Abstract

Two methods of producing the long pulse lengths that promote efficient extraction of energy from low-gain, quasi-four-level lasers are analyzed. A long pulse length output can mitigate laser-induced damage effects and can be generated in quasi-four-level lasers by two disparate methods. One method utilizes Q-switching techniques in resonators designed to extend the pulse length and another utilizes the first pulse in a relaxation oscillation pulse train. Models for quasi-four-level lasers are derived here taking into account the nonnegligible thermal population of the lower laser level. Closed-form expressions are derived for both modes of operation of quasi-four-level laser systems so the parametric dependencies of both forms of operation become obvious, allowing facile comparison. In addition, a combined absorption and quantum efficiency, germane for flash-lamp pumping, is calculated for both Cr and Er sensitizers. Although the former has the advantage of broad absorption bands, the latter has the advantage of a quantum efficiency approaching 3.

© 1997 Optical Society of America

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  1. R. Dunsmuir, “Theory of relaxation oscillations in optical masers,” J. Electron. Control 10, 453–458 (1963).
  2. R. B. Chesler, M. A. Karr, J. E. Geusic, “An experimental and theoretical study of high repetition rate Q-switched Nd:YAG lasers,” Proc. IEEE 58, 1899–1914 (1970).
    [CrossRef]
  3. W. Koechener, Solid State Laser Engineering (Springer-Verlag, New York, 1976), pp. 245–281.
    [CrossRef]
  4. P. L. Cross, N. P. Barnes, M. W. Skolaut, M. E. Storm, “Blackbody absorption efficiencies for six lamp pumped Nd laser materials,” Appl. Opt. 29, 791–797 (1990).
    [CrossRef] [PubMed]
  5. W. G. Wagner, B. A. Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
    [CrossRef]
  6. A. C. Selden, “Theoretical assessment of a high power continuous wave 4-level solid laser,” Br. J. Appl. Phys. 17, 729–736 (1966).
    [CrossRef]
  7. N. G. Badov, N. N. Morosov, V. N. Oralvsky, “Theory of pulsating condition for lasers,” IEEE J. Quantum Electron. QE-2, 542–548 (1966).
  8. D. G. Carlson, “Dynamics of a repetitively pulse pumped Nd:YAG laser,” J. Appl. Phys. 39, 4369–4374 (1968).
    [CrossRef]
  9. H. Statz, G. de Mars, “Transients and oscillation pulses in Masers,” in Quantum Electronics, C. H. Townes, ed. (Columbia U. Press, New York, 1960), pp. 530–537.
  10. C. L. Tang, H. Statz, G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
    [CrossRef]
  11. T. Y. Fan, E. Huber, R. L. Byer, P. Mitzschertich, “Spectroscopy and diode laser pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. QE-24, 924–933 (1988).
    [CrossRef]
  12. A. E. Seigman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 954–1021.
  13. M. G. Jani, N. P. Barnes, K. E. Murray, “Flash-lamp-pumped Ho:Tm:Cr:YAG and Ho:Tm:Er:YLF lasers: experimental results of a single, long pulse length comparison,” Appl. Opt. 36, 3357–3362 (1997).
    [CrossRef] [PubMed]
  14. N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–569 (1990).
    [CrossRef]
  15. V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
    [CrossRef]
  16. N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho:Tm laser I: modeling,” IEEE J. Quantum Electron. 32, 92–104 (1996).
    [CrossRef]
  17. G. J. Kintz, R. Allen, L. Esterowitz, “Two for one photon conversion observed in alexandrite pumped Tm3+, Ho3+, YAG at room temperature,” in Conference on Lasers and Electro-Optics, Vol. 14 of OSA 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987).
  18. A. Brenier, R. Moncorge, C. Pedrini, “Er3+ → Tm3+ energy transfer in YLiF4 (YLF),” IEEE J. Quantum Electron. 26, 967–971 (1990).
    [CrossRef]
  19. G. Armagan, A. M. Buoncristiani, A. T. Inge, B. DiBartolo, “Comparison of spectroscopic properties of Tm and Ho in YAG crystals,” in Advanced Solid State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).
  20. T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
    [CrossRef]
  21. I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
    [CrossRef]
  22. E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).
  23. N. P. Barnes, R. E. Allen, L. Esterowitz, M. G. Knights, “Performance of Er:YLF at 1.73 µm,” IEEE J. Quantum Electron. QE-22, 337–343 (1986).
    [CrossRef]
  24. M. A. Rogenov, V. A. Smirnov, I. A. Scherbakov, “Nonlinear population processes of Er3+ laser levels in chromium-doped garnet crystals,” Opt. Quantum Electron. 22, 561–574 (1990).
    [CrossRef]
  25. W. Q. Shi, M. Bass, M. Birnbaum, “Effects of energy transfer among Er3+ ions on the fluorescence decay and lasing properties of heavily doped Er:Y3Al5O12,” J. Opt. Soc. Am. B 7, 1456–1462 (1990).
    [CrossRef]
  26. D. C. Cronemeyer, “Optical absorption characteristics of ruby,” J. Opt. Soc. Am. 56, 1703–1706 (1966).
    [CrossRef]
  27. G. Bruno, M. I. Nathan, “Quantum efficiency of ruby,” J. Appl. Phys. 34, 703–705 (1963).
    [CrossRef]

