Abstract

Nonexponential fluorescence decay has been observed from both 4I11/2 and 4I13/2 states of Er3+ ions in heavily doped Er: YAG at room temperature. Processes of cross relaxation that originate in these states are shown to be responsible. Rate equations that include cross-relaxation processes are written and numerically solved, to result in the determination of the cross-relaxation coefficients. It is found that these coefficients do not change with Er3+ concentration. The effects of the cross-relaxation processes of Er3+ ions on fluorescence decay and lasing properties are discussed.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
    [CrossRef]
  2. Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
    [CrossRef]
  3. M. Bass, W. Q. Shi, R. Kurtz, M. Kokta, H. Diegl, “Operation of the high dopant density Er:YAG at 2.94 μ m,” in Tunable Solid State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds., Vol. 52 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986), pp. 300–305.
    [CrossRef]
  4. V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
    [CrossRef]
  5. A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981).
  6. Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).
  7. S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.
  8. V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
    [CrossRef]
  9. E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
    [CrossRef]
  10. See, for example, C. E. Pearson, Numerical Method in Engineering and Science (Van Nostrand Reinhold, New York, 1986).
  11. H. Chou, “Upconversion processes and Cr-sensitization of Er- and Er, Ho-activated solid state materials,” Tech. Rep. 26 (Massachusetts Institute of Technology, Cambridge, Mass., February1989).
  12. 1/α for 50 at. % Er:YAG is estimated to be less than 10 μ m by using the absorption spectrum of Er:YAG.
  13. 1/α′for 50 at. % Er:YAG is estimated to be less than 50 μ m by using the absorption spectrum of Er:YAG.
  14. V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Efficient cross-relaxation laser emission at λ = 2.94 μ m,” Sov. J. Quantum Electron. 13, 1235 (1983).
    [CrossRef]
  15. V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Cooperative phenomena in yttrium erbium aluminum garnet crystals,” Sov. J. Quantum Electron. 14, 128 (1984).
    [CrossRef]

1986 (1)

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

1984 (2)

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Cooperative phenomena in yttrium erbium aluminum garnet crystals,” Sov. J. Quantum Electron. 14, 128 (1984).
[CrossRef]

1983 (2)

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Efficient cross-relaxation laser emission at λ = 2.94 μ m,” Sov. J. Quantum Electron. 13, 1235 (1983).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
[CrossRef]

1980 (1)

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

1977 (1)

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

1975 (1)

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Bagdasarov, Kh. S.

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
[CrossRef]

Bass, M.

M. Bass, W. Q. Shi, R. Kurtz, M. Kokta, H. Diegl, “Operation of the high dopant density Er:YAG at 2.94 μ m,” in Tunable Solid State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds., Vol. 52 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986), pp. 300–305.
[CrossRef]

Chou, H.

H. Chou, “Upconversion processes and Cr-sensitization of Er- and Er, Ho-activated solid state materials,” Tech. Rep. 26 (Massachusetts Institute of Technology, Cambridge, Mass., February1989).

Diegl, H.

M. Bass, W. Q. Shi, R. Kurtz, M. Kokta, H. Diegl, “Operation of the high dopant density Er:YAG at 2.94 μ m,” in Tunable Solid State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds., Vol. 52 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986), pp. 300–305.
[CrossRef]

Georgescu, S.

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

Kaminskii, A. A.

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

Kokta, M.

M. Bass, W. Q. Shi, R. Kurtz, M. Kokta, H. Diegl, “Operation of the high dopant density Er:YAG at 2.94 μ m,” in Tunable Solid State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds., Vol. 52 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986), pp. 300–305.
[CrossRef]

Kulevskii, L. A.

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Kurtz, R.

M. Bass, W. Q. Shi, R. Kurtz, M. Kokta, H. Diegl, “Operation of the high dopant density Er:YAG at 2.94 μ m,” in Tunable Solid State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds., Vol. 52 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986), pp. 300–305.
[CrossRef]

Labachev, V. A.

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

Lobachev, V. A.

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Cooperative phenomena in yttrium erbium aluminum garnet crystals,” Sov. J. Quantum Electron. 14, 128 (1984).
[CrossRef]

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Efficient cross-relaxation laser emission at λ = 2.94 μ m,” Sov. J. Quantum Electron. 13, 1235 (1983).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
[CrossRef]

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

Lupei, V.

