Abstract

Many solid-state lasers of current interest exhibit reabsorption loss. Previous modeling calculations of laser performance with longitudinal pumping either have neglected reabsorption loss or have been valid only for certain special cases of the ratio of the pump- and laser-beam waists. Rigorous numerical modeling calculations have been carried out to provide a comprehensive understanding of the behavior of longitudinally pumped solid-state lasers, including reabsorption loss and for arbitrary sizes of the pump- and laser-beam waists. In addition, certain aspects of laser behavior that have traditionally not been discussed in papers on laser modeling, such as clamping, saturation, and spatial distribution of the population-inversion density, are investigated to provide a general understanding of laser performance. The results are applied to a particular solid-state laser of current practical interest, the 946-nm Nd:YAG laser.

© 1988 Optical Society of America

Full Article  |  PDF Article

Corrections

W. P. Risk, "Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses: errata," J. Opt. Soc. Am. B 14, 3457-3457 (1997)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-14-12-3457

References

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  1. L. F. Johnson, R. A. Thomas, “Maser oscillations at 0.9 and 1.35 microns in CaWO4:Nd3+,” Phys. Rev. 131, 2038 (1963).
    [CrossRef]
  2. R. W. Wallace, S. E. Harris, “Oscillation and doubling of the 0.946 μm line in Nd3+:YAG,” Appl. Phys. Lett. 15, 111 (1969).
    [CrossRef]
  3. M. Birnbaum, A. W. Tucker, C. L. Fincher, “Cw room-temperature laser operation of Nd:CAMGAR at 0.941 and 1.059 μm,” J. Appl. Phys. 49, 2984 (1978).
    [CrossRef]
  4. T. Y. Fan, R. L. Byer, “Continuous-wave operation at a room-temperature, diode-laser-pumped, 946-nm Nd:YAG laser,” Opt. Lett. 12, 809 (1987).
    [CrossRef] [PubMed]
  5. W. P. Risk, W. Lenth, “Room temperature, cw 946-nm Nd:YAG laser pumped by laser-diode arrays and intracavity frequency doubling to 473 nm,” Opt. Lett. 12, 993 (1987).
    [CrossRef] [PubMed]
  6. E. W. Duczynski, G. Huber, P. Mitzscherlich, “Laser action of Cr, Nd, Tm, Ho-doped garnets,” in Tunable Solid-State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds. (Springer-Verlag, Berlin, 1986), p. 282.
    [CrossRef]
  7. R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
    [CrossRef]
  8. T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Continuous-wave operation at 2.1 μm of a diode-laser-pumped, Tmsensitized Ho:Y3Al5O12 laser at 300 K,” Opt. Lett. 12, 678 (1987).
    [CrossRef] [PubMed]
  9. G. Kintz, L. Esterowitz, R. Allen, “Cascade laser emission at 2.3.1 and 2.08 μm from laser diode pumped Tm, Ho:LiYF4 at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 20.
  10. E. W. Duczynski, G. Huber, K. Petermann, H. Strange, “Continuous wave 1600 nm laser-action in Er-doped garnets at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 197.
  11. A. J. Silversmith, W. Lenth, R. M. Macfarlane, “Green infrared-pumped erbium upconversion laser,” Appl. Phys. Lett. 51, 1977 (1987).
    [CrossRef]
  12. D. L. Sipes, “Highly efficient neodymium:yttrium aluminum garnet laser end pumped by a semiconductor laser array,” Appl. Phys. Lett. 47, 74 (1985).
    [CrossRef]
  13. B. Zhou, T. J. Kane, G. J. Dixon, R. L. Byer, “Efficient, frequency stable laser diode pumped Nd:YAG laser,” Opt. Lett. 10, 62 (1985).
    [CrossRef] [PubMed]
  14. H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).
  15. R. B. Allen, S. J. Scalise, “Continuous operation of a YAlG:Nd laser by injection luminescent pumping,” Appl. Phys. Lett. 14, 188 (1969).
    [CrossRef]
  16. W. J. Kozlovsky, T. Y. Fan, R. L. Byer, “Diode-pumped continuous wave Nd:glass laser,” Opt. Lett. 11, 788 (1986).
    [CrossRef] [PubMed]
  17. T. Y. Fan, G. J. Dixon, R. L. Byer, “Efficient GaAlAs diode-laser-pumped operation of Nd:YLF at 1.047 μm with intracavity doubling to 523.6 nm,” Opt. Lett. 11, 204 (1986).
    [CrossRef]
  18. D. G. Hall, R. J. Smith, R. R. Rice, “Pump-size effects in Nd:YAG lasers,” Appl. Opt. 19, 3041 (1980).
    [CrossRef] [PubMed]
  19. L. W. Casperson, “Laser power calculations: sources of error,” Appl. Opt. 19, 422 (1980).
    [CrossRef] [PubMed]
  20. P. F. Moulton, “An investigation of the Co:MgF2laser system,” IEEE J. Quantum Electron. QE-21, 1582 (1985).
    [CrossRef]
  21. T. Y. Fan, R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. QE-23, 605 (1987).
  22. K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653 (1979).
    [CrossRef]
  23. H. G. Danielmeyer, “Progress in Nd:YAG lasers,” in Lasers: A Series of Advances, A. K. Levine, A. J. DeMaria, eds. (Dekker, New York, 1976).
  24. M. J. F. Digonnet, C. J. Gaeta, “Theoretical analysis of optical fiber laser amplifiers and oscillators,” Appl. Opt. 24, 333 (1985).
    [CrossRef] [PubMed]
  25. Strictly speaking, the normalization of rP is taken over the crystal, whereas the normalization of ϕ0 is taken over the entire cavity. For simplicity, it will be assumed that the crystal and the cavity lengths are the same, as would be the case, for instance, in a monolithic Nd:YAG laser in which the mirror coatings are deposited directly onto the ends of the laser crystal. The case when the crystal and cavity lengths are not the same is easily accounted for with minor modifications to the theory presented here, and the assumption of identical crystal and cavity lengths does not significantly alter the basic results.

