Abstract

A study of passively Q-switched microchip laser pulse trains yields approximate, yet reliable, formulae for the peak power, pulse energy, half-width, period, and the pulse shape in time. The pulse gain differential equation is made integrable by assuming that the laser absorption cross sections for the gain and saturable absorber are equal. We compare our predictions with an experiment which uses Nd:YAG as a gain medium and Cr:YAG as a saturable absorber. The agreement between theory and experiment for the period, pulse width, and the pulse energy is within 10%.

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References

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  1. John J. Zayhowski, "Passively Q-switched Microchip Lasers and Applications,"The Review of Laser Engineering," 26, 841-846 (1998).
  2. John J. Zayhowski, "Microchip Lasers," Optical Materials 11, 255-267 (1999).
    [CrossRef]
  3. J. J. Zayhowski, P. L. Kelly, "Optimization of Q-switched lasers," IEEE J. Quantum. Electron. 27, 2220-2225 (1991).
    [CrossRef]
  4. J. J. Degnan,"Theory of the optimally coupled Q-switched laser," IEEE J. Quantum Electronics 25, 214-220, (1989).
    [CrossRef]
  5. X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, " Optimization of Cr 4+ doped saturable absorber Q-switched lasers," IEEE J. Quantum Electronics 33, 2286-2294, (1997).
    [CrossRef]
  6. A. Agnesi, S Dell'Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, "Diode-pumped Neodymium laser repetitively Q-switched by Cr 4+ :YAG solid-state saturable absorbers," IEEE J. Selected Topics in Quantum Electronics 1, 45-52, (1997).
    [CrossRef]
  7. P. Peterson, A. Gavrielides, M.P. Sharma and T. Erneux, "Dynamics of passively Q-switched microchip lasers," IEEE J. Quant. Electr. 35, 1-10, (1999).
    [CrossRef]
  8. J. J. Zayhowski, C. Dill III, "Diode-pumped passively Q-switched picosecond microchip laser," Opt. Lett. 19, 1427 (1994).
    [CrossRef] [PubMed]
  9. W. G. Wegnar and B. A. Lengel, "Evolution of the giant pulse in a laser," J. Appl. Phys. 42, 2040-2046 (1963).
    [CrossRef]
  10. A. Szabo and R. A. Stein, "Theory of giant pulsing by a saturable absorber," J. Appl. Phys. 36, 1562-1566 (1965).
    [CrossRef]
  11. L. E. Erickson and A Szabo "Effects of saturable absorber lifetime on the performance of giant- pulse lasers," J. Appl. Phys. 37, 4953-4961 (1966).
    [CrossRef]
  12. L. E. Erickson and A Szabo "Behavior of saturable absorber giant-pulse lasers in the limit of large absorber cross section," J. Appl. Phys. 38, 2540-2542 (1967).
    [CrossRef]
  13. J. J. Degnan,"Optimization of passively Q-switched lasers, "IEEE J. Quantum Electron. 31, 1890-1902 (1995).
    [CrossRef]
  14. G. J. Spuhler, R. Paschotta, R. Fluck. B. Braun, M. Moser, G. Zhang, E. Gini, and U. Keller, "Experimentally confirmed design guidelines for passively Q-switched microchip lasers using semiconductor saturable absorbers," J. Opt. Soc. 16, 376-388 (1999).
    [CrossRef]
  15. T. Erneux, P. Peterson, A. Gavrielides, "The pulse shape of a passively Q-switched microchip laser," accepted Europ. J. Physics (1999).
  16. Peter W. Milonni, Joseph H. Eberly, Lasers (John Wiley and Sons, New York, 1998).
  17. Walter Koechner, Solid-State Laser Engineering (Springer, New York, 1992).

Other

John J. Zayhowski, "Passively Q-switched Microchip Lasers and Applications,"The Review of Laser Engineering," 26, 841-846 (1998).

John J. Zayhowski, "Microchip Lasers," Optical Materials 11, 255-267 (1999).
[CrossRef]

J. J. Zayhowski, P. L. Kelly, "Optimization of Q-switched lasers," IEEE J. Quantum. Electron. 27, 2220-2225 (1991).
[CrossRef]

J. J. Degnan,"Theory of the optimally coupled Q-switched laser," IEEE J. Quantum Electronics 25, 214-220, (1989).
[CrossRef]

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, " Optimization of Cr 4+ doped saturable absorber Q-switched lasers," IEEE J. Quantum Electronics 33, 2286-2294, (1997).
[CrossRef]

A. Agnesi, S Dell'Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, "Diode-pumped Neodymium laser repetitively Q-switched by Cr 4+ :YAG solid-state saturable absorbers," IEEE J. Selected Topics in Quantum Electronics 1, 45-52, (1997).
[CrossRef]

P. Peterson, A. Gavrielides, M.P. Sharma and T. Erneux, "Dynamics of passively Q-switched microchip lasers," IEEE J. Quant. Electr. 35, 1-10, (1999).
[CrossRef]

J. J. Zayhowski, C. Dill III, "Diode-pumped passively Q-switched picosecond microchip laser," Opt. Lett. 19, 1427 (1994).
[CrossRef] [PubMed]

