  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.