1987 (5)

1986 (4)

R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
[CrossRef]

W. J. Kozlovsky, T. Y. Fan, R. L. Byer, “Diode-pumped continuous wave Nd:glass laser,” Opt. Lett. 11, 788 (1986).
[CrossRef] [PubMed]

T. Y. Fan, G. J. Dixon, R. L. Byer, “Efficient GaAlAs diode-laser-pumped operation of Nd:YLF at 1.047 μm with intracavity doubling to 523.6 nm,” Opt. Lett. 11, 204 (1986).
[CrossRef]

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

1985 (4)

P. F. Moulton, “An investigation of the Co:MgF2laser system,” IEEE J. Quantum Electron. QE-21, 1582 (1985).
[CrossRef]

D. L. Sipes, “Highly efficient neodymium:yttrium aluminum garnet laser end pumped by a semiconductor laser array,” Appl. Phys. Lett. 47, 74 (1985).
[CrossRef]

B. Zhou, T. J. Kane, G. J. Dixon, R. L. Byer, “Efficient, frequency stable laser diode pumped Nd:YAG laser,” Opt. Lett. 10, 62 (1985).
[CrossRef] [PubMed]

M. J. F. Digonnet, C. J. Gaeta, “Theoretical analysis of optical fiber laser amplifiers and oscillators,” Appl. Opt. 24, 333 (1985).
[CrossRef] [PubMed]

1980 (2)

1979 (1)

K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653 (1979).
[CrossRef]

1978 (1)

M. Birnbaum, A. W. Tucker, C. L. Fincher, “Cw room-temperature laser operation of Nd:CAMGAR at 0.941 and 1.059 μm,” J. Appl. Phys. 49, 2984 (1978).
[CrossRef]

1969 (2)

R. B. Allen, S. J. Scalise, “Continuous operation of a YAlG:Nd laser by injection luminescent pumping,” Appl. Phys. Lett. 14, 188 (1969).
[CrossRef]

R. W. Wallace, S. E. Harris, “Oscillation and doubling of the 0.946 μm line in Nd3+:YAG,” Appl. Phys. Lett. 15, 111 (1969).
[CrossRef]

1963 (1)

L. F. Johnson, R. A. Thomas, “Maser oscillations at 0.9 and 1.35 microns in CaWO4:Nd3+,” Phys. Rev. 131, 2038 (1963).
[CrossRef]

Allen, R.

R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
[CrossRef]

G. Kintz, L. Esterowitz, R. Allen, “Cascade laser emission at 2.3.1 and 2.08 μm from laser diode pumped Tm, Ho:LiYF4 at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 20.

Allen, R. B.

