” in Digest of the Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989).

Berenberg, V. A.

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

Brachouskaya, N. B.

L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
[CrossRef]

Brecker, C.

C. Brecker, L. A. Riseberg, M. J. Weber, “Line-narrowed fluorescence spectra and site-dependent transition probabilities of Nd3+ in oxide and fluoride glasses,” Phys. Rev. B 18, 5799 (1978).
[CrossRef]

Buchenkov, V. A.

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

Caird, J. A.

Chase, L. L.

Recently the multiphonon decay rates for excited Nd3+ions were found to exceed the rates predicted by the exponential gap law (see Refs. 14 and 15) by as many as 3 orders of magnitude. See L. L. Chase, Lawrence Livermore National Laboratory, Livermore, Calif. (personal communication) and Refs. 16 and 17.

Clay, R. A.

D. Findlay, R. A. Clay, “Model predicting the temperature dependence of the gain coefficient and the extractable stored energy density in Nd:phosphorus glass lasers,” Phys. Lett. 20, 277 (1966).
[CrossRef]

Crow, T. G.

Dergachev, A. Y.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovski, S. Georgeschu, A. Lupei, “Nonradiative multiphonon relaxation and energy transfer from the strongly quenched high-lying levels on Nd3+ ions in laser crystals,” in Digest of the Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989).

Dergachev, A. Yu.

T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
[CrossRef]

DeShazer, L. G.

M. M. Mann, L. G. DeShazer, “Energy levels and spectral broadening of neodymium ions in laser glass,” J. Appl. Phys. 41, 2951 (1970).
[CrossRef]

Emmett, J. L.

J. L. Emmett, W. F. Krupke, W. R. Sooy, “The potential of high-average power solid state lasers,” UCRL-53571 (Lawrence Livermore National Laboratory, Livermore, Calif., 1984).

Erlandson, A. C.

Evdokimova, V. G.

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

Evstigneev, V. L.

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

Findlay, D.

D. Findlay, R. A. Clay, “Model predicting the temperature dependence of the gain coefficient and the extractable stored energy density in Nd:phosphorus glass lasers,” Phys. Lett. 20, 277 (1966).
[CrossRef]

Flint, G. W.

Fountain, W. D.

Frantz, L. M.

L. M. Frantz, J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346, (1963).
[CrossRef]

Freitas, B. L.

H. F. Robey, G. F. Albrecht, B. L. Freitas, “Flow conditioning for improved optical propagation of beams through regions bounded by surfaces of high solidity,” J. Appl. Phys. 69, 1915 (1991).
[CrossRef]

G. F. Albrecht, S. B. Sutton, H. F. Robey, B. L. Freitas, “Flow, heat transfer and wafefast distortion in a gas cooled disk amplifier,” in High Power and Solid State Lasers II, G. Dube, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1040, 37 (1989).
[CrossRef]

Georgeschu, S.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovski, S. Georgeschu, A. Lupei, “Nonradiative multiphonon relaxation and energy transfer from the strongly quenched high-lying levels on Nd3+ ions in laser crystals,” in Digest of the Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989).

Glaze, J. A.

Goodier, J. M.

S. Timoshenko, J. M. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951), p. 400.

Guch, S.

Haas, R. A.

D. W. Hall, R. A. Haas, W. R. Krupke, M. J. Weber, “Spectral and polarization hole burning in neodymium glass lasers,” IEEE J. Quantum Electron. QE-19, 1716 (1983).

Hall, D. W.

D. W. Hall, R. A. Haas, W. R. Krupke, M. J. Weber, “Spectral and polarization hole burning in neodymium glass lasers,” IEEE J. Quantum Electron. QE-19, 1716 (1983).

Kaminskii, A. A.

A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981).

Khankov, S. I.

V. A. Alekseeva, I. F. Balashov, S. I. Khankov, “Temperature dependence of the gain coefficient of phosphate-neodymium glass,” Sov. J. Opt. Technol. 49, 739 (1982).

Kirpichenkova, E. O.

