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References

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  1. L. W. Casperson, Appl. Opt. 19, 422 (1980).
    [CrossRef] [PubMed]

1980 (1)

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Figures (2)

Fig. 1
Fig. 1

Plots of sI1 (proportional to circulating power) as a function of F (proportional to pump power). The symbol δ indicates on-axis (δ-function) pumping, MMG indicates pumping with a mode-matched Gaussian [see Eq. (9)], and the other three curves are for the cylindrical pumping case for values Ro/W = 1, 2, and 2.

Fig. 2
Fig. 2

Comparison of theoretically predicted and experimentally determined threshold powers as a function of Ro/W. The theoretical curve is obtained by scaling Eq. (18) by a constant.

Equations (18)

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d I d z = g h o I 1 + s I η I ,
I ( r , ϕ , z ) = P ( z ) f ( r , ϕ , z ) ,
f ( r , ϕ , z ) = 2 π w 2 ( z ) exp [ 2 r 2 / w 2 ( z ) ] ,
d P d z = Q ( z ) η P ( z ) ,
Q ( z ) = 0 2 π 0 g h o P ( z ) f ( r , ϕ , z ) 1 + s P ( z ) f ( r , ϕ , z ) r d r d ϕ ,
0 2 π 0 g h o ( r ) r d r d ϕ = G o ,
g h o = G o π R o 2 θ ( r R o ) ,
g h o = G o δ ( x ) δ ( y ) ,
g h o = 2 G o π w 2 exp ( 2 r 2 / w 2 ) = G o f ( r , ϕ , z ) ,
Q 1 ( z ) = G o w 2 2 s R o 2 ln [ 1 + 2 s I 1 1 + 2 s I 1 exp ( 2 R o 2 / w 2 ) ] ,
Q 2 ( z ) = 2 G 0 I 1 1 + 2 s I 1 ,
Q 3 ( z ) = G 0 s [ 1 1 2 s I 1 ln ( 1 + 2 s I 1 ) ] .
Q ( z ) l / P ( z ) = ( 1 R r ) + ( 1 R l ) + η l ,
F = 2 G o l / ( π w 2 ) ( 1 R r ) + ( 1 R l ) + η l ,
F 8 s I 1 w 2 R o 2 ln [ 1 + 4 s I 1 1 + 4 s I 1 exp ( 2 R o 2 / w 2 ) ] = 1 ;
s I 1 = ( F 1 ) / 4 ;
F 4 s I 1 [ 1 1 4 s I 1 ln ( 1 + 4 s I 1 ) ] = 1.
F th = 2 ( R o / w ) 2 1 exp [ 2 ( R o / w ) 2 ] .

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