R. B. Allen, S. J. Scalise, “Continuous operation of a YAlG:Nd laser by injection luminescent pumping,” Appl. Phys. Lett. 14, 188 (1969).
[CrossRef]

Birnbaum, M.

M. Birnbaum, A. W. Tucker, C. L. Fincher, “Cw room-temperature laser operation of Nd:CAMGAR at 0.941 and 1.059 μm,” J. Appl. Phys. 49, 2984 (1978).
[CrossRef]

Byer, R. L.

Casperson, L. W.

Danielmeyer, H. G.

H. G. Danielmeyer, “Progress in Nd:YAG lasers,” in Lasers: A Series of Advances, A. K. Levine, A. J. DeMaria, eds. (Dekker, New York, 1976).

Digonnet, M. J. F.

Dixon, G. J.

Duczynski, E. W.

E. W. Duczynski, G. Huber, K. Petermann, H. Strange, “Continuous wave 1600 nm laser-action in Er-doped garnets at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 197.

E. W. Duczynski, G. Huber, P. Mitzscherlich, “Laser action of Cr, Nd, Tm, Ho-doped garnets,” in Tunable Solid-State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds. (Springer-Verlag, Berlin, 1986), p. 282.
[CrossRef]

Esterowitz, L.

R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
[CrossRef]

G. Kintz, L. Esterowitz, R. Allen, “Cascade laser emission at 2.3.1 and 2.08 μm from laser diode pumped Tm, Ho:LiYF4 at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 20.

Fan, T. Y.

Fincher, C. L.

M. Birnbaum, A. W. Tucker, C. L. Fincher, “Cw room-temperature laser operation of Nd:CAMGAR at 0.941 and 1.059 μm,” J. Appl. Phys. 49, 2984 (1978).
[CrossRef]

Gaeta, C. J.

Goldberg, L.

R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
[CrossRef]

Hakimi, F.

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

Hall, D. G.

Harris, S. E.

R. W. Wallace, S. E. Harris, “Oscillation and doubling of the 0.946 μm line in Nd3+:YAG,” Appl. Phys. Lett. 15, 111 (1969).
[CrossRef]

Huber, G.

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Continuous-wave operation at 2.1 μm of a diode-laser-pumped, Tmsensitized Ho:Y3Al5O12 laser at 300 K,” Opt. Lett. 12, 678 (1987).
[CrossRef] [PubMed]

E. W. Duczynski, G. Huber, K. Petermann, H. Strange, “Continuous wave 1600 nm laser-action in Er-doped garnets at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 197.

E. W. Duczynski, G. Huber, P. Mitzscherlich, “Laser action of Cr, Nd, Tm, Ho-doped garnets,” in Tunable Solid-State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds. (Springer-Verlag, Berlin, 1986), p. 282.
[CrossRef]

Johnson, L. F.

L. F. Johnson, R. A. Thomas, “Maser oscillations at 0.9 and 1.35 microns in CaWO4:Nd3+,” Phys. Rev. 131, 2038 (1963).
[CrossRef]

Kane, T. J.

Kintz, G.

G. Kintz, L. Esterowitz, R. Allen, “Cascade laser emission at 2.3.1 and 2.08 μm from laser diode pumped Tm, Ho:LiYF4 at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 20.

Kozlovsky, W. J.

Kubodera, K.

K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653 (1979).
[CrossRef]

Lenth, W.

A. J. Silversmith, W. Lenth, R. M. Macfarlane, “Green infrared-pumped erbium upconversion laser,” Appl. Phys. Lett. 51, 1977 (1987).
[CrossRef]

W. P. Risk, W. Lenth, “Room temperature, cw 946-nm Nd:YAG laser pumped by laser-diode arrays and intracavity frequency doubling to 473 nm,” Opt. Lett. 12, 993 (1987).
[CrossRef] [PubMed]

Macfarlane, R. M.

A. J. Silversmith, W. Lenth, R. M. Macfarlane, “Green infrared-pumped erbium upconversion laser,” Appl. Phys. Lett. 51, 1977 (1987).
[CrossRef]

Mansfield, R. J.

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

McCollum, B. C.

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

Mitzscherlich, P.

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Continuous-wave operation at 2.1 μm of a diode-laser-pumped, Tmsensitized Ho:Y3Al5O12 laser at 300 K,” Opt. Lett. 12, 678 (1987).
[CrossRef] [PubMed]

E. W. Duczynski, G. Huber, P. Mitzscherlich, “Laser action of Cr, Nd, Tm, Ho-doped garnets,” in Tunable Solid-State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds. (Springer-Verlag, Berlin, 1986), p. 282.
[CrossRef]

Moulton, P. F.