1997 (1)

1996 (1)

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho:Tm laser I: modeling,” IEEE J. Quantum Electron. 32, 92–104 (1996).
[CrossRef]

1990 (5)

A. Brenier, R. Moncorge, C. Pedrini, “Er3+ → Tm3+ energy transfer in YLiF4 (YLF),” IEEE J. Quantum Electron. 26, 967–971 (1990).
[CrossRef]

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–569 (1990).
[CrossRef]

M. A. Rogenov, V. A. Smirnov, I. A. Scherbakov, “Nonlinear population processes of Er3+ laser levels in chromium-doped garnet crystals,” Opt. Quantum Electron. 22, 561–574 (1990).
[CrossRef]

W. Q. Shi, M. Bass, M. Birnbaum, “Effects of energy transfer among Er3+ ions on the fluorescence decay and lasing properties of heavily doped Er:Y3Al5O12,” J. Opt. Soc. Am. B 7, 1456–1462 (1990).
[CrossRef]

P. L. Cross, N. P. Barnes, M. W. Skolaut, M. E. Storm, “Blackbody absorption efficiencies for six lamp pumped Nd laser materials,” Appl. Opt. 29, 791–797 (1990).
[CrossRef] [PubMed]

1989 (2)

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

1988 (2)

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

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

1986 (1)

N. P. Barnes, R. E. Allen, L. Esterowitz, M. G. Knights, “Performance of Er:YLF at 1.73 µm,” IEEE J. Quantum Electron. QE-22, 337–343 (1986).
[CrossRef]

1970 (1)

R. B. Chesler, M. A. Karr, J. E. Geusic, “An experimental and theoretical study of high repetition rate Q-switched Nd:YAG lasers,” Proc. IEEE 58, 1899–1914 (1970).
[CrossRef]

1968 (1)

D. G. Carlson, “Dynamics of a repetitively pulse pumped Nd:YAG laser,” J. Appl. Phys. 39, 4369–4374 (1968).
[CrossRef]

1966 (3)

A. C. Selden, “Theoretical assessment of a high power continuous wave 4-level solid laser,” Br. J. Appl. Phys. 17, 729–736 (1966).
[CrossRef]

N. G. Badov, N. N. Morosov, V. N. Oralvsky, “Theory of pulsating condition for lasers,” IEEE J. Quantum Electron. QE-2, 542–548 (1966).

