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%.

© 1999 Optical Society of America

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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 and 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 Cr4+ 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 Cr4+: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 and 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, and A. Gavrielides, “The pulse shape of a passively Q-switched microchip laser,” accepted Europ. J. Physics (1999).
  16. Peter W. Milonni and Joseph H. Eberly, Lasers (John Wiley and Sons, New York, 1998).
  17. Walter Koechner, Solid-State Laser Engineering (Springer, New York, 1992).

1999 (3)

John J. Zayhowski, “Microchip Lasers.” Optical Materials 11, 255–267 (1999).
[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]

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]

1997 (2)

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+ 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 Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

1995 (1)

J. J. Degnan,“Optimization of passively Q-switched lasers, ”IEEE J. Quantum Electron. 31, 1890–1902 (1995).
[Crossref]

1994 (1)

1991 (1)

J. J. Zayhowski and P. L. Kelly, “Optimization of Q-switched lasers,” IEEE J. Quantum. Electron. 27, 2220–2225 (1991).
[Crossref]

1989 (1)

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

1967 (1)

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]

1966 (1)

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]

1965 (1)

A. Szabo and R. A. Stein, “Theory of giant pulsing by a saturable absorber,” J. Appl. Phys. 36, 1562–1566 (1965).
[Crossref]

1963 (1)

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

Agnesi, A.

A. Agnesi, S Dell’Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, “Diode-pumped Neodymium laser repetitively Q-switched by Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

Braun, B.

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]

Degnan, J. J.

J. J. Degnan,“Optimization of passively Q-switched lasers, ”IEEE J. Quantum Electron. 31, 1890–1902 (1995).
[Crossref]

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

Dell’Acqua, S

A. Agnesi, S Dell’Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, “Diode-pumped Neodymium laser repetitively Q-switched by Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

Dill III, C.

Eberly, Joseph H.

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

Erickson, L. E.

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]

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]

Erneux, T.

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]

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

Fluck, R.

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]

Gavrielides, A.

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]

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

Gini, E.

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]

Keller, U.

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]

Kelly, P. L.

J. J. Zayhowski and P. L. Kelly, “Optimization of Q-switched lasers,” IEEE J. Quantum. Electron. 27, 2220–2225 (1991).
[Crossref]

Koechner, Walter

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

Lengel, B. A.

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

Milonni, Peter W.

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

Morello, C.

A. Agnesi, S Dell’Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, “Diode-pumped Neodymium laser repetitively Q-switched by Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

Moser, M.

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]

Paschotta, R.

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]

Peterson, P.

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]

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

Piccino, G

A. Agnesi, S Dell’Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, “Diode-pumped Neodymium laser repetitively Q-switched by Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

Reali, G. C.

A. Agnesi, S Dell’Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, “Diode-pumped Neodymium laser repetitively Q-switched by Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

Sharma, M.P.

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]

Spuhler, G. J.

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]

Stein, R. A.

A. Szabo and R. A. Stein, “Theory of giant pulsing by a saturable absorber,” J. Appl. Phys. 36, 1562–1566 (1965).
[Crossref]

Sun, L.

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+ doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electronics 33, 2286–2294, (1997).
[Crossref]

Sun, Z.

A. Agnesi, S Dell’Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, “Diode-pumped Neodymium laser repetitively Q-switched by Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

Szabo, A

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]

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]

Szabo, A.

A. Szabo and R. A. Stein, “Theory of giant pulsing by a saturable absorber,” J. Appl. Phys. 36, 1562–1566 (1965).
[Crossref]

Wang, Q.

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+ doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electronics 33, 2286–2294, (1997).
[Crossref]

Wegnar, W. G.

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

Zayhowski, J. J.

J. J. Zayhowski and C. Dill III, “Diode-pumped passively Q-switched picosecond microchip laser ’,” Opt. Lett. 19, 1427 (1994).
[Crossref] [PubMed]

J. J. Zayhowski and P. L. Kelly, “Optimization of Q-switched lasers,” IEEE J. Quantum. Electron. 27, 2220–2225 (1991).
[Crossref]

Zayhowski, John J.

John J. Zayhowski, “Microchip Lasers.” Optical Materials 11, 255–267 (1999).
[Crossref]

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

Zhang, G.

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]

Zhang, Q.

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+ doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electronics 33, 2286–2294, (1997).
[Crossref]

Zhang, S.

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+ doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electronics 33, 2286–2294, (1997).
[Crossref]

Zhang, X.

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+ doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electronics 33, 2286–2294, (1997).
[Crossref]

Zhao, S

X. Zhang, S Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+ doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electronics 33, 2286–2294, (1997).
[Crossref]

IEEE J. Quant.Electr. (1)

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]

IEEE J. Quantum Electron. (1)

J. J. Degnan,“Optimization of passively Q-switched lasers, ”IEEE J. Quantum Electron. 31, 1890–1902 (1995).
[Crossref]

IEEE J. Quantum Electronics (2)

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 Cr4+ doped saturable absorber Q-switched lasers,” IEEE J. Quantum Electronics 33, 2286–2294, (1997).
[Crossref]

IEEE J. Quantum. Electron. (1)

J. J. Zayhowski and P. L. Kelly, “Optimization of Q-switched lasers,” IEEE J. Quantum. Electron. 27, 2220–2225 (1991).
[Crossref]

IEEE J. Selected Topics in Quantum Electronics (1)

A. Agnesi, S Dell’Acqua, C. Morello, G Piccino, G. C. Reali, and Z. Sun, “Diode-pumped Neodymium laser repetitively Q-switched by Cr4+:YAG solid-state saturable absorbers,” IEEE J. Selected Topics in Quantum Electronics 1, 45–52, (1997).
[Crossref]

J. Appl. Phys. (4)

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. Opt. Soc. (1)

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]

Opt. Lett. (1)

Optical Materials (1)

John J. Zayhowski, “Microchip Lasers.” Optical Materials 11, 255–267 (1999).
[Crossref]

Other (4)

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

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

Peter W. Milonni and 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)

Equations on this page are rendered with MathJax. Learn more.

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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