Approximating the KTP/LBO length.....
From Nicolaas Bloembergen's book...
The first order approximation for SHG conversion is
Pout (SHG) = (K^2) * (L^2/A) * P
Where K is a constant
L is the interaction length
A is the cross sectional beam area
P is the circulating power
The A term increases power when the beam is tighter in diameter. Ie a beam waist sets in the crystal.
The K term comes from SNLO and is a constant based on the material.
If you have a short waist, there is no reason for the crystal to be much longer then the waist. If there is no waist, A is about 1 for our purposes, and the crystal needs to be longer. A=1 is a very bad assumption, but its the best I can do for a narrow, parallel, beam.
Now you know why KTP532 and other lasers have a cavity waist at the crystal.
Steve


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