W. G. Wegnar and B. A. Lengel, "Evolution of the giant pulse in a laser," J. Appl. Phys. 42, 2040-2046 (1963).
[CrossRef]

A. Szabo and R. A. Stein, "Theory of giant pulsing by a saturable absorber," J. Appl. Phys. 36, 1562-1566 (1965).
[CrossRef]

L. E. Erickson and A Szabo "Effects of saturable absorber lifetime on the performance of giant- pulse lasers," J. Appl. Phys. 37, 4953-4961 (1966).
[CrossRef]

L. E. Erickson and A Szabo "Behavior of saturable absorber giant-pulse lasers in the limit of large absorber cross section," J. Appl. Phys. 38, 2540-2542 (1967).
[CrossRef]

J. J. Degnan,"Optimization of passively Q-switched lasers, "IEEE J. Quantum Electron. 31, 1890-1902 (1995).
[CrossRef]

G. J. Spuhler, R. Paschotta, R. Fluck. B. Braun, M. Moser, G. Zhang, E. Gini, and U. Keller, "Experimentally confirmed design guidelines for passively Q-switched microchip lasers using semiconductor saturable absorbers," J. Opt. Soc. 16, 376-388 (1999).
[CrossRef]

T. Erneux, P. Peterson, A. Gavrielides, "The pulse shape of a passively Q-switched microchip laser," accepted Europ. J. Physics (1999).

Peter W. Milonni, Joseph H. Eberly, Lasers (John Wiley and Sons, New York, 1998).

Walter Koechner, Solid-State Laser Engineering (Springer, New York, 1992).

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Figures (3)

Figure 1.
Figure 1.

Simulated pulse shapes as a function of time. (a), the three differential equations, eq. (5); (b), the gain differential equation for the actual microchip pa- rameters m=3:2, eq.(10); (c), gain differential equation for m=1, eq. (10); (d), the implicit solution, eq. (19).

Figure 2.
Figure 2.

Pulse shape as a function of time in 200psec/division. Experimental, dashed curve, simulation, solid curve.

Figure 3.
Figure 3.

The pulse rise time as a function of pump power.

Equations (22)

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N ˙ 2 = N ˙ 0 = P γ a N 0 R γ e N 2 N 2 τ g
G ˙ = 1 τ g [ 2 L g N T P Γ τ g ( 1 + γ a τ g P + γ e τ g R ) G ]
G ˙ s = 1 τ s [ 2 L s 𝒩 0 σ a ( 1 + σ + τ s R ) G s ]
R ˙ = 1 τ c [ G + G s ( ln ( 1 r ) + L ) ] R .
dI ds = I ( 1 + AD + A - D - ) , dD ds = γ ( 1 D ( 1 + I ) ) , d D - ds = γ - ( 1 D - ( 1 + α I ) ) ,
D ( 1 + γ a τ g P ) G 2 L g N T P Γ τ g , D - G s 2 L s 𝒩 0 σ a , I γ e τ g R ( 1 + γ ' a τ g P ) .
A = 2 L g N T ( P Γ τ g γ a ) α L ( 1 + γ a τ g P ) , A - = 2 L s σ a 𝒩 0 α L , γ = τ c ( 1 + γ a τ g P ) τ g α L , γ - = τ c τ s α L ,
α = σ + τ s γ a τ g ( 1 + γ a τ g P ) , α L = ln ( 1 r ) + L , s = α L t τ c .
γ I = A D b ( 1 η ) + ln η + γ A - D - b α γ - [ 1 η m ] ,
d η ds = η ( A D b ( 1 η ) + ln η + γ A - D - b α γ - [ 1 η m ] ) , where η = D D b , m = ( α γ - γ ) .
d η ds η ( ln η + A D b β ( 1 η ) ) , where β = 1 A - γ α γ - A D b .
Δ s ln [ ln η + C ( 1 η ) ] C C 1 ln ( 1 η ) + 1 C 1 ln ( C η + C 2 ) ,
γ I ln η + C ( 1 η )
γ I p ln ( 1 A D b ) + C ( 1 1 A D b ) .
γ I t , r ln η t , r + C ( 1 η t , r ) = γ I p 2 .
η t exp ( γ I p 2 C ) , and η r 1 + γ I p 2 C 1 C .
Δ s FW C C 1 ln [ 2 ( C 1 ) γ I p ] + 1 C 1 ln [ 2 ( C 1 ) 2 + C γ I p 2 ( C 1 ) ( C 2 ) ] .
γ I t exp ( Δ s ) .
γ I r = C exp ( ( C 2 ) Δ s ) C 2 + exp ( ( C 2 ) Δ s ) + ln ( C 2 C 2 + exp ( ( C 2 ) Δ s ) ) .
( 1 + A A - ) X A ( 1 exp ( X ) ) + A - γ γ - = 0 , where D b = 1 exp ( X ) ,
ε t ( Area ) h ν γ e [ A D b A - γ α γ - ]
γ = 1.75 × 10 6 , γ - = 6.35 × 10 5 , A - = 3.96 , α = 0.0852 .

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