The mode profile of Gaussian beams in our PPKTP crystals was calculated.
I confirmed that the Rayleigh range of the incoming beam (1064 nm) and that of the outgoing beam (532 nm) is the same.
And it turned out that the waist postion for the incoming beam and the outgoing beam should be different by 13.4 mm toward the direction of propagation.
These facts will help us making optical layouts precisely for our green locking.
The result is shown in the attached figure, which is essentially the same as the previous one (see the entry).
The horizontal axis is the length of the propagation direction, the vertical axis is the waist size of Gaussian beams.
Here I put x=0 as the entering surface of the crystal, and x=30 mm as the other surface.
The red and green solid curve represent the incoming beam and the outgoing beam respectively. They are supposed to propagate in free space.
And the dashed curve represents the beams inside the crystal.
A trick in this calculation is that: we can assume that the waist size of 532 nm is equal to that of 1064 nm divided by sqrt(2) .
If you want to know about this treatment in detail, you can find some descriptions in this paper;
"Third-harmonic generation by use of focused Gaussian beams in an optical super lattice" J.Opt.Soc.Am.B 20,360 (2003)"
If I understand your elog, you are just calculating the the offset in position space that you get by having a refractive index.
Did you end up changing the mode matching so that the rayleigh range (which changes with refractive index) was confocally focused inside the crystal (e.g. Zr = 15 mm?