D. C. Cronemeyer, “Optical absorption characteristics of ruby,” J. Opt. Soc. Am. 56, 1703–1706 (1966).
[CrossRef]

1963 (4)

G. Bruno, M. I. Nathan, “Quantum efficiency of ruby,” J. Appl. Phys. 34, 703–705 (1963).
[CrossRef]

C. L. Tang, H. Statz, G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

R. Dunsmuir, “Theory of relaxation oscillations in optical masers,” J. Electron. Control 10, 453–458 (1963).

W. G. Wagner, B. A. Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[CrossRef]

Allen, R.

G. J. Kintz, R. Allen, L. Esterowitz, “Two for one photon conversion observed in alexandrite pumped Tm3+, Ho3+, YAG at room temperature,” in Conference on Lasers and Electro-Optics, Vol. 14 of OSA 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987).

Allen, R. E.

N. P. Barnes, R. E. Allen, L. Esterowitz, M. G. Knights, “Performance of Er:YLF at 1.73 µm,” IEEE J. Quantum Electron. QE-22, 337–343 (1986).
[CrossRef]

Armagan, G.

G. Armagan, A. M. Buoncristiani, A. T. Inge, B. DiBartolo, “Comparison of spectroscopic properties of Tm and Ho in YAG crystals,” in Advanced Solid State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Badov, N. G.

N. G. Badov, N. N. Morosov, V. N. Oralvsky, “Theory of pulsating condition for lasers,” IEEE J. Quantum Electron. QE-2, 542–548 (1966).

Barnes, N. P.

M. G. Jani, N. P. Barnes, K. E. Murray, “Flash-lamp-pumped Ho:Tm:Cr:YAG and Ho:Tm:Er:YLF lasers: experimental results of a single, long pulse length comparison,” Appl. Opt. 36, 3357–3362 (1997).
[CrossRef] [PubMed]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho:Tm laser I: modeling,” IEEE J. Quantum Electron. 32, 92–104 (1996).
[CrossRef]

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–569 (1990).
[CrossRef]

P. L. Cross, N. P. Barnes, M. W. Skolaut, M. E. Storm, “Blackbody absorption efficiencies for six lamp pumped Nd laser materials,” Appl. Opt. 29, 791–797 (1990).
[CrossRef] [PubMed]

N. P. Barnes, R. E. Allen, L. Esterowitz, M. G. Knights, “Performance of Er:YLF at 1.73 µm,” IEEE J. Quantum Electron. QE-22, 337–343 (1986).
[CrossRef]

Basiev, T. T.

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Bass, M.

Birnbaum, M.

Brenier, A.

A. Brenier, R. Moncorge, C. Pedrini, “Er3+ → Tm3+ energy transfer in YLiF4 (YLF),” IEEE J. Quantum Electron. 26, 967–971 (1990).
[CrossRef]

Bruno, G.

G. Bruno, M. I. Nathan, “Quantum efficiency of ruby,” J. Appl. Phys. 34, 703–705 (1963).
[CrossRef]

Budnik, V. N.

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

Buoncristiani, A. M.

G. Armagan, A. M. Buoncristiani, A. T. Inge, B. DiBartolo, “Comparison of spectroscopic properties of Tm and Ho in YAG crystals,” in Advanced Solid State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Byer, R. L.

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

Carlson, D. G.

D. G. Carlson, “Dynamics of a repetitively pulse pumped Nd:YAG laser,” J. Appl. Phys. 39, 4369–4374 (1968).
[CrossRef]

Chesler, R. B.

R. B. Chesler, M. A. Karr, J. E. Geusic, “An experimental and theoretical study of high repetition rate Q-switched Nd:YAG lasers,” Proc. IEEE 58, 1899–1914 (1970).
[CrossRef]

Chicklis, E. P.

E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).

Cronemeyer, D. C.

Cross, P. L.

P. L. Cross, N. P. Barnes, M. W. Skolaut, M. E. Storm, “Blackbody absorption efficiencies for six lamp pumped Nd laser materials,” Appl. Opt. 29, 791–797 (1990).
[CrossRef] [PubMed]

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–569 (1990).
[CrossRef]

de Mars, G.