P. F. Moulton, “An investigation of the Co:MgF2laser system,” IEEE J. Quantum Electron. QE-21, 1582 (1985).
[CrossRef]

Otsuka, K.

K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653 (1979).
[CrossRef]

Petermann, K.

E. W. Duczynski, G. Huber, K. Petermann, H. Strange, “Continuous wave 1600 nm laser-action in Er-doped garnets at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 197.

Po, H.

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

Rice, R. R.

Risk, W. P.

Scalise, S. J.

R. B. Allen, S. J. Scalise, “Continuous operation of a YAlG:Nd laser by injection luminescent pumping,” Appl. Phys. Lett. 14, 188 (1969).
[CrossRef]

Silversmith, A. J.

A. J. Silversmith, W. Lenth, R. M. Macfarlane, “Green infrared-pumped erbium upconversion laser,” Appl. Phys. Lett. 51, 1977 (1987).
[CrossRef]

Sipes, D. L.

D. L. Sipes, “Highly efficient neodymium:yttrium aluminum garnet laser end pumped by a semiconductor laser array,” Appl. Phys. Lett. 47, 74 (1985).
[CrossRef]

Smith, R. J.

Snitzer, E.

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

Storm, M.

R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
[CrossRef]

Strange, H.

E. W. Duczynski, G. Huber, K. Petermann, H. Strange, “Continuous wave 1600 nm laser-action in Er-doped garnets at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 197.

Thomas, R. A.

L. F. Johnson, R. A. Thomas, “Maser oscillations at 0.9 and 1.35 microns in CaWO4:Nd3+,” Phys. Rev. 131, 2038 (1963).
[CrossRef]

Tucker, A. W.

M. Birnbaum, A. W. Tucker, C. L. Fincher, “Cw room-temperature laser operation of Nd:CAMGAR at 0.941 and 1.059 μm,” J. Appl. Phys. 49, 2984 (1978).
[CrossRef]

Tumminelli, R. P.

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

Wallace, R. W.

R. W. Wallace, S. E. Harris, “Oscillation and doubling of the 0.946 μm line in Nd3+:YAG,” Appl. Phys. Lett. 15, 111 (1969).
[CrossRef]

Weller, J. F.

R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
[CrossRef]

Zhou, B.

Appl. Opt. (3)

Appl. Phys. Lett. (4)

R. B. Allen, S. J. Scalise, “Continuous operation of a YAlG:Nd laser by injection luminescent pumping,” Appl. Phys. Lett. 14, 188 (1969).
[CrossRef]

A. J. Silversmith, W. Lenth, R. M. Macfarlane, “Green infrared-pumped erbium upconversion laser,” Appl. Phys. Lett. 51, 1977 (1987).
[CrossRef]

D. L. Sipes, “Highly efficient neodymium:yttrium aluminum garnet laser end pumped by a semiconductor laser array,” Appl. Phys. Lett. 47, 74 (1985).
[CrossRef]

R. W. Wallace, S. E. Harris, “Oscillation and doubling of the 0.946 μm line in Nd3+:YAG,” Appl. Phys. Lett. 15, 111 (1969).
[CrossRef]

Electron. Lett. (1)

R. Allen, L. Esterowitz, L. Goldberg, J. F. Weller, M. Storm, “Diode-pumped 2 μm holmium laser,” Electron. Lett. 22, 947 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

P. F. Moulton, “An investigation of the Co:MgF2laser system,” IEEE J. Quantum Electron. QE-21, 1582 (1985).
[CrossRef]

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

J. Appl. Phys. (2)

K. Kubodera, K. Otsuka, “Single-transverse-mode LiNdP4O12 slab waveguide laser,” J. Appl. Phys. 50, 653 (1979).
[CrossRef]

M. Birnbaum, A. W. Tucker, C. L. Fincher, “Cw room-temperature laser operation of Nd:CAMGAR at 0.941 and 1.059 μm,” J. Appl. Phys. 49, 2984 (1978).
[CrossRef]

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

H. Po, F. Hakimi, R. J. Mansfield, R. P. Tumminelli, B. C. McCollum, E. Snitzer, “Neodymium fiber lasers at 0.905, 1.06, and 1.4 μm,” J. Opt. Soc. Am. A 3(13), P103 (1986).

