Abstract

We have measured the terminal level lifetime (τ11/2) for the 1-μm neodymium transition in several laser media, using a novel pump (2.41-μm) and probe (1.06-μm) technique. This method allows us to populate the 4I13/2 level directly and subsequently to monitor the terminal level 4I11/2 population as a function of time by observing the change in integrated fluoresence of the 0.88-μm emission for each time delay between the pump and the probe pulses. We developed a computer model to analyze the data and determined the upper and lower limits for the τ11/2 lifetime. The results for some of the materials investigated are 115–225 ps for Nd:Y3Al5O12, 250–450 ps for Nd:LG-750 (phosphate glass), 535–740 ps for Nd:LG-660 (silicate glass), 896–1900 ps for Nd:YAlO3, and 10.5–20 ns for Nd:YLiF4. In addition, we found the lifetimes to be independent of the neodymium doping concentration for the phosphate and silicate glass samples investigated.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Beach, P. Reichert, W. Benett, B. Freitas, S. Mitchell, A. Velsko, J. Davin, and R. Solarz, "Scalable diode-end-pumping technology applied to a 100-mJ Q-switched Nd3+:YLF laser oscillator," Opt. Lett. 18, 1326 (1993).
    [CrossRef] [PubMed]
  2. T. Y. Fan, "Effect of finite lower level lifetime on Q-switched lasers," IEEE J. Quantum Electron. 24, 2345 (1988).
    [CrossRef]
  3. J. Trenholme, Laser Program, Lawrence Livermore National Laboratory, Livermore, Calif. 94550 (personal communication, 1993).
  4. T. T. Basiev, A. Y. Dergachev, Y. V. Orlovskii, and A. M. Prokhorov, "Multiphonon nonradiative relaxation from high-lying levels of Nd3+ ions in fluoride and oxide laser materials," in Advanced Solid-State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 358.
  5. J. Cruz, G. Giuliani, and H. M. Van Driel, "Measurement of the subnanosecond, nonradiative relaxation time from excited states of Nd3+ in a Nd:YAG crystal," Opt. Lett. 15, 282 (1990).
    [CrossRef] [PubMed]
  6. T. Kushida, S. Kinoshita, T. Ohtsuki, and T. Yamada, "Multiphonon relaxation rate from pumped level to upper laser level in YAG:Nd," Solid State Commun. 44, 1363 (1982).
    [CrossRef]
  7. G. M. Zverev, G. Ya. Kolodnyi, and A. M. Onishchenko, "Nonradiative transitions between levels of trivalent rare-earth ions in yttrium-aluminum garnet crystals," Sov. Phys. JETP 33, 497 (1971).
  8. K. Palombo, S. Matthews, S. Sheldrake, and D. Capps, "Determination of the effective lower level lifetime for Nd:YLF and Nd:YAG through experimental measurement and computer modeling," in Advanced Solid-State Lasers, Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), p. 78.
  9. F. E. Hovis, M. Stuff, C. J. Kennedy, and B. Vivian, "Lower level relaxation of Nd:YAG," IEEE J. Quantum Electron. 28, 39 (1992).
    [CrossRef]
  10. A. A. Zlenko, V. A. Sychugov, and G. P. Shipulo, "Measurement of the relaxation time τ21 of a Y3Al5O12:Nd3+ crystal," Sov. J. Quantum Electron. 2, 474 (1973).
    [CrossRef]
  11. V. V. Grigor'yants, M. E. Zhabotinskii, and V. M. Markushev, "Determination of the probability of relaxation of the population of the 4I11/2 level of neodymium ions from luminescence dumping in a small external sample," Sov. J. Quantum Electron. 12, 1010 (1983).
    [CrossRef]
  12. V. P. Gaponstev, M. R. Sirtlanov, A. K. Gromov, and A. A. Isineev, "New data on nonradiative relaxation of impurity center excitations in laser materials," in Proceedings of Lasers 1981 (STS, McLean, Va., 1981), p. 63.
  13. Y. E. Perlin, "Modern methods in the theory of many-phonon processes," Sov. Phys. 6, 542 (1963).
    [CrossRef]
  14. K. Huang and A. Rhys, "Theory of light absorption and nonradiative transmission in F centres," Proc. R. Soc. of London Ser. A 204, 406 (1950).
    [CrossRef]
  15. A. E. Kiel, "The interaction of paramagnetic ions with lattice vibrations," Ph.D. dissertation (Johns Hopkins University, Baltimore, Md., 1962).
  16. R. Orbach, Optical Properties of Ions in Solids (Wiley-Interscience, New York, 1967), p. 445.
  17. W. D. Partlow and H. W. Moos, "Multiphonon relaxation in LaCl3:Nd3+," Phys. Rev. 157, 252 (1967).
    [CrossRef]
  18. T. Miyakawa and D. L. Dexter, "Phonon sidebands, multiphonon relaxation of excited states, and phonon assisted energy transfer between ions in solids," Phys. Rev. B 1, 2961 (1970).
    [CrossRef]
  19. S. F. Fischer, "Correlation function approach to radiationless transitions," J. Chem. Phys. 53, 3195 (1970).
    [CrossRef]
  20. T. F. Soules and C. B. Duke, "Resonant energy transfer between localized electronic states in a crystal," Phys. Rev. B 3, 262 (1971).
    [CrossRef]
  21. F. K. Fong, S. L. Naberhuis, and M. M. Miller, "Theory of radiationless relaxation of rare-earth ions in crystals," J. Chem. Phys. 56, 4020 (1972).
    [CrossRef]
  22. C. W. Struck and W. H. Fonger, "Unified model of the temperature quenching of narrow-line and broad-band emissions," J. Lumin. 10, 1 (1975).
    [CrossRef]
  23. L. A. Riseberg and H. W. Moos, "Multiphonon orbit-lattice relaxation of excited states of rare earth ions in crystals," Phys. Rev. 174, 429 (1968).
    [CrossRef]
  24. C. B. Layne, W. H. Lowdermilk, and M. J. Weber, "Multiphonon relaxation of rare-earth ions in oxide glasses," Phys. Rev. B 16, 10 (1977).
    [CrossRef]
  25. Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).
  26. K. Huang and Z. Gu, "Phonon analysis in multiphonon transitions," Commun. Theor. Phys. 1, 535 (1982).
  27. V. Gapontsev and M. Sirtlanov, "Progress in understanding of mechanisms of RE3+-excited states nonradiative relaxation in crystals," J. Lumin. 31 & 32, 201 (1984).
    [CrossRef]
  28. G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 129.
  29. B. R. Judd, "Optical absorption intensities of rare-earth ions," Phys. Rev. 127, 750 (1962).
    [CrossRef]
  30. G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511 (1962).
    [CrossRef]
  31. I. M. Thomas, S. A. Payne, and G. D. Wilke, "Optical properties and laser demonstration of Nd-doped sol-gel silica glasses," J. Non-Cryst. Solids 151, 183 (1992).
    [CrossRef]
  32. G. V. Maksimova and A. A. Sobol, "Nd3+ Optical centers in crystals of calcium and strontium fluorophosphates," Proc. P. N. Lebedev Phys. Inst. 60, 59 (1974).
  33. K. A. Gschneidner, Jr., and L. Eyring, Handbook on the Physics and Chemistry of Rare Earths (North-Holland, New York, 1982), Vol. 5, Chap. 46.
    [CrossRef]
  34. J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
    [CrossRef]
  35. Y. E. Kariss, M. N. Tolstoi, and P. P. Feofilov, "On the luminescence and absorption of trivalent neodymium in crystals of the fluorite type," Opt. Spectrosc. (USSR) 18, 247 (1965).
  36. S. R. Levitt, K. C. Blakeslee, and R. A. Condrate, Sr., "Infrared spectra and laser-Raman spectra of several apatites," Mem. Soc. R. Sci. Liege 5, 121 (1970).
  37. D. Heiman, R. W. Hellwarth, and D. S. Hamilton, "Raman scattering and nonlinear refractive index measurements of optical glasses," J. Non-Cryst. Solids 34, 63 (1979).
    [CrossRef]
  38. M. J. Weber, "Multiphonon relaxation of rare-earth ions in yttrium orthoaluminate," Phys. Rev. B 8, 54 (1973).
    [CrossRef]
  39. P. Zhang, Y. Liu, and Y. Mo, "The Raman spectrum of single crystal Gd3Ga5O12," Chin. Phys. 4, 530 (1984).
  40. J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
    [CrossRef]
  41. I. Richman, "Vibronic spectra of SrF2:Sm2+ and BaF2:Sm2+," Phys. Rev. 133, A1364 (1964).
    [CrossRef]
  42. S. A. Miller, H. E. Rast, and H. H. Caspers, "Lattice vibrations of LiYF4," J. Chem. Phys. 52, 4172 (1970).
    [CrossRef]
  43. E. B. Sveshnikova, A. A. Stroganov, and L. N. Urusovskaya, "Mechanism of nonradiative transitions in rare-earth ions in fluorozirconate bases," Opt. Spectrosc. (USSR) 63, 618 (1987).
  44. E. D. Reed, Jr. and H. W. Moos, "Multiphonon relaxation of excited states of rare earths in YVO4, YAsO4, and YPO4," Phys. Rev. B 8, 980 (1973).
    [CrossRef]
  45. A. M. Tkachuk, A. V. Khilko, and M. V. Petrov, "Probabilities for nonradiative intermultiplet transitions in the holmium ion in lithium–yttrium double fluoride crystals and stimulated emission," Opt. Spectrosc. (USSR) 58, 216 (1985).
  46. S. M. Yarema and D. Milam, "Gain saturation in phosphate laser glasses," IEEE J. Quantum Electron. QE-18, 1941 (1982).
    [CrossRef]
  47. C. Bibeau, J. B. Trenholme, and S. A. Payne, "Pulse length and terminal level lifetime dependence of energy extraction for neodymium doped phosphate amplifier glass," submitted to IEEE J. Quantum Electron.
  48. W. E. Martin and D. Milam, "Direct measurement of gain recovery in a saturated Nd–glass amplifier," Appl. Phys. Lett. 32, 816 (1978).
    [CrossRef]
  49. W. F. Krupke, "Induced-emission cross sections in neodymium laser glasses," IEEE J. Quantum Electron. QE-10, 450 (1974).
    [CrossRef]
  50. W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, Energy Level Structure and Transition Probabilities of the Trivalent Lanthanides in LaF3 (Argonne National Laboratory, Argonne, Ill.).