C. L. Tang, H. Statz, G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

H. Statz, G. de Mars, “Transients and oscillation pulses in Masers,” in Quantum Electronics, C. H. Townes, ed. (Columbia U. Press, New York, 1960), pp. 530–537.

DiBartolo, B.

G. Armagan, A. M. Buoncristiani, A. T. Inge, B. DiBartolo, “Comparison of spectroscopic properties of Tm and Ho in YAG crystals,” in Advanced Solid State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Dunsmuir, R.

R. Dunsmuir, “Theory of relaxation oscillations in optical masers,” J. Electron. Control 10, 453–458 (1963).

Esterowitz, L.

N. P. Barnes, R. E. Allen, L. Esterowitz, M. G. Knights, “Performance of Er:YLF at 1.73 µm,” IEEE J. Quantum Electron. QE-22, 337–343 (1986).
[CrossRef]

G. J. Kintz, R. Allen, L. Esterowitz, “Two for one photon conversion observed in alexandrite pumped Tm3+, Ho3+, YAG at room temperature,” in Conference on Lasers and Electro-Optics, Vol. 14 of OSA 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987).

Fan, T. Y.

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

Filer, E. D.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho:Tm laser I: modeling,” IEEE J. Quantum Electron. 32, 92–104 (1996).
[CrossRef]

Folweiler, R. C.

E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).

Gabbe, D. R.

E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).

Georgescu, S.

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Geusic, J. E.

R. B. Chesler, M. A. Karr, J. E. Geusic, “An experimental and theoretical study of high repetition rate Q-switched Nd:YAG lasers,” Proc. IEEE 58, 1899–1914 (1970).
[CrossRef]

Gondra, A. D.

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

Huber, E.

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

Inge, A. T.

G. Armagan, A. M. Buoncristiani, A. T. Inge, B. DiBartolo, “Comparison of spectroscopic properties of Tm and Ho in YAG crystals,” in Advanced Solid State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Jani, M. G.

Jenssen, H. P.

E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).

Karr, M. A.

R. B. Chesler, M. A. Karr, J. E. Geusic, “An experimental and theoretical study of high repetition rate Q-switched Nd:YAG lasers,” Proc. IEEE 58, 1899–1914 (1970).
[CrossRef]

Kintz, G. J.

G. J. Kintz, R. Allen, L. Esterowitz, “Two for one photon conversion observed in alexandrite pumped Tm3+, Ho3+, YAG at room temperature,” in Conference on Lasers and Electro-Optics, Vol. 14 of OSA 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987).

Knights, M. G.

N. P. Barnes, R. E. Allen, L. Esterowitz, M. G. Knights, “Performance of Er:YLF at 1.73 µm,” IEEE J. Quantum Electron. QE-22, 337–343 (1986).
[CrossRef]

Koechener, W.

W. Koechener, Solid State Laser Engineering (Springer-Verlag, New York, 1976), pp. 245–281.
[CrossRef]

Lee, C. J.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho:Tm laser I: modeling,” IEEE J. Quantum Electron. 32, 92–104 (1996).
[CrossRef]

Lengyel, B. A.

W. G. Wagner, B. A. Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[CrossRef]

Linz, A.

E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).

Lobackev, V. A.

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

Lupei, A.

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

Lupei, V.

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Mitzschertich, P.

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

Moncorge, R.

A. Brenier, R. Moncorge, C. Pedrini, “Er3+ → Tm3+ energy transfer in YLiF4 (YLF),” IEEE J. Quantum Electron. 26, 967–971 (1990).
[CrossRef]

Morosov, N. N.

N. G. Badov, N. N. Morosov, V. N. Oralvsky, “Theory of pulsating condition for lasers,” IEEE J. Quantum Electron. QE-2, 542–548 (1966).

Morrison, C. A.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho:Tm laser I: modeling,” IEEE J. Quantum Electron. 32, 92–104 (1996).
[CrossRef]

Murina, T. M.

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Murray, K. E.

Naiman, C. S.

E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).

Nathan, M. I.

