Frequency doubling of monolithic Nd:YAG laser in external enhancement cavity

[damien88]

1. LiNbO3 is a negative uniaxial crystal. Consider a LiNbO3 crystal used for frequency doubling a laser operating at 1064 nm. The non-linear coefficient is d=3.4x10-23. For the setup considered it is desirable to have a non-linear conversion efficiency of 0.04 %/W,
Assume constant fundamental power throughout the crystal. Determine the crystal length required in
i. the plane wave approximation assuming a Gaussian focus waist of 10x10^-6m



Ok, so I have calculated the refractive index n0 and ne and established phase matching is possible in the previous question. Now I was intending to use the equation for the second harmonic intensity to help with calculating the crystal length but my problem is how I calculate the fundamental intensity. I have spent a lot of time on it but I don't feel like I have a very good grasp of the question itself and was hoping for any pointers as to where I should look to begin solving this question.

Thanks

 

[damien88]

I should add, I am unsure as to what I should use the gaussian waist value for. Is there a way for me to calculate the fundamental power using this?

Thanks again