1993

K. Palombo, S. Matthews, S. Sheldrake, and D. Capps, "Determination of the effective lower level lifetime for Nd:YLF and Nd:YAG through experimental measurement and computer modeling," in Advanced Solid-State Lasers, Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), p. 78.

J. Trenholme, Laser Program, Lawrence Livermore National Laboratory, Livermore, Calif. 94550 (personal communication, 1993).

R. Beach, P. Reichert, W. Benett, B. Freitas, S. Mitchell, A. Velsko, J. Davin, and R. Solarz, "Scalable diode-end-pumping technology applied to a 100-mJ Q-switched Nd3+:YLF laser oscillator," Opt. Lett. 18, 1326 (1993).
[CrossRef] [PubMed]

1992

F. E. Hovis, M. Stuff, C. J. Kennedy, and B. Vivian, "Lower level relaxation of Nd:YAG," IEEE J. Quantum Electron. 28, 39 (1992).
[CrossRef]

I. M. Thomas, S. A. Payne, and G. D. Wilke, "Optical properties and laser demonstration of Nd-doped sol-gel silica glasses," J. Non-Cryst. Solids 151, 183 (1992).
[CrossRef]

1991

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovskii, and A. M. Prokhorov, "Multiphonon nonradiative relaxation from high-lying levels of Nd3+ ions in fluoride and oxide laser materials," in Advanced Solid-State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 358.

1990

1988

T. Y. Fan, "Effect of finite lower level lifetime on Q-switched lasers," IEEE J. Quantum Electron. 24, 2345 (1988).
[CrossRef]

J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
[CrossRef]

1987

E. B. Sveshnikova, A. A. Stroganov, and L. N. Urusovskaya, "Mechanism of nonradiative transitions in rare-earth ions in fluorozirconate bases," Opt. Spectrosc. (USSR) 63, 618 (1987).

1985

A. M. Tkachuk, A. V. Khilko, and M. V. Petrov, "Probabilities for nonradiative intermultiplet transitions in the holmium ion in lithium–yttrium double fluoride crystals and stimulated emission," Opt. Spectrosc. (USSR) 58, 216 (1985).

1984

P. Zhang, Y. Liu, and Y. Mo, "The Raman spectrum of single crystal Gd3Ga5O12," Chin. Phys. 4, 530 (1984).

V. Gapontsev and M. Sirtlanov, "Progress in understanding of mechanisms of RE3+-excited states nonradiative relaxation in crystals," J. Lumin. 31 & 32, 201 (1984).
[CrossRef]

1983

V. V. Grigor'yants, M. E. Zhabotinskii, and V. M. Markushev, "Determination of the probability of relaxation of the population of the 4I11/2 level of neodymium ions from luminescence dumping in a small external sample," Sov. J. Quantum Electron. 12, 1010 (1983).
[CrossRef]

1982

T. Kushida, S. Kinoshita, T. Ohtsuki, and T. Yamada, "Multiphonon relaxation rate from pumped level to upper laser level in YAG:Nd," Solid State Commun. 44, 1363 (1982).
[CrossRef]

Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).

K. Huang and Z. Gu, "Phonon analysis in multiphonon transitions," Commun. Theor. Phys. 1, 535 (1982).

S. M. Yarema and D. Milam, "Gain saturation in phosphate laser glasses," IEEE J. Quantum Electron. QE-18, 1941 (1982).
[CrossRef]

1981

V. P. Gaponstev, M. R. Sirtlanov, A. K. Gromov, and A. A. Isineev, "New data on nonradiative relaxation of impurity center excitations in laser materials," in Proceedings of Lasers 1981 (STS, McLean, Va., 1981), p. 63.

1979

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, "Raman scattering and nonlinear refractive index measurements of optical glasses," J. Non-Cryst. Solids 34, 63 (1979).
[CrossRef]

1978

W. E. Martin and D. Milam, "Direct measurement of gain recovery in a saturated Nd–glass amplifier," Appl. Phys. Lett. 32, 816 (1978).
[CrossRef]

1977

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, "Multiphonon relaxation of rare-earth ions in oxide glasses," Phys. Rev. B 16, 10 (1977).
[CrossRef]

1975

C. W. Struck and W. H. Fonger, "Unified model of the temperature quenching of narrow-line and broad-band emissions," J. Lumin. 10, 1 (1975).
[CrossRef]

1974

G. V. Maksimova and A. A. Sobol, "Nd3+ Optical centers in crystals of calcium and strontium fluorophosphates," Proc. P. N. Lebedev Phys. Inst. 60, 59 (1974).

