Abstract

Using a space-dependent rate-equation analysis and considering the gain medium within the confocal region, we developed a method to calculate the output power in longitudinally pumped cw lasers as a function of a single parameter: the active medium length. It is possible to find an optimum laser design for maximum output power for a specified laser medium and pump wavelength. Some well-known longitudinally pumped laser systems, Ti:Al2O3, KCl:Tl0(1), and Cr:LiSAF, are discussed. In particular, we also analyzed the Nd:YLF laser under two pumping conditions: pumped by a diode laser at λP = 797 nm and pumped by an argon-ion laser at λP = 514.5 nm. For the diode-pumped configuration, efficiencies as high as 50% can be expected.

© 1995 Optical Society of America

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References

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  1. T. Y. Fan and R. L. Byer, "Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser," IEEE J. Quantum Electron. 23, 605 (1987).
    [CrossRef]
  2. W. P. Risk, "Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses," J. Opt. Soc. Am. B 5, 1412 (1988).
    [CrossRef]
  3. T. Y. Fan and R. L. Byer, "Diode laser pumped solid state lasers," IEEE J. Quantum Electron. 24, 895 (1988).
    [CrossRef]
  4. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).
    [CrossRef]
  5. A. J. Alfrey, "Modeling of longitudinally pumped cw Ti:sapphire laser oscillators," IEEE J. Quantum Electron. 25, 760 (1989).
    [CrossRef]
  6. J. C. Walling, "Tunable paramagnetic-ion solid-state lasers," in Tunable Lasers, L. F. Mollenauer and J. C. White, eds. (Springer-Verlag, Berlin, 1987).
    [CrossRef]
  7. P. F. Moulton, "Spectroscopic and laser characteristics of Ti:Al2O3," J. Opt. Soc. Am. B 3, 125 (1986).
    [CrossRef]
  8. L. F. Mollenauer, "Color center lasers," in Laser Handbook, M. L. Stitch and M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4.
  9. L. F. Mollenauer, N. D. Vieira, Jr., and L. Szeto, "Mode locking via synchronous pumping using a gain medium with microsecond decay times," Opt. Lett. 7, 414 (1982).
    [CrossRef] [PubMed]
  10. S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
    [CrossRef]
  11. S. A. Payne, L. L. Chase, and G. D. Wilke, "Optical spectroscopy of the new laser materials, LiSrAlF6:Cr3+ and LiCaAlF6:Cr3+," J. Luminesc. 44, 167 (1989).
    [CrossRef]
  12. R. Scheps, "Cr-doped solid state lasers pumped by visible laser diodes," Opt. Mater. 1, 1 (1992).
    [CrossRef]
  13. A. L. Harmer, A. Linz, and D. R. Gabbe, "Fluorescence of Nd3+ in lithium yttrium fluoride," J. Phys. Chem. Solids 30, 1483 (1969).
    [CrossRef]
  14. N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
    [CrossRef]
  15. E. P. Maldonado, I. M. Ranieri, N. D. Vieira, Jr., and S. P. Morato, "A high-efficiency argon-laser-pumped, Nd:YLF laser system," Appl. Opt. 34, 4295–4297 (1995).
    [CrossRef] [PubMed]
  16. E. P. Maldonado, G. E. C. Nogueira, and N. D. Vieira, Jr., "Determination of the fundamental laser parameters using an acoustooptical device," IEEE J. Quantum Electron. 29, 1218 (1993).
    [CrossRef]

1995

1993

E. P. Maldonado, G. E. C. Nogueira, and N. D. Vieira, Jr., "Determination of the fundamental laser parameters using an acoustooptical device," IEEE J. Quantum Electron. 29, 1218 (1993).
[CrossRef]

1992

N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
[CrossRef]

R. Scheps, "Cr-doped solid state lasers pumped by visible laser diodes," Opt. Mater. 1, 1 (1992).
[CrossRef]

1989

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
[CrossRef]

S. A. Payne, L. L. Chase, and G. D. Wilke, "Optical spectroscopy of the new laser materials, LiSrAlF6:Cr3+ and LiCaAlF6:Cr3+," J. Luminesc. 44, 167 (1989).
[CrossRef]

A. J. Alfrey, "Modeling of longitudinally pumped cw Ti:sapphire laser oscillators," IEEE J. Quantum Electron. 25, 760 (1989).
[CrossRef]

1988

W. P. Risk, "Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses," J. Opt. Soc. Am. B 5, 1412 (1988).
[CrossRef]

T. Y. Fan and R. L. Byer, "Diode laser pumped solid state lasers," IEEE J. Quantum Electron. 24, 895 (1988).
[CrossRef]

1987

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

1986

1982

1969

A. L. Harmer, A. Linz, and D. R. Gabbe, "Fluorescence of Nd3+ in lithium yttrium fluoride," J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Alfrey, A. J.