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

Manenkov, A. A.

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

Murina, T. M.

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Cooperative phenomena in yttrium erbium aluminum garnet crystals,” Sov. J. Quantum Electron. 14, 128 (1984).
[CrossRef]

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Efficient cross-relaxation laser emission at λ = 2.94 μ m,” Sov. J. Quantum Electron. 13, 1235 (1983).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
[CrossRef]

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

Osiko, V. V.

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Pearson, C. E.

See, for example, C. E. Pearson, Numerical Method in Engineering and Science (Van Nostrand Reinhold, New York, 1986).

Prokhorov, A. M.

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Cooperative phenomena in yttrium erbium aluminum garnet crystals,” Sov. J. Quantum Electron. 14, 128 (1984).
[CrossRef]

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Efficient cross-relaxation laser emission at λ = 2.94 μ m,” Sov. J. Quantum Electron. 13, 1235 (1983).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
[CrossRef]

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

Savel’ev, A. D.

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Shcherbakov, I. A.

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

Shevel, A. F.

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

Shi, W. Q.

M. Bass, W. Q. Shi, R. Kurtz, M. Kokta, H. Diegl, “Operation of the high dopant density Er:YAG at 2.94 μ m,” in Tunable Solid State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds., Vol. 52 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986), pp. 300–305.
[CrossRef]

Smirnov, V. V.

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Starikov, B. P.

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Studenikin, M. I.

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

Timoshechkin, M. I.

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Ursu, I.

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

Zharikov, E. V.

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Zhekov, V. I.

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Cooperative phenomena in yttrium erbium aluminum garnet crystals,” Sov. J. Quantum Electron. 14, 128 (1984).
[CrossRef]

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Efficient cross-relaxation laser emission at λ = 2.94 μ m,” Sov. J. Quantum Electron. 13, 1235 (1983).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
[CrossRef]

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

Zubov, B. V.

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

Izv. Akad. Nauk SSSR Ser. Fiz. (1)

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Labachev, A. A. Manenkov, T. M. Murina, A. M. Prokhorov, “Cross relaxation of a laser based on yttrium-aluminum garnet with Er3+,” Izv. Akad. Nauk SSSR Ser. Fiz. 48, 1765 (1984).

Sov. J. Quantum Electron. (7)

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Efficient cross-relaxation laser emission at λ = 2.94 μ m,” Sov. J. Quantum Electron. 13, 1235 (1983).
[CrossRef]

V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Cooperative phenomena in yttrium erbium aluminum garnet crystals,” Sov. J. Quantum Electron. 14, 128 (1984).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, L. A. Kulevskii, T. M. Murina, V. V. Osiko, A. M. Prokhorov, A. D. Savel’ev, V. V. Smirnov, B. P. Starikov, M. I. Timoshechkin, “Stimulated emission from Er3+ions in yttrium aluminum garnet crystals at γ = 2.94 μ,” Sov. J. Quantum Electron. 4, 1039 (1975).
[CrossRef]

Kh. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “Steady-state emission from a Y3Al5O12:Er laser (λ = 2.94 μ, T= 300 °K),” Sov. J. Quantum Electron. 13, 262 (1983).
[CrossRef]

V. I. Zhekov, T. M. Murina, A. M. Prokhorov, M. I. Studenikin, S. Georgescu, V. Lupei, I. Ursu, “Cooperative process in Y3Al5O12:Er +crystals,” Sov. J. Quantum Electron. 16, 274 (1986).
[CrossRef]

V. I. Zhekov, B. V. Zubov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, A. F. Shevel, “Mechanism of a population inversion between the 4I11/2and 4I13/2levels of the Er3+ions in Y3AI5O12crystals,” Sov. J. Quantum Electron. 10, 428 (1980).
[CrossRef]

E. V. Zharikov, V. I. Zhekov, T. M. Murina, V. V. Osiko, M. I. Timoshechkin, I. A. Shcherbakov, “Cross section of the 4I11/2–4I13/2laser transition in Er3+ions in yttrium-erbium-aluminum garnet crystals,” Sov. J. Quantum Electron. 7, 117 (1977).
[CrossRef]

Other (7)

See, for example, C. E. Pearson, Numerical Method in Engineering and Science (Van Nostrand Reinhold, New York, 1986).