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

1973

M. J. Weber, "Multiphonon relaxation of rare-earth ions in yttrium orthoaluminate," Phys. Rev. B 8, 54 (1973).
[CrossRef]

E. D. Reed, Jr. and H. W. Moos, "Multiphonon relaxation of excited states of rare earths in YVO4, YAsO4, and YPO4," Phys. Rev. B 8, 980 (1973).
[CrossRef]

A. A. Zlenko, V. A. Sychugov, and G. P. Shipulo, "Measurement of the relaxation time τ21 of a Y3Al5O12:Nd3+ crystal," Sov. J. Quantum Electron. 2, 474 (1973).
[CrossRef]

1972

F. K. Fong, S. L. Naberhuis, and M. M. Miller, "Theory of radiationless relaxation of rare-earth ions in crystals," J. Chem. Phys. 56, 4020 (1972).
[CrossRef]

1971

T. F. Soules and C. B. Duke, "Resonant energy transfer between localized electronic states in a crystal," Phys. Rev. B 3, 262 (1971).
[CrossRef]

G. M. Zverev, G. Ya. Kolodnyi, and A. M. Onishchenko, "Nonradiative transitions between levels of trivalent rare-earth ions in yttrium-aluminum garnet crystals," Sov. Phys. JETP 33, 497 (1971).

1970

T. Miyakawa and D. L. Dexter, "Phonon sidebands, multiphonon relaxation of excited states, and phonon assisted energy transfer between ions in solids," Phys. Rev. B 1, 2961 (1970).
[CrossRef]

S. F. Fischer, "Correlation function approach to radiationless transitions," J. Chem. Phys. 53, 3195 (1970).
[CrossRef]

S. R. Levitt, K. C. Blakeslee, and R. A. Condrate, Sr., "Infrared spectra and laser-Raman spectra of several apatites," Mem. Soc. R. Sci. Liege 5, 121 (1970).

S. A. Miller, H. E. Rast, and H. H. Caspers, "Lattice vibrations of LiYF4," J. Chem. Phys. 52, 4172 (1970).
[CrossRef]

1968

J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
[CrossRef]

L. A. Riseberg and H. W. Moos, "Multiphonon orbit-lattice relaxation of excited states of rare earth ions in crystals," Phys. Rev. 174, 429 (1968).
[CrossRef]

1967

W. D. Partlow and H. W. Moos, "Multiphonon relaxation in LaCl3:Nd3+," Phys. Rev. 157, 252 (1967).
[CrossRef]

1965

Y. E. Kariss, M. N. Tolstoi, and P. P. Feofilov, "On the luminescence and absorption of trivalent neodymium in crystals of the fluorite type," Opt. Spectrosc. (USSR) 18, 247 (1965).

1964

I. Richman, "Vibronic spectra of SrF2:Sm2+ and BaF2:Sm2+," Phys. Rev. 133, A1364 (1964).
[CrossRef]

1963

Y. E. Perlin, "Modern methods in the theory of many-phonon processes," Sov. Phys. 6, 542 (1963).
[CrossRef]

1962

A. E. Kiel, "The interaction of paramagnetic ions with lattice vibrations," Ph.D. dissertation (Johns Hopkins University, Baltimore, Md., 1962).

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

G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511 (1962).
[CrossRef]

1950

K. Huang and A. Rhys, "Theory of light absorption and nonradiative transmission in F centres," Proc. R. Soc. of London Ser. A 204, 406 (1950).
[CrossRef]

Basiev, T. T.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovskii, and A. M. Prokhorov, "Multiphonon nonradiative relaxation from high-lying levels of Nd3+ ions in fluoride and oxide laser materials," in Advanced Solid-State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 358.

Bauman, R. P.

J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
[CrossRef]

Beach, R.

Benett, W.

Bibeau, C.

C. Bibeau, J. B. Trenholme, and S. A. Payne, "Pulse length and terminal level lifetime dependence of energy extraction for neodymium doped phosphate amplifier glass," submitted to IEEE J. Quantum Electron.

Blakeslee, K. C.

S. R. Levitt, K. C. Blakeslee, and R. A. Condrate, Sr., "Infrared spectra and laser-Raman spectra of several apatites," Mem. Soc. R. Sci. Liege 5, 121 (1970).

Blazha, M. G.

Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).

Capps, D.

K. Palombo, S. Matthews, S. Sheldrake, and D. Capps, "Determination of the effective lower level lifetime for Nd:YLF and Nd:YAG through experimental measurement and computer modeling," in Advanced Solid-State Lasers, Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), p. 78.

Carnall, W. T.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, Energy Level Structure and Transition Probabilities of the Trivalent Lanthanides in LaF3 (Argonne National Laboratory, Argonne, Ill.).

Caspers, H. H.

S. A. Miller, H. E. Rast, and H. H. Caspers, "Lattice vibrations of LiYF4," J. Chem. Phys. 52, 4172 (1970).
[CrossRef]

Chang, I. F.

J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
[CrossRef]

Condrate, R. A.

S. R. Levitt, K. C. Blakeslee, and R. A. Condrate, Sr., "Infrared spectra and laser-Raman spectra of several apatites," Mem. Soc. R. Sci. Liege 5, 121 (1970).

Crosswhite, H.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, Energy Level Structure and Transition Probabilities of the Trivalent Lanthanides in LaF3 (Argonne National Laboratory, Argonne, Ill.).

Crosswhite, H. M.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, Energy Level Structure and Transition Probabilities of the Trivalent Lanthanides in LaF3 (Argonne National Laboratory, Argonne, Ill.).

Cruz, J.

Davin, J.

Dergachev, A. Y.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovskii, and A. M. Prokhorov, "Multiphonon nonradiative relaxation from high-lying levels of Nd3+ ions in fluoride and oxide laser materials," in Advanced Solid-State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 358.

Dexter, D. L.

T. Miyakawa and D. L. Dexter, "Phonon sidebands, multiphonon relaxation of excited states, and phonon assisted energy transfer between ions in solids," Phys. Rev. B 1, 2961 (1970).
[CrossRef]

Driel, H. M. Van

Duke, C. B.

T. F. Soules and C. B. Duke, "Resonant energy transfer between localized electronic states in a crystal," Phys. Rev. B 3, 262 (1971).
[CrossRef]

Enakii, V. N.

Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).

Eyring, L.

K. A. Gschneidner, Jr., and L. Eyring, Handbook on the Physics and Chemistry of Rare Earths (North-Holland, New York, 1982), Vol. 5, Chap. 46.
[CrossRef]

Fan, T. Y.

T. Y. Fan, "Effect of finite lower level lifetime on Q-switched lasers," IEEE J. Quantum Electron. 24, 2345 (1988).
[CrossRef]

Feofilov, P. P.

Y. E. Kariss, M. N. Tolstoi, and P. P. Feofilov, "On the luminescence and absorption of trivalent neodymium in crystals of the fluorite type," Opt. Spectrosc. (USSR) 18, 247 (1965).

Fischer, S. F.

S. F. Fischer, "Correlation function approach to radiationless transitions," J. Chem. Phys. 53, 3195 (1970).
[CrossRef]

Fong, F. K.