Opt. Lett. (6)

Phys. Rev. (1)

L. F. Johnson, R. A. Thomas, “Maser oscillations at 0.9 and 1.35 microns in CaWO4:Nd3+,” Phys. Rev. 131, 2038 (1963).
[CrossRef]

Other (5)

H. G. Danielmeyer, “Progress in Nd:YAG lasers,” in Lasers: A Series of Advances, A. K. Levine, A. J. DeMaria, eds. (Dekker, New York, 1976).

G. Kintz, L. Esterowitz, R. Allen, “Cascade laser emission at 2.3.1 and 2.08 μm from laser diode pumped Tm, Ho:LiYF4 at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 20.

E. W. Duczynski, G. Huber, K. Petermann, H. Strange, “Continuous wave 1600 nm laser-action in Er-doped garnets at room temperature,” in Digest of Topical Meeting on Tunable Solid-State Lasers (Optical Society of America, Washington, D.C., 1987), p. 197.

E. W. Duczynski, G. Huber, P. Mitzscherlich, “Laser action of Cr, Nd, Tm, Ho-doped garnets,” in Tunable Solid-State Lasers II, A. B. Budgor, L. Esterowitz, L. G. DeShazer, eds. (Springer-Verlag, Berlin, 1986), p. 282.
[CrossRef]

Strictly speaking, the normalization of rP is taken over the crystal, whereas the normalization of ϕ0 is taken over the entire cavity. For simplicity, it will be assumed that the crystal and the cavity lengths are the same, as would be the case, for instance, in a monolithic Nd:YAG laser in which the mirror coatings are deposited directly onto the ends of the laser crystal. The case when the crystal and cavity lengths are not the same is easily accounted for with minor modifications to the theory presented here, and the assumption of identical crystal and cavity lengths does not significantly alter the basic results.

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Figures (10)

Fig. 1
Fig. 1

(a) Idealized energy-level diagram and (b) energy-level diagram for Nd:YAG.

Fig. 2
Fig. 2

Plots of the normalized population-inversion density [integrated over z, i.e., the quantity plotted on the vertical axis is 0 l Δ N ( r , z ) d z] as a function of the radial coordinate for different values of normalized internal laser power S. Vertical-axis units are arbitrary but are consistent from figure to figure: (a) ratio of pump-mode waist to laser-mode waist a = 0.2, with the laser field profile indicated by the dashed line; (b) a = 1.0, with the laser field profile identical to the curve for S = 0; (c) a = 5.0, with the laser field profile indicated by the dashed line.

Fig. 3
Fig. 3

Ratio of total population inversion to total population inversion at threshold as a function of the ratio of the normalized pumping rate F to the normalized pumping rate at threshold Fth for different values of the ratio a = wP/wL.

Fig. 4
Fig. 4

Numerically generated plots of normalized slope efficiency dS/dF as a function of F/Fth for different values of a: (a) B = 0, (b) B = 0.5, (c) B = 1, (d) B = 2, (e) B = 5.

Fig. 5
Fig. 5

Numerically generated plots of normalized slope efficiency dS/dF as a function of a = wP/wL for different values of S: (a) B = 0, (b) B = 0.5, (c) B = 1, (d) B = 2, (e) B = 5.

Fig. 6
Fig. 6

Numerically generated plots of normalized slope efficiency dS/dF as a function of F/Fth for different values of B: (a) a = 0, (b) a = 0.5, (c) a = 1.0, (d) a = 1.5, (e) a = 2.0.

Fig. 7
Fig. 7

Radial distribution of gain (integrated over z) for F/Fth = 10 and a = 2 for different values of B. Vertical-axis units are arbitrary. The dashed line indicates the laser profile.

Fig. 8
Fig. 8

(a) Normalized laser power S versus normalized pump power F for several values of a and for B = 0. (b) Normalized laser power S versus normalized pump power F for several values of a and for B = 5.

Fig. 9
Fig. 9

(a) Normalized laser power S versus normalized pump power F as numerically generated from the modeling presented in this paper for a 946-nm laser and a 1.06-μm laser with identical cavities. (b) The curves of Fig. 8(a) recast in terms of actual emitted laser power and incident pump power.

Fig. 10
Fig. 10

Comparison of theoretical predictions with experimental results for a 946-nm laser pumped by an infrared dye laser and laser-diode arrays. The solid lines representing experimental data are least-squares-fit straight lines to the data of Ref. 6. The dashed curves are theoretical.

