Second harmonic generation in photonic crystals: numerical simulation

In this paper, we want to present a simple and efficient numerical method for SHG analysis in one-dimensional photonic crystals (PhCs) based on full nonlinear system of equations. For solving the nonlinear SHG problem we used a simple method of finite elements coupled with fixed point iteration. Our model does not need additional analytic approximation compared with some existing methods, and it can be easily extended to study the SHG problem in two-dimensional photonic crystals. We used the FlexPDE Professional program to plot the diagrams varying the parameters. At the end we obtained two maximum intensities of the second harmonic wave within each high index layer, that being in contrast to the fundamental wave peak. This result can be found also in the literature. In addition, we have plotted the lattice using the Optiwave FDTD software and we observed the propagation of the field in time.