F. K. Fong, S. L. Naberhuis, and M. M. Miller, "Theory of radiationless relaxation of rare-earth ions in crystals," J. Chem. Phys. 56, 4020 (1972).
[CrossRef]

Fonger, W. H.

C. W. Struck and W. H. Fonger, "Unified model of the temperature quenching of narrow-line and broad-band emissions," J. Lumin. 10, 1 (1975).
[CrossRef]

Forsythe, G. E.

G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 129.

Freitas, B.

Gaponstev, V. P.

V. P. Gaponstev, M. R. Sirtlanov, A. K. Gromov, and A. A. Isineev, "New data on nonradiative relaxation of impurity center excitations in laser materials," in Proceedings of Lasers 1981 (STS, McLean, Va., 1981), p. 63.

Gapontsev, V.

V. Gapontsev and M. Sirtlanov, "Progress in understanding of mechanisms of RE3+-excited states nonradiative relaxation in crystals," J. Lumin. 31 & 32, 201 (1984).
[CrossRef]

Giuliani, G.

Grigor'yants, V. V.

V. V. Grigor'yants, M. E. Zhabotinskii, and V. M. Markushev, "Determination of the probability of relaxation of the population of the 4I11/2 level of neodymium ions from luminescence dumping in a small external sample," Sov. J. Quantum Electron. 12, 1010 (1983).
[CrossRef]

Gromov, A. K.

V. P. Gaponstev, M. R. Sirtlanov, A. K. Gromov, and A. A. Isineev, "New data on nonradiative relaxation of impurity center excitations in laser materials," in Proceedings of Lasers 1981 (STS, McLean, Va., 1981), p. 63.

Gruber, J. B.

J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
[CrossRef]

Gschneidner, K. A.

K. A. Gschneidner, Jr., and L. Eyring, Handbook on the Physics and Chemistry of Rare Earths (North-Holland, New York, 1982), Vol. 5, Chap. 46.
[CrossRef]

Gu, Z.

K. Huang and Z. Gu, "Phonon analysis in multiphonon transitions," Commun. Theor. Phys. 1, 535 (1982).

Hamilton, D. S.

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, "Raman scattering and nonlinear refractive index measurements of optical glasses," J. Non-Cryst. Solids 34, 63 (1979).
[CrossRef]

Heiman, D.

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, "Raman scattering and nonlinear refractive index measurements of optical glasses," J. Non-Cryst. Solids 34, 63 (1979).
[CrossRef]

Hellwarth, R. W.

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, "Raman scattering and nonlinear refractive index measurements of optical glasses," J. Non-Cryst. Solids 34, 63 (1979).
[CrossRef]

Hills, M. E.

J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
[CrossRef]

Hovis, F. E.

F. E. Hovis, M. Stuff, C. J. Kennedy, and B. Vivian, "Lower level relaxation of Nd:YAG," IEEE J. Quantum Electron. 28, 39 (1992).
[CrossRef]

Huang, K.

K. Huang and Z. Gu, "Phonon analysis in multiphonon transitions," Commun. Theor. Phys. 1, 535 (1982).

K. Huang and A. Rhys, "Theory of light absorption and nonradiative transmission in F centres," Proc. R. Soc. of London Ser. A 204, 406 (1950).
[CrossRef]

Hurrell, J. P.

J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
[CrossRef]

Isineev, A. A.

V. P. Gaponstev, M. R. Sirtlanov, A. K. Gromov, and A. A. Isineev, "New data on nonradiative relaxation of impurity center excitations in laser materials," in Proceedings of Lasers 1981 (STS, McLean, Va., 1981), p. 63.

Judd, B. R.

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

Kaminskii, A. A.

Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).

Kariss, Y. E.

Y. E. Kariss, M. N. Tolstoi, and P. P. Feofilov, "On the luminescence and absorption of trivalent neodymium in crystals of the fluorite type," Opt. Spectrosc. (USSR) 18, 247 (1965).

Kennedy, C. J.

F. E. Hovis, M. Stuff, C. J. Kennedy, and B. Vivian, "Lower level relaxation of Nd:YAG," IEEE J. Quantum Electron. 28, 39 (1992).
[CrossRef]

Khilko, A. V.

A. M. Tkachuk, A. V. Khilko, and M. V. Petrov, "Probabilities for nonradiative intermultiplet transitions in the holmium ion in lithium–yttrium double fluoride crystals and stimulated emission," Opt. Spectrosc. (USSR) 58, 216 (1985).

Kiel, A. E.

A. E. Kiel, "The interaction of paramagnetic ions with lattice vibrations," Ph.D. dissertation (Johns Hopkins University, Baltimore, Md., 1962).

Kinoshita, S.

T. Kushida, S. Kinoshita, T. Ohtsuki, and T. Yamada, "Multiphonon relaxation rate from pumped level to upper laser level in YAG:Nd," Solid State Commun. 44, 1363 (1982).
[CrossRef]

Kokta, M. R.

J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
[CrossRef]

Kolodnyi, G. Ya.

G. M. Zverev, G. Ya. Kolodnyi, and A. M. Onishchenko, "Nonradiative transitions between levels of trivalent rare-earth ions in yttrium-aluminum garnet crystals," Sov. Phys. JETP 33, 497 (1971).

Krupke, W. F.

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

Kushida, T.

T. Kushida, S. Kinoshita, T. Ohtsuki, and T. Yamada, "Multiphonon relaxation rate from pumped level to upper laser level in YAG:Nd," Solid State Commun. 44, 1363 (1982).
[CrossRef]

Layne, C. B.

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, "Multiphonon relaxation of rare-earth ions in oxide glasses," Phys. Rev. B 16, 10 (1977).
[CrossRef]

Levitt, S. R.

S. R. Levitt, K. C. Blakeslee, and R. A. Condrate, Sr., "Infrared spectra and laser-Raman spectra of several apatites," Mem. Soc. R. Sci. Liege 5, 121 (1970).

Liu, Y.

P. Zhang, Y. Liu, and Y. Mo, "The Raman spectrum of single crystal Gd3Ga5O12," Chin. Phys. 4, 530 (1984).

Lowdermilk, W. H.

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, "Multiphonon relaxation of rare-earth ions in oxide glasses," Phys. Rev. B 16, 10 (1977).
[CrossRef]

Maksimova, G. V.

G. V. Maksimova and A. A. Sobol, "Nd3+ Optical centers in crystals of calcium and strontium fluorophosphates," Proc. P. N. Lebedev Phys. Inst. 60, 59 (1974).

Malcolm, M. A.

G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 129.

Markushev, V. M.

V. V. Grigor'yants, M. E. Zhabotinskii, and V. M. Markushev, "Determination of the probability of relaxation of the population of the 4I11/2 level of neodymium ions from luminescence dumping in a small external sample," Sov. J. Quantum Electron. 12, 1010 (1983).
[CrossRef]

Martin, W. E.

W. E. Martin and D. Milam, "Direct measurement of gain recovery in a saturated Nd–glass amplifier," Appl. Phys. Lett. 32, 816 (1978).
[CrossRef]

Matthews, S.

K. Palombo, S. Matthews, S. Sheldrake, and D. Capps, "Determination of the effective lower level lifetime for Nd:YLF and Nd:YAG through experimental measurement and computer modeling," in Advanced Solid-State Lasers, Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), p. 78.

