Abstract

A computational model was developed to predict solid-state laser performance in the start-up transient regime of a repetitive pulse operation. Laser output in this regime is sensitive to the interaction of rate-equation, thermal-transport, and beam-propagation effects. A high-repetition-rate operation produces pulse trains that decay at a rate determined by the competition between energy deposition in the rod and surface cooling. Selected pulses in a train turn on and off as the repetition rate is increased because of the varying residual population inversion between pulses.

© 1992 Optical Society of America

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References

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  1. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, New York, 1988).
  2. R. L. Byer, R. L. Herbst, “The unstable-resonator YAG,” Laser Focus 7(7), 48–57 (1978).
  3. G. Herziger, H. Weber, “Equivalent optical resonators,” Appl. Opt. 23, 1450–1452 (1984).
    [CrossRef] [PubMed]
  4. V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25, 107–117 (1986).
    [CrossRef] [PubMed]
  5. R. F. Hotz, “Thermal transient effects in repetitively pulsed flashlamp-pumped YAG:Nd and YAG:Nd,Lu laser material,” Appl. Opt. 12, 1834–1838 (1973).
    [CrossRef] [PubMed]
  6. D. Metcalf, P. de Giovanni, J. Zachorowski, M. Leduc, “Laser resonators containing self-focusing elements,” Appl. Opt. 26, 4508–4517 (1987).
    [CrossRef] [PubMed]
  7. T. Y. Fan, “Effect of finite lower level lifetime on Q-switched lasers,” IEEE J. Quantum Electron. 24, 2345–2349 (1988).
    [CrossRef]
  8. R. L. Burden, J. D. Faires, Numerical Analysis (PWS-Kent, Boston, Mass., 1985).
  9. E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).
  10. D. R. Pitts, L. E. Sissom, Heat Transfer, Schaum’s Outline Series-McGraw-Hill, New York, 1977).
  11. A. J. Chapman, Heat Transfer, 4th ed. (Macmillan, New York, 1974).
  12. J. T. Verdeyen, Laser Electronics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  13. H. P. Kortz, R. Ifflander, H. Weber, “Stability and beam divergence of multimode lasers with internal variable lenses,” Appl. Opt. 20, 4124–4134 (1981).
    [CrossRef] [PubMed]
  14. R. C. Knight, R. J. Dewhurst, S. A. Ramsden, “Efficient burst-mode operation of a very high repetition-rate Nd:YAG laser,” J. Phys. E 13, 1339–1342 (1980).
    [CrossRef]

1988 (1)

T. Y. Fan, “Effect of finite lower level lifetime on Q-switched lasers,” IEEE J. Quantum Electron. 24, 2345–2349 (1988).
[CrossRef]

1987 (1)

1986 (1)

1984 (1)

1981 (1)

1980 (1)

R. C. Knight, R. J. Dewhurst, S. A. Ramsden, “Efficient burst-mode operation of a very high repetition-rate Nd:YAG laser,” J. Phys. E 13, 1339–1342 (1980).
[CrossRef]

1978 (1)

R. L. Byer, R. L. Herbst, “The unstable-resonator YAG,” Laser Focus 7(7), 48–57 (1978).

1973 (1)

Burden, R. L.

R. L. Burden, J. D. Faires, Numerical Analysis (PWS-Kent, Boston, Mass., 1985).

Byer, R. L.

R. L. Byer, R. L. Herbst, “The unstable-resonator YAG,” Laser Focus 7(7), 48–57 (1978).

Chapman, A. J.

A. J. Chapman, Heat Transfer, 4th ed. (Macmillan, New York, 1974).

de Giovanni, P.

Dewhurst, R. J.

R. C. Knight, R. J. Dewhurst, S. A. Ramsden, “Efficient burst-mode operation of a very high repetition-rate Nd:YAG laser,” J. Phys. E 13, 1339–1342 (1980).
[CrossRef]

Drake, R. M.

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).

Eckert, E. R. G.

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).

Faires, J. D.

R. L. Burden, J. D. Faires, Numerical Analysis (PWS-Kent, Boston, Mass., 1985).

Fan, T. Y.

T. Y. Fan, “Effect of finite lower level lifetime on Q-switched lasers,” IEEE J. Quantum Electron. 24, 2345–2349 (1988).
[CrossRef]

Herbst, R. L.

R. L. Byer, R. L. Herbst, “The unstable-resonator YAG,” Laser Focus 7(7), 48–57 (1978).

Herziger, G.

Hotz, R. F.

Ifflander, R.