G. Bruno, M. I. Nathan, “Quantum efficiency of ruby,” J. Appl. Phys. 34, 703–705 (1963).
[CrossRef]

Oralvsky, V. N.

N. G. Badov, N. N. Morosov, V. N. Oralvsky, “Theory of pulsating condition for lasers,” IEEE J. Quantum Electron. QE-2, 542–548 (1966).

Pedrini, C.

A. Brenier, R. Moncorge, C. Pedrini, “Er3+ → Tm3+ energy transfer in YLiF4 (YLF),” IEEE J. Quantum Electron. 26, 967–971 (1990).
[CrossRef]

Prokhorov, A. M.

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Rogenov, M. A.

M. A. Rogenov, V. A. Smirnov, I. A. Scherbakov, “Nonlinear population processes of Er3+ laser levels in chromium-doped garnet crystals,” Opt. Quantum Electron. 22, 561–574 (1990).
[CrossRef]

Scherbakoo, A. A.

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

Scherbakov, I. A.

M. A. Rogenov, V. A. Smirnov, I. A. Scherbakov, “Nonlinear population processes of Er3+ laser levels in chromium-doped garnet crystals,” Opt. Quantum Electron. 22, 561–574 (1990).
[CrossRef]

Seigman, A. E.

A. E. Seigman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 954–1021.

Selden, A. C.

A. C. Selden, “Theoretical assessment of a high power continuous wave 4-level solid laser,” Br. J. Appl. Phys. 17, 729–736 (1966).
[CrossRef]

Shi, W. Q.

Skolaut, M. W.

P. L. Cross, N. P. Barnes, M. W. Skolaut, M. E. Storm, “Blackbody absorption efficiencies for six lamp pumped Nd laser materials,” Appl. Opt. 29, 791–797 (1990).
[CrossRef] [PubMed]

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–569 (1990).
[CrossRef]

Sludenikin, M. I.

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Smirnov, V. A.

M. A. Rogenov, V. A. Smirnov, I. A. Scherbakov, “Nonlinear population processes of Er3+ laser levels in chromium-doped garnet crystals,” Opt. Quantum Electron. 22, 561–574 (1990).
[CrossRef]

Statz, H.

C. L. Tang, H. Statz, G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

H. Statz, G. de Mars, “Transients and oscillation pulses in Masers,” in Quantum Electronics, C. H. Townes, ed. (Columbia U. Press, New York, 1960), pp. 530–537.

Storm, M. E.

P. L. Cross, N. P. Barnes, M. W. Skolaut, M. E. Storm, “Blackbody absorption efficiencies for six lamp pumped Nd laser materials,” Appl. Opt. 29, 791–797 (1990).
[CrossRef] [PubMed]

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–569 (1990).
[CrossRef]

Studenkin, M. I.

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

Tang, C. L.

C. L. Tang, H. Statz, G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

Terent’ev, Yu. I.

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

Ursu, I.

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

Wagner, W. G.

W. G. Wagner, B. A. Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[CrossRef]

Zhekov, V. I.

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Appl. Opt. (2)

Br. J. Appl. Phys. (1)

A. C. Selden, “Theoretical assessment of a high power continuous wave 4-level solid laser,” Br. J. Appl. Phys. 17, 729–736 (1966).
[CrossRef]

IEEE J. Quantum Electron. (6)

N. G. Badov, N. N. Morosov, V. N. Oralvsky, “Theory of pulsating condition for lasers,” IEEE J. Quantum Electron. QE-2, 542–548 (1966).

