Scaling law of enhanced second harmonic generation in finite Bragg stacks

The second-harmonic generation (SHG) in finite Bragg stacks of alternating linear and nonlinear optical films is studied with the exact Green function under the assumption of perturbation theory. Various mechanisms of enhanced SHG are investigated analytically, and the scaling law with respect to the number N of stacking layers is derived for each mechanism. In particular, it is shown that there is a simple mechanism of the enhanced SHG having N;4 scaling, in which both the enhancement of the Green function and the phase matching condition peculiar to finite Bragg stacks are fulfilled simultaneously.