Knight, R. C.

R. C. Knight, R. J. Dewhurst, S. A. Ramsden, “Efficient burst-mode operation of a very high repetition-rate Nd:YAG laser,” J. Phys. E 13, 1339–1342 (1980).
[CrossRef]

Koechner, W.

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

Kortz, H. P.

Leduc, M.

Magni, V.

Metcalf, D.

Pitts, D. R.

D. R. Pitts, L. E. Sissom, Heat Transfer, Schaum’s Outline Series-McGraw-Hill, New York, 1977).

Ramsden, S. A.

R. C. Knight, R. J. Dewhurst, S. A. Ramsden, “Efficient burst-mode operation of a very high repetition-rate Nd:YAG laser,” J. Phys. E 13, 1339–1342 (1980).
[CrossRef]

Sissom, L. E.

D. R. Pitts, L. E. Sissom, Heat Transfer, Schaum’s Outline Series-McGraw-Hill, New York, 1977).

Verdeyen, J. T.

J. T. Verdeyen, Laser Electronics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Weber, H.

Zachorowski, J.

Appl. Opt. (5)

IEEE J. Quantum Electron. (1)

T. Y. Fan, “Effect of finite lower level lifetime on Q-switched lasers,” IEEE J. Quantum Electron. 24, 2345–2349 (1988).
[CrossRef]

J. Phys. E (1)

R. C. Knight, R. J. Dewhurst, S. A. Ramsden, “Efficient burst-mode operation of a very high repetition-rate Nd:YAG laser,” J. Phys. E 13, 1339–1342 (1980).
[CrossRef]

Laser Focus (1)

R. L. Byer, R. L. Herbst, “The unstable-resonator YAG,” Laser Focus 7(7), 48–57 (1978).

Other (6)

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

R. L. Burden, J. D. Faires, Numerical Analysis (PWS-Kent, Boston, Mass., 1985).

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).

D. R. Pitts, L. E. Sissom, Heat Transfer, Schaum’s Outline Series-McGraw-Hill, New York, 1977).

A. J. Chapman, Heat Transfer, 4th ed. (Macmillan, New York, 1974).

J. T. Verdeyen, Laser Electronics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989).

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Figures (5)

Fig. 1
Fig. 1

Single pulse outputs calculated from rate equations.

Fig. 2
Fig. 2

Train of 40 pulses at a 625-Hz repetition rate.

Fig. 3
Fig. 3

Peak power for a 100-pulse train at different repetition rates.

Fig. 4
Fig. 4

Beam divergence angle for a 100-pulse train.

Fig. 5
Fig. 5

Pulse energy for selected pulses in a 40-pulse train as the repetition rate is varied. The average is taken over the set of 40 pulses at each repetition rate.

Equations (16)

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d Φ dt = Φ σ c n ( N 2 g 2 g 1 N 1 ) L rod L cav Φ δ τ r e + S ,
d N 3 d t = N 3 τ 3 + R 3 ,
d N 2 d t = Φ σ c n ( N 2 g 2 g 1 N 1 ) f 2 + N 3 τ 32 f 2 N 2 τ 2 + R 2 f 2 ,
d N 1 d t = Φ σ c n ( N 2 g 2 g 1 N 1 ) f 1 + N 2 τ 21 f 1 f 2 + N 3 τ 31 f 1 N 1 τ 10 + R 1 f 1 ,
d N 0 d t = N 1 τ 10 f 1 + N 2 τ 20 f 2 + N 3 τ 30 R 1 R 2 R 3 .
N 3 R 3 τ 32 [ 1 exp ( t τ 32 ) ] .
ρ c p d T d t = k 2 T + q * .
d T ( r = R , t ) d r = h k [ T ( r = R , t ) T film ] .
h water L V = 3058 + 23 . 9 T film 0 . 0453 T film 2 + 2 . 801 × 10 5 T film 3 ,
h air L V = 4 . 046 5 . 829 × 10 4 T film + 1 . 924 × 10 7 T film 2 1 . 985 × 10 11 T film 3 .
n ( r ) = n ( r = 0 ) + [ T ( r ) T ( 0 ) ] d n d T ,
n ( r = 0 ) = n ( T = 300 K ) [ 300 T ( r = 0 ) ] d n d T .
M = [ cos ( b ) L rod n 0 b sin ( b ) n 0 b L rod sin ( b ) cos ( b ) ] .
b = L rod η n 0 ,
n R = n 0 η R 2 2 .
V mode = 0 L π [ w ( z ) ] 2 d z .

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