N. P. Barnes, M. E. Storm, P. L. Cross, M. W. Skolaut, “Efficiency of Nd laser materials with laser diode pumping,” IEEE J. Quantum Electron. 26, 558–569 (1990).
[CrossRef]

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

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho:Tm laser I: modeling,” IEEE J. Quantum Electron. 32, 92–104 (1996).
[CrossRef]

A. Brenier, R. Moncorge, C. Pedrini, “Er3+ → Tm3+ energy transfer in YLiF4 (YLF),” IEEE J. Quantum Electron. 26, 967–971 (1990).
[CrossRef]

N. P. Barnes, R. E. Allen, L. Esterowitz, M. G. Knights, “Performance of Er:YLF at 1.73 µm,” IEEE J. Quantum Electron. QE-22, 337–343 (1986).
[CrossRef]

J. Appl. Phys. (4)

C. L. Tang, H. Statz, G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

G. Bruno, M. I. Nathan, “Quantum efficiency of ruby,” J. Appl. Phys. 34, 703–705 (1963).
[CrossRef]

D. G. Carlson, “Dynamics of a repetitively pulse pumped Nd:YAG laser,” J. Appl. Phys. 39, 4369–4374 (1968).
[CrossRef]

W. G. Wagner, B. A. Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[CrossRef]

J. Electron. Control (1)

R. Dunsmuir, “Theory of relaxation oscillations in optical masers,” J. Electron. Control 10, 453–458 (1963).

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

I. Ursu, A. Lupei, S. Georgescu, V. Lupei, A. M. Prokhorov, V. I. Zhekov, T. M. Murina, M. I. Studenkin, “Energy transfer characteristics of the 4S3/2 level of Er3+ in YAG,” Opt. Commun. 72, 209–211 (1989).
[CrossRef]

Opt. Quantum Electron. (1)

M. A. Rogenov, V. A. Smirnov, I. A. Scherbakov, “Nonlinear population processes of Er3+ laser levels in chromium-doped garnet crystals,” Opt. Quantum Electron. 22, 561–574 (1990).
[CrossRef]

Proc. IEEE (1)

R. B. Chesler, M. A. Karr, J. E. Geusic, “An experimental and theoretical study of high repetition rate Q-switched Nd:YAG lasers,” Proc. IEEE 58, 1899–1914 (1970).
[CrossRef]

Sov. J. Quantum Electron. (2)

V. N. Budnik, A. D. Gondra, V. I. Zhekov, V. A. Lobackev, T. M. Murina, Yu. I. Terent’ev, A. A. Scherbakoo, “Mathematical modeling of energy processes in YAG:Er3+ lasers,” Sov. J. Quantum Electron. 19, 1076–1083 (1989).
[CrossRef]

T. T. Basiev, S. Georgescu, V. I. Zhekov, V. Lupei, T. M. Murina, A. M. Prokhorov, M. I. Sludenikin, “Characteristics of concentration quenching of luminescence from the 4S3/2 level of the Er3+ ion in a (Y1-xErx)3 Al2O5 crystal,” Sov. J. Quantum Electron. 18, 1123–1125 (1988).
[CrossRef]

Other (6)

E. P. Chicklis, R. C. Folweiler, C. S. Naiman, D. R. Gabbe, A. Linz, H. P. Jenssen, “Development of multiple sensitized Ho:YLF as a laser material,” (U.S. Army Electronics Command, Fort Monmouth, N.J. 07703, 1974).

A. E. Seigman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 954–1021.

G. Armagan, A. M. Buoncristiani, A. T. Inge, B. DiBartolo, “Comparison of spectroscopic properties of Tm and Ho in YAG crystals,” in Advanced Solid State Lasers, Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

G. J. Kintz, R. Allen, L. Esterowitz, “Two for one photon conversion observed in alexandrite pumped Tm3+, Ho3+, YAG at room temperature,” in Conference on Lasers and Electro-Optics, Vol. 14 of OSA 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987).

W. Koechener, Solid State Laser Engineering (Springer-Verlag, New York, 1976), pp. 245–281.
[CrossRef]

H. Statz, G. de Mars, “Transients and oscillation pulses in Masers,” in Quantum Electronics, C. H. Townes, ed. (Columbia U. Press, New York, 1960), pp. 530–537.

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Figures (5)

Fig. 1
Fig. 1

Energy level diagrams of Cr, Ho, Er, and Tm.

Fig. 2
Fig. 2

Pump efficiency of Cr:YAG versus rod radius and Cr concentration product.

