Frequency doubling and gaussian beam problem.

[damien88]

1. A Nd:YAG laser operates at a wavelength of 1064 nm and is used for frequency doubling in the non-linear material LiNbO3.
The laser outputs 1 W of power in a TEM00 mode with a beam waist ω0 = 1.0 mm on the output mirror.
A lens of focal length of 50 mm is placed immediately outside the laser. Estimate the focused spot size ωf and z0 of the beam inside the LiNbO3 crystal placed at this focus.

The refractive indices for LiNbO3 are; 1064nm no=2.2238 and at 532 no=2.3143
1064nm ne=2.1456 and at 532 ne=2.2218





3. My attempt at the problem so far is is ωf= fλ/∏ω0=(1065x10^-9m)(50x10^-3m)/∏(1x10^-3m)=1.69x10^-5
z0=∏(ω0^2)/λ=2.95.
I am along the right lines with this? Do I also need to also take into account the refractive indices?

Thanks in advance

 

[member 553083]

.Yes, you need to take into account the refractive indices. The focal length of the lens will change according to the refractive indices of the medium, so the spot size and z0 should be calculated accordingly. For this problem, you would have to calculate the new focal length and then use it to calculate the new spot size and z0.