Milam, D.

S. M. Yarema and D. Milam, "Gain saturation in phosphate laser glasses," IEEE J. Quantum Electron. QE-18, 1941 (1982).
[CrossRef]

W. E. Martin and D. Milam, "Direct measurement of gain recovery in a saturated Nd–glass amplifier," Appl. Phys. Lett. 32, 816 (1978).
[CrossRef]

Miller, M. M.

F. K. Fong, S. L. Naberhuis, and M. M. Miller, "Theory of radiationless relaxation of rare-earth ions in crystals," J. Chem. Phys. 56, 4020 (1972).
[CrossRef]

Miller, S. A.

S. A. Miller, H. E. Rast, and H. H. Caspers, "Lattice vibrations of LiYF4," J. Chem. Phys. 52, 4172 (1970).
[CrossRef]

Mitchell, S.

Mitra, S. S.

J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
[CrossRef]

Miyakawa, T.

T. Miyakawa and D. L. Dexter, "Phonon sidebands, multiphonon relaxation of excited states, and phonon assisted energy transfer between ions in solids," Phys. Rev. B 1, 2961 (1970).
[CrossRef]

Mo, Y.

P. Zhang, Y. Liu, and Y. Mo, "The Raman spectrum of single crystal Gd3Ga5O12," Chin. Phys. 4, 530 (1984).

Moler, C. B.

G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 129.

Moos, H. W.

E. D. Reed, Jr. and H. W. Moos, "Multiphonon relaxation of excited states of rare earths in YVO4, YAsO4, and YPO4," Phys. Rev. B 8, 980 (1973).
[CrossRef]

L. A. Riseberg and H. W. Moos, "Multiphonon orbit-lattice relaxation of excited states of rare earth ions in crystals," Phys. Rev. 174, 429 (1968).
[CrossRef]

W. D. Partlow and H. W. Moos, "Multiphonon relaxation in LaCl3:Nd3+," Phys. Rev. 157, 252 (1967).
[CrossRef]

Morrison, C. A.

J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
[CrossRef]

Naberhuis, S. L.

F. K. Fong, S. L. Naberhuis, and M. M. Miller, "Theory of radiationless relaxation of rare-earth ions in crystals," J. Chem. Phys. 56, 4020 (1972).
[CrossRef]

Ofelt, G. S.

G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511 (1962).
[CrossRef]

Ohtsuki, T.

T. Kushida, S. Kinoshita, T. Ohtsuki, and T. Yamada, "Multiphonon relaxation rate from pumped level to upper laser level in YAG:Nd," Solid State Commun. 44, 1363 (1982).
[CrossRef]

Onishchenko, A. M.

G. M. Zverev, G. Ya. Kolodnyi, and A. M. Onishchenko, "Nonradiative transitions between levels of trivalent rare-earth ions in yttrium-aluminum garnet crystals," Sov. Phys. JETP 33, 497 (1971).

Orbach, R.

R. Orbach, Optical Properties of Ions in Solids (Wiley-Interscience, New York, 1967), p. 445.

Orlovskii, Y. V.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovskii, and A. M. Prokhorov, "Multiphonon nonradiative relaxation from high-lying levels of Nd3+ ions in fluoride and oxide laser materials," in Advanced Solid-State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 358.

Palombo, K.

K. Palombo, S. Matthews, S. Sheldrake, and D. Capps, "Determination of the effective lower level lifetime for Nd:YLF and Nd:YAG through experimental measurement and computer modeling," in Advanced Solid-State Lasers, Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), p. 78.

Partlow, W. D.

W. D. Partlow and H. W. Moos, "Multiphonon relaxation in LaCl3:Nd3+," Phys. Rev. 157, 252 (1967).
[CrossRef]

Payne, S. A.

I. M. Thomas, S. A. Payne, and G. D. Wilke, "Optical properties and laser demonstration of Nd-doped sol-gel silica glasses," J. Non-Cryst. Solids 151, 183 (1992).
[CrossRef]

C. Bibeau, J. B. Trenholme, and S. A. Payne, "Pulse length and terminal level lifetime dependence of energy extraction for neodymium doped phosphate amplifier glass," submitted to IEEE J. Quantum Electron.

Perlin, Y. E.

Y. E. Perlin, "Modern methods in the theory of many-phonon processes," Sov. Phys. 6, 542 (1963).
[CrossRef]

Perlin, Y. U.

Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).

Petrov, M. V.

A. M. Tkachuk, A. V. Khilko, and M. V. Petrov, "Probabilities for nonradiative intermultiplet transitions in the holmium ion in lithium–yttrium double fluoride crystals and stimulated emission," Opt. Spectrosc. (USSR) 58, 216 (1985).

Porto, S. P. S.

J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
[CrossRef]

Prokhorov, A. M.

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovskii, and A. M. Prokhorov, "Multiphonon nonradiative relaxation from high-lying levels of Nd3+ ions in fluoride and oxide laser materials," in Advanced Solid-State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 358.

Rast, H. E.

S. A. Miller, H. E. Rast, and H. H. Caspers, "Lattice vibrations of LiYF4," J. Chem. Phys. 52, 4172 (1970).
[CrossRef]

Reed, E. D.

E. D. Reed, Jr. and H. W. Moos, "Multiphonon relaxation of excited states of rare earths in YVO4, YAsO4, and YPO4," Phys. Rev. B 8, 980 (1973).
[CrossRef]

Reichert, P.

Rhys, A.

K. Huang and A. Rhys, "Theory of light absorption and nonradiative transmission in F centres," Proc. R. Soc. of London Ser. A 204, 406 (1950).
[CrossRef]

Richman, I.

I. Richman, "Vibronic spectra of SrF2:Sm2+ and BaF2:Sm2+," Phys. Rev. 133, A1364 (1964).
[CrossRef]

Riseberg, L. A.

L. A. Riseberg and H. W. Moos, "Multiphonon orbit-lattice relaxation of excited states of rare earth ions in crystals," Phys. Rev. 174, 429 (1968).
[CrossRef]

Ryabchenkov, V. V.

Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).

Sheldrake, S.

K. Palombo, S. Matthews, S. Sheldrake, and D. Capps, "Determination of the effective lower level lifetime for Nd:YLF and Nd:YAG through experimental measurement and computer modeling," in Advanced Solid-State Lasers, Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), p. 78.

Shipulo, G. P.

A. A. Zlenko, V. A. Sychugov, and G. P. Shipulo, "Measurement of the relaxation time τ21 of a Y3Al5O12:Nd3+ crystal," Sov. J. Quantum Electron. 2, 474 (1973).
[CrossRef]

Sirtlanov, M.

V. Gapontsev and M. Sirtlanov, "Progress in understanding of mechanisms of RE3+-excited states nonradiative relaxation in crystals," J. Lumin. 31 & 32, 201 (1984).
[CrossRef]

Sirtlanov, M. R.

V. P. Gaponstev, M. R. Sirtlanov, A. K. Gromov, and A. A. Isineev, "New data on nonradiative relaxation of impurity center excitations in laser materials," in Proceedings of Lasers 1981 (STS, McLean, Va., 1981), p. 63.

Sobol, A. A.

G. V. Maksimova and A. A. Sobol, "Nd3+ Optical centers in crystals of calcium and strontium fluorophosphates," Proc. P. N. Lebedev Phys. Inst. 60, 59 (1974).

Solarz, R.

