Optimizing H1 cavities for the generation of entangled photon pairs

We report on the theoretical investigation of photonic crystal cavities etched on a suspended membrane for the generation of polarization entangled photon pairs using the biexciton cascade in a single quantum dot. The implementation of spontaneous emission enhancement effect increases the entanglement visibility, while the concomitant preferential funneling of the emission in the cavity mode increases the collection of both entangled photons. We demonstrate and quantify that standard cavity designs present a polarization dependent emission diagram, detrimental to entanglement. The optimization of H1 cavities allows to obtain both high collection efficiencies and polarization independent emission, while keeping high Purcell factors necessary for high quality entangled photon sources.