Abstract

The performance of an intracavity mode-locked and frequency-doubled Nd:YAG laser has been analyzed using a method that takes into account the transverse spatial variation of both the gain and the laser mode. The technique leads to a simple numerical procedure that determines the second harmonic power and pulse width in terms of the parameters that characterize the various spatial distributions.

© 1983 Optical Society of America

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References

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  1. R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
    [CrossRef]
  2. O. Bernecker, IEEE J. Quantum Electron. QE-9, 897 (1973).
    [CrossRef]
  3. J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
    [CrossRef]
  4. C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 793 (1975).
    [CrossRef]
  5. C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 857 (1975).
    [CrossRef]
  6. R. R. Rice, G. H. Burkhart, J. R. Teague, J. Appl. Phys. 47, 3045 (1976).
    [CrossRef]
  7. L. W. Casperson, Appl. Opt. 19, 422 (1980).
    [CrossRef] [PubMed]
  8. D. G. Hall, R. J. Smith, R. R. Rice, Appl. Opt. 19, 3041 (1980).
    [CrossRef] [PubMed]
  9. D. G. Hall, Appl. Opt. 20, 1579 (1981).
    [CrossRef] [PubMed]
  10. A. E. Siegman, J-M. Heritier, IEEE J. Quantum Electron. QE-16, 324 (1980).
    [CrossRef]

1981

1980

1976

R. R. Rice, G. H. Burkhart, J. R. Teague, J. Appl. Phys. 47, 3045 (1976).
[CrossRef]

1975

J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
[CrossRef]

C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 793 (1975).
[CrossRef]

C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 857 (1975).
[CrossRef]

1973

O. Bernecker, IEEE J. Quantum Electron. QE-9, 897 (1973).
[CrossRef]

1970

R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
[CrossRef]

Bernecker, O.

O. Bernecker, IEEE J. Quantum Electron. QE-9, 897 (1973).
[CrossRef]

Burkhart, G. H.

R. R. Rice, G. H. Burkhart, J. R. Teague, J. Appl. Phys. 47, 3045 (1976).
[CrossRef]

Casperson, L. W.

Falk, J.

J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
[CrossRef]

Hall, D. G.

Heritier, J-M.

A. E. Siegman, J-M. Heritier, IEEE J. Quantum Electron. QE-16, 324 (1980).
[CrossRef]

Kennedy, C. J.

C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 793 (1975).
[CrossRef]

C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 857 (1975).
[CrossRef]

Rice, R. R.

D. G. Hall, R. J. Smith, R. R. Rice, Appl. Opt. 19, 3041 (1980).
[CrossRef] [PubMed]

R. R. Rice, G. H. Burkhart, J. R. Teague, J. Appl. Phys. 47, 3045 (1976).
[CrossRef]

Siegman, A. E.

A. E. Siegman, J-M. Heritier, IEEE J. Quantum Electron. QE-16, 324 (1980).
[CrossRef]

Smith, R. G.

R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
[CrossRef]

Smith, R. J.

Teague, J. R.

R. R. Rice, G. H. Burkhart, J. R. Teague, J. Appl. Phys. 47, 3045 (1976).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

A. E. Siegman, J-M. Heritier, IEEE J. Quantum Electron. QE-16, 324 (1980).
[CrossRef]

R. G. Smith, IEEE J. Quantum Electron. QE-6, 215 (1970).
[CrossRef]

O. Bernecker, IEEE J. Quantum Electron. QE-9, 897 (1973).
[CrossRef]

J. Falk, IEEE J. Quantum Electron. QE-11, 21 (1975).
[CrossRef]

C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 793 (1975).
[CrossRef]

C. J. Kennedy, IEEE J. Quantum Electron. QE-11, 857 (1975).
[CrossRef]

J. Appl. Phys.

R. R. Rice, G. H. Burkhart, J. R. Teague, J. Appl. Phys. 47, 3045 (1976).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Average second harmonic power P2 as a function of the pump parameter G0/(πw2) for three values of α = R0/w and parameters specified in the text. Note that w is a constant for these plots (w = 0.05 cm), so each curve corresponds to a value of R0.

Fig. 2
Fig. 2

Second harmonic pulse width τ2 as a function of G0/(πw2) for four values of α = R0/w and the same laser parameters used in Fig. 1. Again, w is a constant so each curve corresponds to a value of R0.

Equations (25)

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

d I d z = g 0 I 1 + 2 W 1 / W sat η I ,
W 1 = I ( t ) dt
I ( r , ϕ , z , t ) = P ( z , t ) f ( r , ϕ , z ) ,
f ( r , ϕ , z ) = 2 π w 2 exp ( 2 r 2 w 2 ) ,
ɛ 1 = P ( z , t ) dt .
W 1 = f ( r , ϕ , z ) ɛ 1 .
dP ( z , t ) dz = ( Q η ) P ( z , t ) ,
Q = 0 2 π 0 g 0 f ( r , ϕ , z ) 1 + 2 f ( r , ϕ , z ) ɛ 1 / W sat rdrd ϕ .
g 0 = { G 0 π R 0 2 0 r R 0 , 0 r > R 0 ,
Q = G 0 w 2 4 R 0 2 W sat ɛ 1 ln 1 + ( 4 π w 2 ) ( ɛ 1 / W sat ) 1 + ( 4 π w 2 ) ( ɛ 1 / W sat ) exp ( 2 R 0 2 / w 2 ) .
Δ P ( z , t ) = 2 ( Q η ) P ( z , t ) ,
Δ I = 2 a 2 I 2 + 2 I δ sin 2 ( ω a t ) ,
Δ P ( z , t ) = 2 a 2 π w 2 P 2 ( z , t ) + 2 δ P ( z , t ) sin 2 ( ω a t ) .
( Q η ) P ( z , t ) 2 = 2 a 2 π w 2 P 2 ( z , t ) + 2 δ P ( z , t ) sin 2 ( ω a t ) .
P ( z , t ) = π w 2 a 2 [ ( Q η ) δ sin 2 ( ω a t ) ] .
t c = ( 1 ω a ) sin 1 [ ( Q η ) δ ] 1 / 2 ,
ɛ 1 = π w 2 t c a 2 { ( Q η ) 2 δ [ 1 sinc ( 2 ω a t c ) ] } ,
ɛ 1 = t c a 2 W sat { 2 ( Q η ) δ [ 1 sinc ( 2 ω a t c ) ] } ,
Q = ( G 0 π R 0 2 ) 1 4 ɛ 1 ln [ 1 + 4 ɛ 1 1 + 4 ɛ 1 exp ( 2 R 0 2 / w 2 ) ] .
I 2 = a 2 I 2 ,
ɛ 2 = I 2 ( r , ϕ , z , t ) rdrd ϕ dt .
ɛ 2 = a 2 t c π w 2 { 2 A 2 2 AB [ 1 sinc ( 2 ω a t c ) ] + B 2 [ ¾ sinc ( 2 ω a t c ) + ¼ sinc ( 4 ω a t c ) ] } ,
A = π w 2 a 2 ( Q η ) ,
B = π w 2 δ a 2 .
τ 2 = 2 ω a sin 1 [ A B ( 1 1 2 ) ] 1 / 2 .

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