Soules, T. F.

T. F. Soules and C. B. Duke, "Resonant energy transfer between localized electronic states in a crystal," Phys. Rev. B 3, 262 (1971).
[CrossRef]

Stroganov, A. A.

E. B. Sveshnikova, A. A. Stroganov, and L. N. Urusovskaya, "Mechanism of nonradiative transitions in rare-earth ions in fluorozirconate bases," Opt. Spectrosc. (USSR) 63, 618 (1987).

Struck, C. W.

C. W. Struck and W. H. Fonger, "Unified model of the temperature quenching of narrow-line and broad-band emissions," J. Lumin. 10, 1 (1975).
[CrossRef]

Stuff, M.

F. E. Hovis, M. Stuff, C. J. Kennedy, and B. Vivian, "Lower level relaxation of Nd:YAG," IEEE J. Quantum Electron. 28, 39 (1992).
[CrossRef]

Sveshnikova, E. B.

E. B. Sveshnikova, A. A. Stroganov, and L. N. Urusovskaya, "Mechanism of nonradiative transitions in rare-earth ions in fluorozirconate bases," Opt. Spectrosc. (USSR) 63, 618 (1987).

Sychugov, V. A.

A. A. Zlenko, V. A. Sychugov, and G. P. Shipulo, "Measurement of the relaxation time τ21 of a Y3Al5O12:Nd3+ crystal," Sov. J. Quantum Electron. 2, 474 (1973).
[CrossRef]

Thomas, I. M.

I. M. Thomas, S. A. Payne, and G. D. Wilke, "Optical properties and laser demonstration of Nd-doped sol-gel silica glasses," J. Non-Cryst. Solids 151, 183 (1992).
[CrossRef]

Tkachuk, A. M.

A. M. Tkachuk, A. V. Khilko, and M. V. Petrov, "Probabilities for nonradiative intermultiplet transitions in the holmium ion in lithium–yttrium double fluoride crystals and stimulated emission," Opt. Spectrosc. (USSR) 58, 216 (1985).

Tolstoi, M. N.

Y. E. Kariss, M. N. Tolstoi, and P. P. Feofilov, "On the luminescence and absorption of trivalent neodymium in crystals of the fluorite type," Opt. Spectrosc. (USSR) 18, 247 (1965).

Trenholme, J.

J. Trenholme, Laser Program, Lawrence Livermore National Laboratory, Livermore, Calif. 94550 (personal communication, 1993).

Trenholme, J. B.

C. Bibeau, J. B. Trenholme, and S. A. Payne, "Pulse length and terminal level lifetime dependence of energy extraction for neodymium doped phosphate amplifier glass," submitted to IEEE J. Quantum Electron.

Turner, G. A.

J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
[CrossRef]

Urusovskaya, L. N.

E. B. Sveshnikova, A. A. Stroganov, and L. N. Urusovskaya, "Mechanism of nonradiative transitions in rare-earth ions in fluorozirconate bases," Opt. Spectrosc. (USSR) 63, 618 (1987).

Velsko, A.

Vivian, B.

F. E. Hovis, M. Stuff, C. J. Kennedy, and B. Vivian, "Lower level relaxation of Nd:YAG," IEEE J. Quantum Electron. 28, 39 (1992).
[CrossRef]

Weber, M. J.

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, "Multiphonon relaxation of rare-earth ions in oxide glasses," Phys. Rev. B 16, 10 (1977).
[CrossRef]

M. J. Weber, "Multiphonon relaxation of rare-earth ions in yttrium orthoaluminate," Phys. Rev. B 8, 54 (1973).
[CrossRef]

Wilke, G. D.

I. M. Thomas, S. A. Payne, and G. D. Wilke, "Optical properties and laser demonstration of Nd-doped sol-gel silica glasses," J. Non-Cryst. Solids 151, 183 (1992).
[CrossRef]

Yamada, T.

T. Kushida, S. Kinoshita, T. Ohtsuki, and T. Yamada, "Multiphonon relaxation rate from pumped level to upper laser level in YAG:Nd," Solid State Commun. 44, 1363 (1982).
[CrossRef]

Yarema, S. M.

S. M. Yarema and D. Milam, "Gain saturation in phosphate laser glasses," IEEE J. Quantum Electron. QE-18, 1941 (1982).
[CrossRef]

Zhabotinskii, M. E.

V. V. Grigor'yants, M. E. Zhabotinskii, and V. M. Markushev, "Determination of the probability of relaxation of the population of the 4I11/2 level of neodymium ions from luminescence dumping in a small external sample," Sov. J. Quantum Electron. 12, 1010 (1983).
[CrossRef]

Zhang, P.

P. Zhang, Y. Liu, and Y. Mo, "The Raman spectrum of single crystal Gd3Ga5O12," Chin. Phys. 4, 530 (1984).

Zlenko, A. A.

A. A. Zlenko, V. A. Sychugov, and G. P. Shipulo, "Measurement of the relaxation time τ21 of a Y3Al5O12:Nd3+ crystal," Sov. J. Quantum Electron. 2, 474 (1973).
[CrossRef]

Zverev, G. M.

G. M. Zverev, G. Ya. Kolodnyi, and A. M. Onishchenko, "Nonradiative transitions between levels of trivalent rare-earth ions in yttrium-aluminum garnet crystals," Sov. Phys. JETP 33, 497 (1971).

Appl. Phys. Lett.

W. E. Martin and D. Milam, "Direct measurement of gain recovery in a saturated Nd–glass amplifier," Appl. Phys. Lett. 32, 816 (1978).
[CrossRef]

Chin. Phys.

P. Zhang, Y. Liu, and Y. Mo, "The Raman spectrum of single crystal Gd3Ga5O12," Chin. Phys. 4, 530 (1984).

Commun. Theor. Phys.

K. Huang and Z. Gu, "Phonon analysis in multiphonon transitions," Commun. Theor. Phys. 1, 535 (1982).

IEEE J. Quantum Electron.

F. E. Hovis, M. Stuff, C. J. Kennedy, and B. Vivian, "Lower level relaxation of Nd:YAG," IEEE J. Quantum Electron. 28, 39 (1992).
[CrossRef]

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

T. Y. Fan, "Effect of finite lower level lifetime on Q-switched lasers," IEEE J. Quantum Electron. 24, 2345 (1988).
[CrossRef]

S. M. Yarema and D. Milam, "Gain saturation in phosphate laser glasses," IEEE J. Quantum Electron. QE-18, 1941 (1982).
[CrossRef]

J. Chem. Phys.

S. F. Fischer, "Correlation function approach to radiationless transitions," J. Chem. Phys. 53, 3195 (1970).
[CrossRef]

F. K. Fong, S. L. Naberhuis, and M. M. Miller, "Theory of radiationless relaxation of rare-earth ions in crystals," J. Chem. Phys. 56, 4020 (1972).
[CrossRef]

G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511 (1962).
[CrossRef]

S. A. Miller, H. E. Rast, and H. H. Caspers, "Lattice vibrations of LiYF4," J. Chem. Phys. 52, 4172 (1970).
[CrossRef]

J. Lumin.

V. Gapontsev and M. Sirtlanov, "Progress in understanding of mechanisms of RE3+-excited states nonradiative relaxation in crystals," J. Lumin. 31 & 32, 201 (1984).
[CrossRef]

C. W. Struck and W. H. Fonger, "Unified model of the temperature quenching of narrow-line and broad-band emissions," J. Lumin. 10, 1 (1975).
[CrossRef]

J. Non-Cryst. Solids

I. M. Thomas, S. A. Payne, and G. D. Wilke, "Optical properties and laser demonstration of Nd-doped sol-gel silica glasses," J. Non-Cryst. Solids 151, 183 (1992).
[CrossRef]

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, "Raman scattering and nonlinear refractive index measurements of optical glasses," J. Non-Cryst. Solids 34, 63 (1979).
[CrossRef]

Mem. Soc. R. Sci. Liege

S. R. Levitt, K. C. Blakeslee, and R. A. Condrate, Sr., "Infrared spectra and laser-Raman spectra of several apatites," Mem. Soc. R. Sci. Liege 5, 121 (1970).