H. Chou, “Upconversion processes and Cr-sensitization of Er- and Er, Ho-activated solid state materials,” Tech. Rep. 26 (Massachusetts Institute of Technology, Cambridge, Mass., February1989).

1/α for 50 at. % Er:YAG is estimated to be less than 10 μ m by using the absorption spectrum of Er:YAG.

1/α′for 50 at. % Er:YAG is estimated to be less than 50 μ m by using the absorption spectrum of Er:YAG.

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

M. Bass, W. Q. Shi, R. Kurtz, M. Kokta, H. Diegl, “Operation of the high dopant density Er:YAG at 2.94 μ m,” in Tunable Solid State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds., Vol. 52 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986), pp. 300–305.
[CrossRef]

S. Georgescu, V. Lupei, I. Ursu, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov, “The role of the cross-relaxation mechanisms in the quasistationary generation regime of the YAG:Er laser,” presented at the Second International Conference on Trends in Quantum Electronics, Bucharest, Romania, September 1985.

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 (6)

Fig. 1
Fig. 1

Energy-level diagram for Er:YAG showing various radiative (straight arrows) and nonradiative (wavy arrows) transitions and cross-relaxation processes.

Fig. 2
Fig. 2

Log of fluorescence strength versus time for the experimental (○) and calculated (solid curve) decay functions of the Er3+ 4I11/2 level of (a) 16.7 at. % Er:YAG, (b) 33.3 at. % Er:YAG, (c) 50 at. % Er:YAG. All data are normalized to unity at t = 0. The calculated decay functions were obtained by using a rate-equation analysis.

Fig. 3
Fig. 3

Log of fluorescence strength versus time for the experimental (○. Δ, ∇) and calculated (solid curve) decay functions of the Er3+ 4I13/2 level in 16.7, 33.3, and 50 at. % Er:YAG. The straight line for 16.7 at. % Er:YAG was obtained with weak pumping, whereas all curves were obtained with strong pumping. All data are normalized to unity at t = 0. The calculated decay functions were obtained by using a rate-equation analysis.

Fig. 4
Fig. 4

Oscillogram of the decay of the Er3+ 4I13/2 state (50 at. % Er:YAG) under weak (upper) and strong (lower) excitation. The time scale is 2 msec/division, and the vertical scale is arbitrary for both curves.

Fig. 5
Fig. 5

Decay of the Er+ 4I11/2 level in the presence of cross-relaxation processes.

Fig. 6
Fig. 6

(a) Time evolution of the initial Er3+ 4I13/2 population 16.7 at. % Er:YAG. (b) Effective lifetime of the Er3+ 4I11/2 state in 16.7 at. %Er:YAG.

Tables (3)

Tables Icon

Table 1 Fluorescence Decay Lifetimes of Er:Y3Al6O12

Tables Icon

Table 2 Parameters Used in Rate-Equation Calculations

Tables Icon

Table 3 Cross-Relaxation Coefficients of Er:Y3Al5O12

Equations (7)

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

d n 0 d t = W 04 n 0 + n 1 τ 1 ( n 0 W ) n 4 + ( C W 1 ) n 1 2 + ( C W 2 ) n 2 2 ,
d n 1 d t = n 2 τ 2 n 1 τ 1 + ( n 0 W ) n 4 ( 2 C W 1 ) n 1 2 ,
d n 2 d t = n 3 τ 3 n 2 τ 2 + ( n 0 W ) n 4 + ( C W 1 ) n 1 2 ( 2 C W 2 ) n 2 2 ,
d n 3 d t = W 43 mp n 4 n 3 τ 3 ,
d n 4 d t = W 04 n 0 n 4 τ 4 + ( C W 2 ) n 2 2 ,
d n 2 d t = n 2 τ 2 + ( C W 1 ) n 1 2 ( 2 C W 2 ) n 2 2 = n 2 τ 2 [ 1 ( C W 1 ) n 1 2 n 2 / τ 2 + ( 2 C W 2 ) n 2 2 n 2 / τ 2 ] = n 2 τ 2 [ 1 d 1 ( t ) + d 2 ( t ) ] = n 2 τ 2 [ 1 + D ( t ) ] = n 2 τ 2 / [ 1 + D ( t ) ] ,
τ 2 eff = τ 2 1 + D ( t ) ,

Metrics