T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
[CrossRef]

Krupke, W. F.

W. F. Krupke, “Solid state laser driver for an ICF reactor,” Fusion Technol. 15, 377 (1989).

J. L. Emmett, W. F. Krupke, W. R. Sooy, “The potential of high-average power solid state lasers,” UCRL-53571 (Lawrence Livermore National Laboratory, Livermore, Calif., 1984).

Krupke, W. R.

D. W. Hall, R. A. Haas, W. R. Krupke, M. J. Weber, “Spectral and polarization hole burning in neodymium glass lasers,” IEEE J. Quantum Electron. QE-19, 1716 (1983).

Lunter, G. S.

L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
[CrossRef]

Lupei, A.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovski, S. Georgeschu, A. Lupei, “Nonradiative multiphonon relaxation and energy transfer from the strongly quenched high-lying levels on Nd3+ ions in laser crystals,” in Digest of the Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989).

Mann, M. M.

M. M. Mann, L. G. DeShazer, “Energy levels and spectral broadening of neodymium ions in laser glass,” J. Appl. Phys. 41, 2951 (1970).
[CrossRef]

Martin, W. E.

W. E. Martin, D. Milam, “Gain saturation in Nd:doped laser materials,” IEEE J. Quantum Electron. QE-18, 1155 (1982).
[CrossRef]

McCumber, D. E.

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. A 136, 954 (1969).

Milam, D.

W. E. Martin, D. Milam, “Gain saturation in Nd:doped laser materials,” IEEE J. Quantum Electron. QE-18, 1155 (1982).
[CrossRef]

Nodvik, J. S.

L. M. Frantz, J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346, (1963).
[CrossRef]

Orlovski, Y. V.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovski, S. Georgeschu, A. Lupei, “Nonradiative multiphonon relaxation and energy transfer from the strongly quenched high-lying levels on Nd3+ ions in laser crystals,” in Digest of the Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989).

Orvlovski, Yu. V.

T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
[CrossRef]

Osiko, V. V.

T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
[CrossRef]

Ostroumov, V. G.

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

Pellegrino, J. M.

J. M. Pellegrino, W. M. Yen, M. J. Weber, “Composition dependence of Nd homogenous linewidth in glasses,” J. Appl. Phys. 51, 6332 (1980).
[CrossRef]

Przhevuskii, A. K.

L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
[CrossRef]

Ramponi, A. J.

Riseberg, L. A.

C. Brecker, L. A. Riseberg, M. J. Weber, “Line-narrowed fluorescence spectra and site-dependent transition probabilities of Nd3+ in oxide and fluoride glasses,” Phys. Rev. B 18, 5799 (1978).
[CrossRef]

Multiphonon decay rates for excited rare-earth ions are generally predicted by an exponential gap law. See L. A. Riseberg, M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 91; C. B. Layne, W. H. Lowdermilk, M. J. Weber, “Nonradiative relaxation of rare-earth ions in silicate laser glass,” IEEE J. Quantum Electron. QE-11, 798 (1975).
[CrossRef]

Robey, H. F.

H. F. Robey, G. F. Albrecht, B. L. Freitas, “Flow conditioning for improved optical propagation of beams through regions bounded by surfaces of high solidity,” J. Appl. Phys. 69, 1915 (1991).
[CrossRef]

G. F. Albrecht, H. F. Robey, A. C. Erlandson, “Optical properties of turbulent channel flow,” Appl. Opt. 29, 3079 (1990).
[CrossRef] [PubMed]

G. F. Albrecht, S. B. Sutton, H. F. Robey, B. L. Freitas, “Flow, heat transfer and wafefast distortion in a gas cooled disk amplifier,” in High Power and Solid State Lasers II, G. Dube, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1040, 37 (1989).
[CrossRef]

S. B. Sutton, G. F. Albrecht, H. F. Robey, “Heat removal and optical distortion in a gas cooled disk amplifier,” J. Am. Inst. Aeronaut Astronaut. (to be published).

Saroyan, R. A.