Opt. Lett.

Opt. Spectrosc.

A. M. Tkachuk, A. V. Khilko, and M. V. Petrov, "Probabilities for nonradiative intermultiplet transitions in the holmium ion in lithium–yttrium double fluoride crystals and stimulated emission," Opt. Spectrosc. (USSR) 58, 216 (1985).

Y. E. Kariss, M. N. Tolstoi, and P. P. Feofilov, "On the luminescence and absorption of trivalent neodymium in crystals of the fluorite type," Opt. Spectrosc. (USSR) 18, 247 (1965).

E. B. Sveshnikova, A. A. Stroganov, and L. N. Urusovskaya, "Mechanism of nonradiative transitions in rare-earth ions in fluorozirconate bases," Opt. Spectrosc. (USSR) 63, 618 (1987).

Phys. Rev.

J. P. Hurrell, S. P. S. Porto, I. F. Chang, S. S. Mitra, and R. P. Bauman, "Optical phonons of yttrium aluminum garnet," Phys. Rev. 173, 851 (1968).
[CrossRef]

I. Richman, "Vibronic spectra of SrF2:Sm2+ and BaF2:Sm2+," Phys. Rev. 133, A1364 (1964).
[CrossRef]

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

L. A. Riseberg and H. W. Moos, "Multiphonon orbit-lattice relaxation of excited states of rare earth ions in crystals," Phys. Rev. 174, 429 (1968).
[CrossRef]

W. D. Partlow and H. W. Moos, "Multiphonon relaxation in LaCl3:Nd3+," Phys. Rev. 157, 252 (1967).
[CrossRef]

Phys. Rev. B

T. Miyakawa and D. L. Dexter, "Phonon sidebands, multiphonon relaxation of excited states, and phonon assisted energy transfer between ions in solids," Phys. Rev. B 1, 2961 (1970).
[CrossRef]

T. F. Soules and C. B. Duke, "Resonant energy transfer between localized electronic states in a crystal," Phys. Rev. B 3, 262 (1971).
[CrossRef]

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, "Multiphonon relaxation of rare-earth ions in oxide glasses," Phys. Rev. B 16, 10 (1977).
[CrossRef]

E. D. Reed, Jr. and H. W. Moos, "Multiphonon relaxation of excited states of rare earths in YVO4, YAsO4, and YPO4," Phys. Rev. B 8, 980 (1973).
[CrossRef]

J. B. Gruber, M. E. Hills, C. A. Morrison, G. A. Turner, and M. R. Kokta, "Absorption spectra and energy levels of Gd3+, Nd3+, and Cr3+ in garnet Gd3Sc2Ga3O12," Phys. Rev. B 37, 8564 (1988).
[CrossRef]

M. J. Weber, "Multiphonon relaxation of rare-earth ions in yttrium orthoaluminate," Phys. Rev. B 8, 54 (1973).
[CrossRef]

Proc. P. N. Lebedev Phys. Inst.

G. V. Maksimova and A. A. Sobol, "Nd3+ Optical centers in crystals of calcium and strontium fluorophosphates," Proc. P. N. Lebedev Phys. Inst. 60, 59 (1974).

Proc. R. Soc. of London Ser. A

K. Huang and A. Rhys, "Theory of light absorption and nonradiative transmission in F centres," Proc. R. Soc. of London Ser. A 204, 406 (1950).
[CrossRef]

Solid State Commun.

T. Kushida, S. Kinoshita, T. Ohtsuki, and T. Yamada, "Multiphonon relaxation rate from pumped level to upper laser level in YAG:Nd," Solid State Commun. 44, 1363 (1982).
[CrossRef]

Sov. J. Quantum Electron.

A. A. Zlenko, V. A. Sychugov, and G. P. Shipulo, "Measurement of the relaxation time τ21 of a Y3Al5O12:Nd3+ crystal," Sov. J. Quantum Electron. 2, 474 (1973).
[CrossRef]

V. V. Grigor'yants, M. E. Zhabotinskii, and V. M. Markushev, "Determination of the probability of relaxation of the population of the 4I11/2 level of neodymium ions from luminescence dumping in a small external sample," Sov. J. Quantum Electron. 12, 1010 (1983).
[CrossRef]

Sov. Phys.

Y. E. Perlin, "Modern methods in the theory of many-phonon processes," Sov. Phys. 6, 542 (1963).
[CrossRef]

Sov. Phys. JETP

G. M. Zverev, G. Ya. Kolodnyi, and A. M. Onishchenko, "Nonradiative transitions between levels of trivalent rare-earth ions in yttrium-aluminum garnet crystals," Sov. Phys. JETP 33, 497 (1971).

Sov. Phys. Solid State

Y. U. Perlin, A. A. Kaminskii, M. G. Blazha, V. N. Enakii, and V. V. Ryabchenkov, "Nonlinear electron-phonon interaction as cause of nonradiative transitions of TR3+ ions in crystals," Sov. Phys. Solid State 24, 386 (1982).

Other

K. Palombo, S. Matthews, S. Sheldrake, and D. Capps, "Determination of the effective lower level lifetime for Nd:YLF and Nd:YAG through experimental measurement and computer modeling," in Advanced Solid-State Lasers, Vol. 15 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993), p. 78.

A. E. Kiel, "The interaction of paramagnetic ions with lattice vibrations," Ph.D. dissertation (Johns Hopkins University, Baltimore, Md., 1962).

R. Orbach, Optical Properties of Ions in Solids (Wiley-Interscience, New York, 1967), p. 445.

V. P. Gaponstev, M. R. Sirtlanov, A. K. Gromov, and A. A. Isineev, "New data on nonradiative relaxation of impurity center excitations in laser materials," in Proceedings of Lasers 1981 (STS, McLean, Va., 1981), p. 63.

G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 129.

K. A. Gschneidner, Jr., and L. Eyring, Handbook on the Physics and Chemistry of Rare Earths (North-Holland, New York, 1982), Vol. 5, Chap. 46.
[CrossRef]

C. Bibeau, J. B. Trenholme, and S. A. Payne, "Pulse length and terminal level lifetime dependence of energy extraction for neodymium doped phosphate amplifier glass," submitted to IEEE J. Quantum Electron.

J. Trenholme, Laser Program, Lawrence Livermore National Laboratory, Livermore, Calif. 94550 (personal communication, 1993).

