**Theoretically the waist position of a Gaussian beam (1064) in our PPKTP crystal differs by ~6.7 mm from that of the incident Gaussian beam.**
So far I have neglected such position change of the beam waist in optical layouts because it is tiny compared with the entire optical path.
But from the point of view of practical experiments, it is better to think about it.
**In fact the result suggests the rough positioning of our PPKTP crystals; **
**we should put our PPKTP crystal so that the center of the crystal is 6.7 mm far from the waist of a Gaussian beam in free space.**
**(How to)**
The calculation is very very simple.
The waist position of a Gaussian beam propagating in a dielectric material should change by a factor of n, where n is the refractive index of the material.
In our case, PPKTP has n=1.8, so that the waist position from the surface of the crystal becomes longer by n.
Now remember the fact that the maximum conversion efficiency can be achieved if the waist locates at exact center of a crystal.
Therefore the waist position in the crystal should be satisfied this relation; z*n=15 mm, where z is the waist position of the incident beam from the surface and 15 mm is half length of our crystal.
Then we can find z must be ~8.3 mm, which is 6.7 mm shorter than the position in crystal.
The attached figure shows the relation clearly. Note that the waist radius doesn't change. |