S. E. Stokowski, R. A. Saroyan, M. J. Weber, “Nd-doped laser glass spectroscopic and physical properties,” M-095 (Lawrence Livermore National Laboratory, Livermore, Calif., 1978).

Shcherbakov, I. A.

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

Smirnov, V. A.

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

Soms, L. N.

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

Sooy, W. R.

J. L. Emmett, W. F. Krupke, W. R. Sooy, “The potential of high-average power solid state lasers,” UCRL-53571 (Lawrence Livermore National Laboratory, Livermore, Calif., 1984).

Staver, P. R.

Stepanov, A. F.

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

Stokowski, S. E.

S. E. Stokowski, R. A. Saroyan, M. J. Weber, “Nd-doped laser glass spectroscopic and physical properties,” M-095 (Lawrence Livermore National Laboratory, Livermore, Calif., 1978).

Stupnikov, V. K.

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

Sutton, S. B.

S. B. Sutton, G. F. Albrecht, H. F. Robey, “Heat removal and optical distortion in a gas cooled disk amplifier,” J. Am. Inst. Aeronaut Astronaut. (to be published).

G. F. Albrecht, S. B. Sutton, H. F. Robey, B. L. Freitas, “Flow, heat transfer and wafefast distortion in a gas cooled disk amplifier,” in High Power and Solid State Lasers II, G. Dube, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1040, 37 (1989).
[CrossRef]

Thornton, J. R.

Timoshenko, S.

S. Timoshenko, J. M. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951), p. 400.

Tolstoi, M. N.

L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
[CrossRef]

Trenholme, J. B.

Vitrishelak, I. B.

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

Weber, M. J.

D. W. Hall, R. A. Haas, W. R. Krupke, M. J. Weber, “Spectral and polarization hole burning in neodymium glass lasers,” IEEE J. Quantum Electron. QE-19, 1716 (1983).

J. M. Pellegrino, W. M. Yen, M. J. Weber, “Composition dependence of Nd homogenous linewidth in glasses,” J. Appl. Phys. 51, 6332 (1980).
[CrossRef]

C. Brecker, L. A. Riseberg, M. J. Weber, “Line-narrowed fluorescence spectra and site-dependent transition probabilities of Nd3+ in oxide and fluoride glasses,” Phys. Rev. B 18, 5799 (1978).
[CrossRef]

Multiphonon decay rates for excited rare-earth ions are generally predicted by an exponential gap law. See L. A. Riseberg, M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 91; C. B. Layne, W. H. Lowdermilk, M. J. Weber, “Nonradiative relaxation of rare-earth ions in silicate laser glass,” IEEE J. Quantum Electron. QE-11, 798 (1975).
[CrossRef]

S. E. Stokowski, R. A. Saroyan, M. J. Weber, “Nd-doped laser glass spectroscopic and physical properties,” M-095 (Lawrence Livermore National Laboratory, Livermore, Calif., 1978).

Yen, W. M.

J. M. Pellegrino, W. M. Yen, M. J. Weber, “Composition dependence of Nd homogenous linewidth in glasses,” J. Appl. Phys. 51, 6332 (1980).
[CrossRef]

Appl. Opt. (3)

Fusion Technol. (1)

W. F. Krupke, “Solid state laser driver for an ICF reactor,” Fusion Technol. 15, 377 (1989).

IEEE J. Quantum Electron. (2)

D. W. Hall, R. A. Haas, W. R. Krupke, M. J. Weber, “Spectral and polarization hole burning in neodymium glass lasers,” IEEE J. Quantum Electron. QE-19, 1716 (1983).

