Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities

We develop a local coupling theory to simultaneously treat the weak and strong interaction between a quantum emitter and photons in arbitrary nanostructures. The local coupling strength proportional to the projected local density of states (PLDOS) for photons is determined by a flexible and efficient method. The recent experimental observation for the photonic crystal (PC) slabs is very well interpreted by our ab initio PLDOS, while the scaling invariant law is found to be inapplicable for these PC slabs. More importantly, a bridge linking the PLDOS and cavity quantum electrodynamics is established by the local coupling strength to account for quality factor, $g$ factor, and vacuum Rabi splitting. Our work enriches the knowledge about the light-matter interaction in nanostructures.