Based upon projected local density of states (PLDOS) for photons, we develop a local coupling theory to simultaneously treat the weak and strong interaction between a quantum emitter and photons in arbitrary nanostructures. The PLDOS is mapped by an
extremely flexible and efficient method. The recent experiment observation for the photonic crystal slabs is very well interpreted by our ab-initio PLDOS. More importantly, a bridge linking the PLDOS and cavity quantum electrodynamics is for the first time established to settle quality factor, g factor and vacuum Rabi splitting. Our work greatly enriches the knowledge about the interaction between light and matter in nanostructures.
