2) I heard that proustite crystal is prohibited due to its poisonous action, while some new IR crystals for upconversion are discovered that are even better. Some Lithuanian company produces them. I will see my mailbox carefully....

3) all depends on phase matching. Imagine that all processes have the same coherence lengths, then SH, DF and SF powers will be just the same

I am not familiar with the QM model, but I would think that one is better. The Maxwell eqs. arrive at NL susceptibilities by a series expansion (phenomenological model) which usually are true for small perturbations, etc. But your intensity should be considerable for NL effects to occur, so you are (theoretically) on shaky ground.

Sorry for #2 and 3, it was a long time ago since I looked at this field.

1. I am also not sure about QM model, but as per my study I was following the nonlinear susceptabilities derived with the help of maxwells equations.

3. In a nonlinear process, due to the polarisation dependency on linear, second order, third order and higher order susceptabilities, we will have many different processes (i.e. second order susceptability is responsible for second order effects like second harmonic generation, sum and difference frequency generation and paramaetric interactions, third order susceptability for third harmonic generations and so on) but with very negligable efficiency and we would enhance the efficiency of particular process or processes by satisfying phase matching conditions required to that particular process or processes.

This is the link for new IR upconversion crystal ZGP - http://eksmaoptics.com/nonlinear-and-laser-crystals/nonlinear-crystals/infrared-nonlinear-aggas2-aggase2-gase-zngep2-crystals/

Answer for question 2: If you want to get basic knowledges concerned d_eff calculations - read Boyd`s book, page 39-43 and related papes. If your interest is practical - use very simple and free computer program "SNLO" for any calculations, related to harmonic generation, parametric interactions, etc. You can download it from National Livermore Laboratory site. Or I can send you SNLO setup to your E-mail.

For #2, I'm a bit sketchy, but what you need to do: look up the symmetry of your crystal (you have it in table1.5.3 already) - go back to table 1.5.2 and see according to this symmetry, how many coefficients (positions in the tensor matrix) are equal to your d_22 and d_15 elements. Just for the sake of argument, say you have 3 elements equal to the value of d_22 and say 10 equal to d_15 (like d_51, d_25 and d_52, and so forth - here is where you need to look at the symmetry of your crystal and from table 1.5.2 figure out which elements are equal to which...) Then do the sum (in my bogus example that would be: 3 x d_22 + 10 x d_15 .  Now it may be that you would have to normalize or not (i.e. for ex., one way would be to divide by 13, since you have 13 elements- you'll need to figure this out as well - how do you normalize/scale your d_eff).

But this is roughly how you would go about doing it. Sorry if I'm too vague, as said this is stuff I learned 20-25 yrs ago andnever applied it after college.