A. J. Alfrey, "Modeling of longitudinally pumped cw Ti:sapphire laser oscillators," IEEE J. Quantum Electron. 25, 760 (1989).
[CrossRef]

Byer, R. L.

T. Y. Fan and R. L. Byer, "Diode laser pumped solid state lasers," IEEE J. Quantum Electron. 24, 895 (1988).
[CrossRef]

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

Chartier, I.

N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
[CrossRef]

Chase, L. L.

S. A. Payne, L. L. Chase, and G. D. Wilke, "Optical spectroscopy of the new laser materials, LiSrAlF6:Cr3+ and LiCaAlF6:Cr3+," J. Luminesc. 44, 167 (1989).
[CrossRef]

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
[CrossRef]

Fan, T. Y.

T. Y. Fan and R. L. Byer, "Diode laser pumped solid state lasers," IEEE J. Quantum Electron. 24, 895 (1988).
[CrossRef]

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

Gabbe, D. R.

A. L. Harmer, A. Linz, and D. R. Gabbe, "Fluorescence of Nd3+ in lithium yttrium fluoride," J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Garapon, C.

N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
[CrossRef]

Harmer, A. L.

A. L. Harmer, A. Linz, and D. R. Gabbe, "Fluorescence of Nd3+ in lithium yttrium fluoride," J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).
[CrossRef]

Kway, W. L.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
[CrossRef]

Linz, A.

A. L. Harmer, A. Linz, and D. R. Gabbe, "Fluorescence of Nd3+ in lithium yttrium fluoride," J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Maldonado, E. P.

E. P. Maldonado, I. M. Ranieri, N. D. Vieira, Jr., and S. P. Morato, "A high-efficiency argon-laser-pumped, Nd:YLF laser system," Appl. Opt. 34, 4295–4297 (1995).
[CrossRef] [PubMed]

E. P. Maldonado, G. E. C. Nogueira, and N. D. Vieira, Jr., "Determination of the fundamental laser parameters using an acoustooptical device," IEEE J. Quantum Electron. 29, 1218 (1993).
[CrossRef]

Mermilliod, N.

N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, N. D. Vieira, Jr., and L. Szeto, "Mode locking via synchronous pumping using a gain medium with microsecond decay times," Opt. Lett. 7, 414 (1982).
[CrossRef] [PubMed]

L. F. Mollenauer, "Color center lasers," in Laser Handbook, M. L. Stitch and M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4.

Moncorgé, R.

N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
[CrossRef]

Morato, S. P.

Moulton, P. F.

Newkirk, H. W.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
[CrossRef]

Nogueira, G. E. C.

E. P. Maldonado, G. E. C. Nogueira, and N. D. Vieira, Jr., "Determination of the fundamental laser parameters using an acoustooptical device," IEEE J. Quantum Electron. 29, 1218 (1993).
[CrossRef]

Payne, S. A.

S. A. Payne, L. L. Chase, and G. D. Wilke, "Optical spectroscopy of the new laser materials, LiSrAlF6:Cr3+ and LiCaAlF6:Cr3+," J. Luminesc. 44, 167 (1989).
[CrossRef]

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
[CrossRef]

Ranieri, I. M.

Risk, W. P.

Romero, R.

N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
[CrossRef]

Scheps, R.

R. Scheps, "Cr-doped solid state lasers pumped by visible laser diodes," Opt. Mater. 1, 1 (1992).
[CrossRef]

Smith, L. K.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
[CrossRef]

Szeto, L.

Vieira, N. D.

Walling, J. C.

J. C. Walling, "Tunable paramagnetic-ion solid-state lasers," in Tunable Lasers, L. F. Mollenauer and J. C. White, eds. (Springer-Verlag, Berlin, 1987).
[CrossRef]

Wilke, G. D.

S. A. Payne, L. L. Chase, and G. D. Wilke, "Optical spectroscopy of the new laser materials, LiSrAlF6:Cr3+ and LiCaAlF6:Cr3+," J. Luminesc. 44, 167 (1989).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

E. P. Maldonado, G. E. C. Nogueira, and N. D. Vieira, Jr., "Determination of the fundamental laser parameters using an acoustooptical device," IEEE J. Quantum Electron. 29, 1218 (1993).
[CrossRef]

N. Mermilliod, R. Romero, I. Chartier, C. Garapon, and R. Moncorgé, "Performance of various diode-pumped Nd:laser materials: influence of inhomogeneous broadening," IEEE J. Quantum Electron. 28, 1179 (1992).
[CrossRef]

