Design and modeling of ?(2) second harmonic amplification in circular photonic crystal

We analyze in this work the second harmonic amplification of ?(2) nonlinear process in membrane type GaAs circular photonic crystal. This unconventional kind of photonic crystal is well suited for the generation of whispering gallery modes due to the circular symmetric periodic pattern. The Gaussian beam of a fundamental pump signal at 1.55 ?m defines a whispering gallery mode resonance and generates a second harmonic mode at 0.775 ?m in the central missing hole micro-cavity. The periodic pattern and the micro-cavity are tailored and optimized in order to generate a second harmonic conversion efficiency of 50 %. We predict the resonances by an accurate 2D time domain model including ?(2) nonlinearity and also by a 3D Finite Element Method FEM. Moreover, by using a 3D membrane configuration, we predict a quality factor of the second harmonic mode of the order of 35000.