Fig. 3
Fig. 3

Pump efficiency of Er:YLF a axis versus rod radius and Er concentration product.

Fig. 4
Fig. 4

Pump efficiency of Er:YLF c axis versus rod radius and Er concentration product.

Fig. 5
Fig. 5

Solution of transcendental equation relating ratio of energy extracted to energy over threshold versus ratio of initial gain to losses.

Tables (1)

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Table 1 Quantum Efficiency Assignment of the Manifolds

Equations (30)

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ηA=λ1λ20π/20π/2λp/λPλpFθ, φ1-exp-Csβ1λplpθ, ϕsin θdθdφdλpλ1λ20π/20π/2PλpFθ, φsin θdθdφdλp,
ηAQ=λ1λ20π/20π/2λp/λPλpηQλpFθ, φ1-exp-Csβ1λplpθ, ϕsin θdθdφdλpλ1λ20π/20π/2PλpFθ, φsin θdθdφdλp.
Zi=gi expEi/kTigi expEi/kT,
N1+N2CANS,
N2τ=-N2τ2+R2-σZ2N2-Z1N1cnNP,  N1t=+N2τ2-R2+σZ2N2-Z1N1cnNP,  NPt+cnNPz=σZ2N2-Z1N1cnNP.
N2t=-N2τ2+R2-2σelcnc2lc×1+Z1Z2N2-Z1Z2CHNSNP,  NPt=2σelc2lc1+Z1Z2N2-Z1Z2CHNS×NP+c2lcNP lnRmRL.
N2T=CHNSZ1Z21+Z1Z2=CHNSγ-1/γ,
NP-NPO=-nllcN2-N20-n lnRmRL2σelcγ×lnN2-N2T/N20-N2T,
N20-N2FN20-N2T=lnRmRL2σelγN20-N2T ln1-N20-N2FN20-N2T.
ELO=πw2lhcλlnRmlnRmRLN20-N2F=w2ar2lnRmlnRmRLESO-ESTN20-N2FN20-N2T,
ESO=πar2lhcN20/λ,  EST=πar2lhcN2T/λ.
PLO=-c2n lnRmhcλπw2NP.
NPmax=-nllcN20-N2T+lnRmRL2σelγ-n lnRmRL2σelγ ln-lnRmRL2σelγN20-N2T.
PLO max=-c2lc lnRmw2a2ESO-EST×1+lnRmRL2σelγN20-N2T×1-ln-lnRmRL2σelγN20-N2T.
τPELO/PLO max=-2lcc lnRmRLN20-N2FN20-N2T×1+lnRmRL2σelγN20-N2T×1-ln-lnRmRL2σelγN20-N2T-1.
τph=-2lc/c lnRmRL.
N2TH=R2THτ2=γ-1CHNS/γ-lnRmRL/2σelγ.
NPO=-2nlc lnRmRLR2-R2TH,
PLO=-πw2lhcλlnRmlnRmRLR2-R2TH,
N2=N20+ΔN2,  NP=NPO+ΔNP.
ΔN2t=-ΔN2τ2-σecγnNPOΔN2-γN20-γ-1CHNSσecnΔNP,  ΔNPt=σeclγlcNPOΔN2.
2ΔN2t2=-1τ2ΔN2t-σecγnNPOΔN2t-γN20-γ-1CHNSσecγnσecllcNPOΔN2.
ΔN2=ΔN20 expst
α=-12γR2-R2TH-lnRmRL/2σelτ2/lnRmRL/2σel=12τ21-lnRmRL2σelγR2-R2THτ2×-lnRmRL2σelγR2-R2THτ2,
ω2=σeclγ/lcR2-R2TH=1τ2c2lc lnRmRL2σelγR2-R2THτ2lnRmRL.
N2t=-N2τ2+R2.
N2N2TH+R2-R2THt,
NP=NPO expγR2-R2THσelc/2lct2.
τe33/γR2-R2THσelc/2lc1/2.
ELO33R2-R2THγσelc/2lc1/2πw2lhcλlnRmlnRmRL.

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