W. E. Martin, D. Milam, “Gain saturation in Nd:doped laser materials,” IEEE J. Quantum Electron. QE-18, 1155 (1982).
[CrossRef]

J. Appl. Phys. (4)

L. M. Frantz, J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346, (1963).
[CrossRef]

M. M. Mann, L. G. DeShazer, “Energy levels and spectral broadening of neodymium ions in laser glass,” J. Appl. Phys. 41, 2951 (1970).
[CrossRef]

H. F. Robey, G. F. Albrecht, B. L. Freitas, “Flow conditioning for improved optical propagation of beams through regions bounded by surfaces of high solidity,” J. Appl. Phys. 69, 1915 (1991).
[CrossRef]

J. M. Pellegrino, W. M. Yen, M. J. Weber, “Composition dependence of Nd homogenous linewidth in glasses,” J. Appl. Phys. 51, 6332 (1980).
[CrossRef]

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

Phys. Lett. (1)

D. Findlay, R. A. Clay, “Model predicting the temperature dependence of the gain coefficient and the extractable stored energy density in Nd:phosphorus glass lasers,” Phys. Lett. 20, 277 (1966).
[CrossRef]

Phys. Rev. A (1)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. A 136, 954 (1969).

Phys. Rev. B (1)

C. Brecker, L. A. Riseberg, M. J. Weber, “Line-narrowed fluorescence spectra and site-dependent transition probabilities of Nd3+ in oxide and fluoride glasses,” Phys. Rev. B 18, 5799 (1978).
[CrossRef]

Sov. J. Opt. Technol. (1)

V. A. Alekseeva, I. F. Balashov, S. I. Khankov, “Temperature dependence of the gain coefficient of phosphate-neodymium glass,” Sov. J. Opt. Technol. 49, 739 (1982).

Sov. J. Quantum Electron. (4)

V. A. Buchenkov, I. B. Vitrishelak, V. G. Evdokimova, L. N. Soms, A. F. Stepanov, V. K. Stupnikov, “Temperature dependence of giant pulse amplification in YAG:Nd3+,” Sov. J. Quantum Electron. 11, 702 (1981).
[CrossRef]

V. A. Berenberg, V. A. Buchenkov, V. L. Evstigneev, V. G. Ostroumov, V. A. Smirnov, I. A. Shcherbakov, “Temperature dependance of the gain and of the lasing cross section of a ~1.06μ m transition in gadolinium scandium gallium garnet crystal doped with chromium and neodymium” Sov. J. Quantum Electron. 16, 1456 (1986).
[CrossRef]

T. T. Basiev, A. Yu. Dergachev, E. O. Kirpichenkova, Yu. V. Orvlovski, V. V. Osiko, “Direct measurement of nonradiative relaxation and luminescence spectra from the 4G7/2, 4G5/2, +2G7/2, and 4F9/2levels of Nd3+ions in LaF3, SrF2and YAlO3laser crystals,” Sov. J. Quantum Electron. 17, 1289 (1987).
[CrossRef]

L. E. Ageeva, N. B. Brachouskaya, G. S. Lunter, A. K. Przhevuskii, M. N. Tolstoi, “Determination of the stimulated emission cross section of neodymium glasses by measurement of the absorption from the thermally populated 4I11/2levels,” Sov. J. Quantum Electron. 7, 1379 (1977).
[CrossRef]

Other (9)

S. B. Sutton, G. F. Albrecht, H. F. Robey, “Heat removal and optical distortion in a gas cooled disk amplifier,” J. Am. Inst. Aeronaut Astronaut. (to be published).

G. F. Albrecht, S. B. Sutton, H. F. Robey, B. L. Freitas, “Flow, heat transfer and wafefast distortion in a gas cooled disk amplifier,” in High Power and Solid State Lasers II, G. Dube, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1040, 37 (1989).
[CrossRef]

S. Timoshenko, J. M. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951), p. 400.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovski, S. Georgeschu, A. Lupei, “Nonradiative multiphonon relaxation and energy transfer from the strongly quenched high-lying levels on Nd3+ ions in laser crystals,” in Digest of the Topical Meeting on Tunable Solid State Lasers (Optical Society of America, Washington, D.C., 1989).

J. L. Emmett, W. F. Krupke, W. R. Sooy, “The potential of high-average power solid state lasers,” UCRL-53571 (Lawrence Livermore National Laboratory, Livermore, Calif., 1984).