T. T. Basiev, A. Y. Dergachev, Y. V. Orlovskii, and A. M. Prokhorov, "Multiphonon nonradiative relaxation from high-lying levels of Nd3+ ions in fluoride and oxide laser materials," in Advanced Solid-State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 358.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, Energy Level Structure and Transition Probabilities of the Trivalent Lanthanides in LaF3 (Argonne National Laboratory, Argonne, Ill.).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

A simplified Nd energy-level scheme that defines the 4F3/2 metastable level, the 1-μm Nd laser transition (4F3/24I11/2), the potentially bottlenecked 4I11/2 level, and the lower-level lifetime (τ11/2).

Fig. 2
Fig. 2

Plot of the normalized saturation fluence Fsat/F0 and extraction efficiency ηextr as a function of the ratio of the pulse length (tp) to lower-level lifetime (τ11/2).

Fig. 3
Fig. 3

Illustration of the pump (2.41-μm) and probe (1.06-μm) method employed in our experiment. (a) A 100-ps pump pulse is used to excite a fraction of the 4I9/2 ground-state population into the 4I13/2 level. (b) After a time τd, a weak probe pulse then probes the 4I11/2 population by exciting a fraction of these ions to the upper 4F3/2 level. (c) The resulting 0.88-μm emission signal is then recorded and integrated. (d) Experimentally, the pump and the probe beams are focused into the sample with a detector placed on the side to record the 0.88-μm emission signal. (e) Therefore, as the 4I11/2 population returns back down to the 4I9/2 ground state, the relative integrated 0.88-μm signal strength will decrease and enable us to infer the τ11/2 lifetime.

Fig. 4
Fig. 4

Detailed schematic of the experimental arrangement used to measure the lower-level lifetime. A 100-ps pulse is first passed through an ~20/80 beam splitter. The more energetic, transmitted beam is focused into a high-pressure H2 Raman cell, where 9% of the incident 1.06-μm energy is converted to the first-Stokes frequency at 1.91 μm. The 1.91-μm light is then combined with the 1.06-μm light from the upper path into a LiNbO3 crystal to generate ~0.5 mJ of 2.41-μm energy. A prism separates the 2.41-μm (pump) beam from the 1.06-μm (probe) beam so that the 1.06-μm beam can be sent into a computer-controlled variable-delay line. The pump and the probe beams are then focused into the sample with a PMT detector placed on the side to record the 0.88-μm signal (S0.88). The 1.06-μm reference detector (R1.06) and the 2.41-μm reference detector (R2.41), also shown, are used to correct for the 4I11/2 thermal population and energy fluctuations in the 1.06- and 2.41-μm energies. All the signals (S0.88, R1.06, and R2.41) are electronically sent into the boxcars integrators and then to the computer where the data are stored for postanalysis.

Fig. 5
Fig. 5

More-detailed diagram of the Nd energy levels showing the additional resonance (dashed line) excited by the 1.06-μm probe beam. The diagram also identifies the populations N0, N1, N2, and Nu, used in the rate equations for the modeling of the data.

Fig. 6
Fig. 6

Plot of the relative fitting error χ2 as a function of (a) the ratio of lifetimes τ13/2/τ11/2 and of (b) the ratio of cross sections σ11/2/σ13/2 as a function of the ratio of lifetimes τ13/2/τ11/2. The shaded band in (a) is based on the maximum allowable fitting error. The shaded band in (b) is based on the factor-of-2 uncertainty in the independent calculation of the ratio cross sections by the Judd–Ofelt analysis. The gap-law theory assumes a decrease in the nonradiative rate with increasing energy gap, and therefore, as the 4I11/24I9/2 gap is always ~200 cm−1 smaller than the 4I13/24I11/2 gap, the ratio of lifetimes should be greater than 1 (vertical dashed lines).

Fig. 7
Fig. 7

Data (dotted curves) and model (continuous curves) for eight of the glasses investigated. The effective lifetimes corresponding to the averaged energy gap are listed. The higher phonon frequencies of the LG-series phosphates lead to shorter lifetimes than for the LG-series silicates.

Fig. 8
Fig. 8

Data (dotted curves) and model (continuous curves) for six of the crystals investigated. The effective lifetimes corresponding to the averaged energy gap are listed. The small energy gaps and high effective phonon frequencies lead to the short lifetimes (~200 ps) measured for the YAG and FAP crystals.

Fig. 9
Fig. 9

Plot of the nonradiative rate as a function of the energy gap for various Nd-doped crystals and glasses that includes the present work and others along with a best fit line through the data.

Tables (3)

Tables Icon

Table 1 Partial List of Methods and Corresponding Lower-Level Lifetimes Reported for Nd:YAGa

Tables Icon

Table 2 Summary of Fitted Results and Energy Gap Parameters: Effective Lifetime (τeff), Ratio of Cross Sections (σ11/2/σ13/2), Averaged Energy Gap (ΔEave), Effective Phonon Energy (eff), and Normalized Energy Gap (pmax)

Tables Icon

Table 3 Summary Table of the τ11/2 Upper and Lower Limits and Corresponding Energy Gaps ΔE11/2a

Equations (22)

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

η extr = 1 ( 1 + d u d l ) ,
η extr ( t p , τ 11 / 2 ) = 1 ( 1 + d u d l × Ω ) ,
Ω = 1 - exp ( - t p / τ 11 / 2 ) t p / τ 11 / 2 ,
F sat ( t p / t 11 / 2 ) = F 0 1 + d u d l × Ω ,
Ω = i = 1 3 b i exp ( - a i × t p / τ 11 / 2 ) ,
W nr = A exp ( - α p ) ,
S = ( S 0.88 R 1.06 - B ratio × R 1.06 ) R 2.41 .
d N u d t = I probe ( t ) h ν 1.06 ( σ 13 / 2 N 2 + σ 11 / 2 N 1 ) - N u τ u ,
d N 2 d t = I pump ( t ) h ν 2.41 σ 0 N 0 - N 2 τ 13 / 2 - I probe ( t ) h ν 1.06 σ 13 / 2 N 2 ,
d N 1 d t = - N 1 τ 11 / 2 + N 2 τ 13 / 2 - I probe ( t ) h ν 1.06 σ 11 / 2 N 1 ,
N 0 const . ,
I probe ( t ) = A probe exp [ - ( t - τ d w probe ) 2 ] ,
I pump ( t ) = A pump exp [ - ( t w pump ) 2 ] ,
τ 13 / 2 τ 11 / 2 = C exp ( - γ Δ E 11 / 2 ) C exp ( - γ Δ E 13 / 2 ) = exp ( γ Δ E diff ) = R life ,
Δ E diff = Δ E 13 / 2 - Δ E 11 / 2 .
τ eff = τ 11 / 2 × τ 13 / 2 .
τ 11 / 2 = τ eff / R life .
σ = 8 π 3 e 2 λ ( n 2 + 2 ) 2 S ( a J ; b J ) 27 c h ( 2 J + 1 ) Δ λ eff n ,
S ( a J : b J ) = t = 2 , 4 , 6 Ω t × a J U ( t ) b J 2 ,
σ 11 / 2 σ 13 / 2 = 14 λ 11 / 2 Δ λ 13 / 2 S 11 / 2 12 λ 13 / 2 Δ λ 11 / 2 S 13 / 2 ,
S 11 / 2 = 0.1423 × Ω 4 + 0.4083 × Ω 6             ( I 4 11 / 2 F 4 3 / 2 ) ,
S 13 / 2 = 0.3314 × Ω 4 + 0.3259 × Ω 6             ( I 4 13 / 2 F 4 7 / 2 , S 4 3 / 2 ) ,

Metrics