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

Ab-initio Mapping of Projected Local Density of States in Arbitrary Nanostructures: Application to Photonic Crystal Slabs and Cavities