Multiphonon decay rates for excited rare-earth ions are generally predicted by an exponential gap law. See L. A. Riseberg, M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, p. 91; C. B. Layne, W. H. Lowdermilk, M. J. Weber, “Nonradiative relaxation of rare-earth ions in silicate laser glass,” IEEE J. Quantum Electron. QE-11, 798 (1975).
[CrossRef]

Recently the multiphonon decay rates for excited Nd3+ions were found to exceed the rates predicted by the exponential gap law (see Refs. 14 and 15) by as many as 3 orders of magnitude. See L. L. Chase, Lawrence Livermore National Laboratory, Livermore, Calif. (personal communication) and Refs. 16 and 17.

S. E. Stokowski, R. A. Saroyan, M. J. Weber, “Nd-doped laser glass spectroscopic and physical properties,” M-095 (Lawrence Livermore National Laboratory, Livermore, Calif., 1978).

A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981).

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Figures (7)

Fig. 1
Fig. 1

Energy-level diagram showing the Stark-split sublevels of Nd3+ in phosphate glass. The energies of levels 1–3 are inferred from line-narrowed fluorescence spectra.11 The energy of the 4F5/2 and 4H9/2 states was inferred from measured absorption spectra.12 The splitting of the 4F3/2 state is from Ref. 13.

Fig. 2
Fig. 2

Findlay–Clay plots for (a) LHG-5 and (b) LHG-8 laser rods.

Fig. 3
Fig. 3

Measured threshold energy plotted versus temperature for (a) LHG-5 and (b) LHG-8 laser rods.

Fig. 4
Fig. 4

Gain-correction factor Fg plotted versus temperature for 3.3% Nd2O3 LHG-5 laser glass.

Fig. 5
Fig. 5

Stored-energy correction factor for short pulses Fs plotted versus temperature for 3.3% Nd2O3 LHG-5 laser glass.

Fig. 6
Fig. 6

Stored-energy correction factor for long pulses Fl plotted versus temperature for 3.3% Nd2O3 LHG-5 laser glass.

Fig. 7
Fig. 7

Maximum heat flux plotted versus Noσ32(To)/g(To) for LHG-5 glass at the given conditions.

Tables (1)

Tables Icon

Table 1 Estimated Uncertainties in the Various Parameters Used to Calculate Fg, Fs, and Fl

Equations (34)