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

T. Y. Fan and R. L. Byer, "Diode laser pumped solid state lasers," IEEE J. Quantum Electron. 24, 895 (1988).
[CrossRef]

A. J. Alfrey, "Modeling of longitudinally pumped cw Ti:sapphire laser oscillators," IEEE J. Quantum Electron. 25, 760 (1989).
[CrossRef]

J. Appl. Phys.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, "Laser performance of LiSrAlF6:Cr3+," J. Appl. Phys. 66, 1051 (1989).
[CrossRef]

J. Luminesc.

S. A. Payne, L. L. Chase, and G. D. Wilke, "Optical spectroscopy of the new laser materials, LiSrAlF6:Cr3+ and LiCaAlF6:Cr3+," J. Luminesc. 44, 167 (1989).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. Solids

A. L. Harmer, A. Linz, and D. R. Gabbe, "Fluorescence of Nd3+ in lithium yttrium fluoride," J. Phys. Chem. Solids 30, 1483 (1969).
[CrossRef]

Opt. Lett.

Opt. Mater.

R. Scheps, "Cr-doped solid state lasers pumped by visible laser diodes," Opt. Mater. 1, 1 (1992).
[CrossRef]

Other

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).
[CrossRef]

L. F. Mollenauer, "Color center lasers," in Laser Handbook, M. L. Stitch and M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4.

J. C. Walling, "Tunable paramagnetic-ion solid-state lasers," in Tunable Lasers, L. F. Mollenauer and J. C. White, eds. (Springer-Verlag, Berlin, 1987).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Energy-level diagram considered.

Fig. 2
Fig. 2

Algorithm to calculate the laser output power.

Fig. 3
Fig. 3

Calculated output power for the vibronic lasers considered.

Fig. 4
Fig. 4

Calculated output power for the Nd:YLF laser. Two configurations are considered for pumping: a diode laser at λP = 797 nm and an Ar laser at λP = 514.5 nm.

Tables (1)

Tables Icon

Table 1 Laser System Parametersa

Equations (19)

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d ( Δ n ) d t ( β 1 + β 2 ) R P - Δ n - Δ n 0 τ - ( β 1 + β 2 ) σ I h ν Δ n ,
R P ( r , z ) = η P h ν P P P α P exp ( - α P z ) f P ( r , z ) ,
Γ 0 = P P [ 1 - exp ( - α P l ) ] 4 η P ( λ P / λ ) β π ( w E 2 + w P 2 ) I S ,
Γ 0 χ ( ξ ) - 2 l σ n 1 0 ln ( 1 + ξ ) ξ - 2 l s = L - ln ( R ) ,
ξ = 4 β P π w E 2 I S ,
χ ( ξ ) = w E 2 + w P 2 w P 2 0 1 ( w E / w P ) 2 1 + ξ d .
α P ( I P , I ) = σ P n 0 1 + I P / I SA ,
τ tot = [ τ - 1 + ( σ I ) / ( h ν ) ] - 1 .
R opt = exp ( L - L x Γ 0 ) .
γ ( r , z ) = γ 0 ( r , z ) 1 + β I ( r , z ) / I S ,
d P ( z ) d z = 2 π 0 [ I ( r , z ) z ] r d r = [ G ( z ) - s ] P ( z ) ,
G ( z ) = 2 π { H ( z ) 0 f P ( r , z ) f E ( r , z ) r 1 + f E ( r , z ) [ 2 β P ( z ) / I S ] d r - σ n 1 0 0 f E ( r , z ) r 1 + f E ( r , z ) [ 2 β P ( z ) / I S ] d r } ,
F E , P ( r , z ) = 2 π w E , P 2 ( z ) exp [ - 2 r 2 / w E , P 2 ( z ) ] ,
G ( z ) = G 0 ( z ) x χ ( ξ ) - σ n 1 0 ln ( 1 + ξ ) ξ ,
ξ = 4 β P π w E 2 I S ,             χ ( ξ ) = w E 2 + w P 2 w P 2 0 1 ( w E / w P ) 2 1 + ξ d
G 0 ( z ) = 2 H ( z ) π ( w E 2 + w P 2 ) = P P α P exp ( - α P z ) 2 η P ( λ P / λ ) β π ( w E 2 + w P 2 ) I S .
2 0 l [ G ( z ) - s ] d z = L - ln ( R ) ,
Γ 0 χ ( ξ ) - 2 l σ n 1 0 ln ( 1 + ξ ) ξ = L - ln ( R ) + 2 l s ,
Γ 0 = P P [ 1 - exp ( - α P l ) ] 4 η P ( λ P / λ ) β π ( w E 2 + w P 2 ) I S ,

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