Equations (33)

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d N 2 ( r , z ) d t = f 2 R r p ( r , z ) N 2 ( r , z ) N 2 0 τ f 2 c σ [ N 2 ( r , z ) N 1 ( r , z ) ] n Φ ϕ 0 ( r , z ) = 0
d N 1 ( r , z ) d t = f 1 R r p ( r , z ) N 1 ( r , z ) N 1 0 τ + f 1 c σ [ N 2 ( r , z ) N 1 ( r , z ) ] n Φ ϕ 0 ( r , z ) = 0
d Δ N ( r , z ) d t = ( f 1 + f 2 ) R r P ( r , z ) Δ N ( r , z ) Δ N 0 τ ( f 1 + f 2 ) c σ Δ N ( r , z ) n Φ ϕ 0 ( r , z ) = 0 ,
r P ( r , z ) d V = 1 .
r P ( r , z ) = 2 α η a π w p 2 exp ( 2 r 2 w P 2 ) exp ( α z ) ,
ϕ 0 ( r , z ) d V = 1 .
ϕ 0 ( r , z ) = 2 π w L 2 l exp ( 2 r 2 w L 2 ) ,
d Φ d t = c σ n Δ N ( r , z ) Φ ϕ 0 ( r , z ) d V Φ τ q = 0 ,
Δ N ( r , z ) = τ ( f 1 + f 2 ) R r p ( r , z ) N 1 0 ,
Δ N ( r , z ) ϕ 0 ( r , z ) d V = n τ q c σ ,
Δ N ( r , z ) = τ f R r P ( r , z ) N 1 0 1 + c σ τ n f Φ ϕ 0 ( r , z ) ,
G ( r , z ) = σ τ f R r P ( r , z ) 1 + c σ τ n f Φ ϕ 0 ( r , z ) N 1 0 σ 1 + c σ τ n f Φ ϕ 0 ( r , z ) .
d I ( r , z ) d z = G ( r , z ) I ( r , z ) .
d I ( r , z ) d z = G 0 ( r , z ) I ( r , z ) 1 + 2 s I ( r , z ) ,
G 0 ( r , z ) = σ τ f R r P ( r , z ) N 1 0 σ ,
s = f σ τ h ν L ,
round trip d P L = 2 0 l d P L d z d z = P L ( L + T ) ,
P L ( z ) = 2 π 0 I ( r , z ) r d r .
4 π 0 l 0 G 0 ( r , z ) I ( r , z ) 1 + 2 s I ( r , z ) r d r d z = P L ( L + T ) .
4 π 0 l 0 [ 2 α σ τ P P f π h ν P w p 2 exp ( 2 r 2 w P 2 ) exp ( α z ) N a 0 σ ] 2 π w L 2 l exp ( 2 r 2 w L 2 ) 1 + 2 f c σ τ Φ π m w L 2 l exp ( 2 r 2 w L 2 ) ( c h ν L Φ 2 n ) r d r d z = P L ( L + T ) .
a = w P w L ,
x = 2 r 2 w P 2 ,
B = 2 N 1 0 σ l ( L + T ) ,
F = 4 P P τ σ η a π h ν p w L 2 ( L + T ) ,
S = 2 c σ τ Φ n π w L 2 l ,
f F 0 [ exp ( x ) B a 2 f F ] exp ( a 2 x ) 1 + f S exp ( a 2 x ) d x = 1 ,
F = 1 + B f S ln ( 1 + f S ) f 0 exp [ ( a 2 + 1 ) x ] 1 + f S exp ( a 2 x ) d x .
F th = ( 1 + a 2 ) ( 1 + B ) f .
P P , th = π h ν P ( w L 2 + w P 2 ) ( L + T + 2 N 1 0 l ) 4 σ τ η a f .
α exp ( α l 0 ) ( 2 σ N 1 0 α + L + T + 2 σ N 1 0 l 0 ) 2 σ N 1 0 = 0.
d S d F = 1 + B f S ln ( 1 + f S ) f 2 F 2 0 [ exp ( x ) B a 2 f S ] exp ( 2 a 2 x ) [ 1 + f S exp ( a 2 x ) ] 2 d x ,
d S d F | S 0 = ( 1 + 2 a 2 ) ( 1 + a 2 ) 2 1 1 + B / 2 1 + a 2 .
d P out d P p = T L + T ν L ν P η a d S d F .

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