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N i ( T ) = N o Z i ( T ) Z ( T ) ,
Z i ( T ) = α e - E i α / k T
Z ( T ) = i Z i ( T ) ,
N 3 ( T ) = Z 43 ( T ) Z 43 ( T o ) N 3 ( T o ) ,
Z 43 ( T ) = Z 3 ( T ) Z 3 ( T ) + Z 4 ( T )
σ 23 ( T ) = σ 32 ( T ) exp ( h c / λ k T ) N 3 ( T ) N 2 ( T ) .
σ 23 = σ 32 g 3 / g 2 ,
E ( T ) = Γ ( T ) N ( T ) σ 32 ( T ) ,
Γ s ( T ) = h c λ [ 1 + σ 23 ( T ) / σ 32 ( T ) ] σ 32 ( T ) .
Γ l ( T ) = h c λ σ 32 ( T ) .
N s ( T ) = N 3 ( T ) - σ 23 ( T ) σ 32 ( T ) N 2 ( T )
N l ( T ) = N 3 ( T ) Z 43 ( T ) - σ 23 ( T ) σ 32 ( T ) N 2 ( T ) .
E s ( T ) = h c λ [ 1 + σ 23 ( T ) σ 32 ( T ) ] [ N 3 ( T ) - σ 23 ( T ) σ 32 ( T )             N 2 ( T ) ] .
E l ( T ) = h c λ [ N 3 ( T ) Z 43 ( T ) - σ 23 ( T ) σ 32 ( T )             N 2 ( T ) ] .
F s ( T ) = E s ( T ) E s ( T o ) = [ 1 + σ 23 ( T o ) σ 32 ( T o ) ] [ N 3 ( T ) - σ 23 ( T ) σ 32 ( T )             N 2 ( T ) ] [ 1 + σ 23 ( T ) σ 32 ( T ) ] ( N 3 ( T o ) - σ 23 ( T o ) σ 32 ( T o )             N 2 ( T o ) ) .
F l ( T ) = E l ( T ) E l ( T o ) = N 3 ( T ) Z 43 ( T ) - σ 23 ( T ) σ 32 ( T )             N 2 ( T ) N 3 ( T o ) Z 43 ( T o ) - σ 23 ( T o ) σ 32 ( T o )             N 2 ( T o ) .
g ( T ) = N 3 ( T ) σ 32 ( T ) - N 2 ( T ) σ 23 ( T ) .
F g ( T ) = N 3 ( T ) σ 32 ( T ) - N 2 ( T ) σ 23 ( T ) g ( T o )
F g ( T ) = g ( T ) g ( T o ) = [ Z 43 ( T ) Z 43 ( T o ) σ 32 ( T ) σ 32 ( T o ) ] [ 1 + N 2 ( T o ) σ 23 ( T o ) g ( T o ) ] - N 2 ( T ) σ 23 ( T ) g ( T o ) .
σ 23 ( T ) = σ 23 ( T o ) exp [ b ( T - T o ) ] ,
2 l p N 3 ( T ) σ 32 ( T ) = 2 l r N 2 ( T ) σ 23 ( T ) + ρ + log e ( 1 R 1 R 2 ) ,
N 3 ( T ) = γ [ Z 3 ( T ) Z 3 ( T ) + Z 4 ( T ) ] E th ( R 2 , T ) ,
E th ( R 2 , T ) = [ 1 2 l p γ σ 32 ( T ) log e ( 1 R 1 R 2 ) + l r l p N 2 ( T ) σ 23 ( T ) γ σ 32 ( T ) + ρ 2 l p γ σ 32 ( T ) ] [ Z 3 ( T ) + Z 4 ( T ) Z 3 ( T ) ] .
( Δ F g ) 2 = ( d F g d X i ) 2 ( Δ X i ) 2 ,
σ 23 ( T ) = σ 32 ( T ) 2.26 exp [ b ( T o - T ) ] , b = 1.37 × 10 - 3 K - 1 ( LHG - 5 ) b = 1.20 × 10 - 3 K - 1 ( LHG - 8 ) ; σ 32 ( T ) = σ 32 ( T o ) exp [ b ( T o - T ) ] , b = 8.0 × 10 - 4 K - 1 ( LHG - 5 ) b = 6.3 × 10 - 4 K - 1 ( LHG - 8 ) ; Z 43 ( T ) = 1 / [ 1 + 4 exp ( - 43 / k T ) ] ,             43 = 0.120 eV ; N 2 ( T ) = N o exp ( - 21 / k T ) ,             21 = 0.240 eV ; N 3 ( T ) = 1.04 N 3 ( T o ) / [ 1 + 4 exp ( - 43 / k T ) ] , N 3 ( T o ) = g ( T o ) / σ 32 ( T o ) + 5.27 × 10 - 5 N o .
T ( z ) = T s + Δ T ( 1 - 4 z 2 / t 2 ) ,
Δ T = P v t 2 8 k = Q t 8 k ,
Q = h ( T s - T g ) ,
E l ( T ) ¯ = E l ( T o ) - t / 2 t / 2 F l [ T ( z ) ] d z ,
F l ( T ) ~ 1 - c N o σ 32 ( T o ) g ( T o ) exp ( - Δ o / k T ) ,
E l ( T ) = E l ( T o ) F l ( T a ) ,
T a = T g + Q ( 1 h + t 6 k ) .
T a < Δ o k log e [ c N o σ 32 ( T o ) / δ g ( T o ) ] .
Q < Δ o k log e [ c N o σ 32 ( T o ) / δ g ( T o ) ] - T g 1 h + t / 6 k .

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