# I Fresnel reflection coefficient for Second Harmonic Generation (SHG)

1. Sep 1, 2016

### Jose Antonio

Hello everyone, this is my first post so I don't know whether or not this is the right thread to be asking this question (if so I am sorry). I am currently working on my thesis where I am determining the thickness of a GaN crystal through second harmonic generation. However in a article published by J. Jerphagnon and S. K. Kurtz, they defined a Fresnel-like transmission coefficient for the second harmonic signal as:

I was wondering if anyone knew a source of how to get this result. I am intrigued on why this transmission coefficient is not the absolute value squared (since it is a capital T) since one could be considering the complex form of the refractive indices. Thanks in advance for any response!

2. Sep 1, 2016

### Andy Resnick

Could you please post a proper citation for the above? Thanks in advance.

3. Sep 1, 2016

4. Sep 1, 2016

### Jose Antonio

I do understand that both transmission and reflection coefficients do somehow need to include both refractive indices at frequencies ω and 2ω, since the bound and free waves have different refractive indices and the solution of the inhomogeneous solution is the sum of the homogeneous solution (free wave) and particular solution (bound wave), however I can't seem to find any source where this result is deduced (and I certainly do can't find a way to find it myself).

Last edited: Sep 1, 2016
5. Sep 1, 2016

### Andy Resnick

Yeesh... rough paper. Looks like the derivation is in Appendix A.