FEM Design and Modeling of $\chi ^{(2)}$ Second-Harmonic Enhancement in Circular Photonic Crystal

In this paper, we analyze the enhancement of ξ⁽²⁾ nonlinear process in membrane-type circular photonic crystal (PhC) based on GaAs. This unconventional kind of PhC is well suited for the generation of whispering gallery modes (WGMs) due to the circular symmetric periodic pattern. By using a laser Gaussian beam at 1.55 μm as pump signal, a WGM at 1.55 μm and a second-harmonic (SH) mode at 0.775 μm are obtained. The SH will be generated in the center of the missing-hole microcavity. The periodic pattern and the microcavity are tailored and optimized providing an SH efficiency conversion as high as 50%. We predict the resonances by an accurate 2-D time-domain model including ξ⁽²⁾ nonlinearity and by a 3-D finite-element method. Finally, by using a 3-D membrane configuration, we found a total quality factor of the SH mode of the order of 35 000.