Quantitative determination of modal photon number density spectrum in arbitrary dielectric structures with a quantum emitter

Understanding the photon number statistics of a quantum emitter (QE) interacting with complex photonic environments is fundamental to advances in quantum optics and nanophotonics. We introduce a general theoretical framework for calculating the modal photon number density spectrum (MPNDS) in arbitrary dielectric structures with an embedded two-level QE. We validate our approach by investigating a system composed of a two-level QE and a photonic crystal (PhC) slab with an L3 cavity and a waveguide, finding that the MPNDS exhibits significant changes in both waveguide and background radiative channels as the interaction between the QE and modal field transitions from weak coupling to strong coupling. We observe that the number of photons guided along the waveguide shows a strong dependence on the QE’s transition frequency and transition dipole moment, but demonstrates robustness to the transition dipole moment when the transition frequency approaches the waveguide cutoff frequency. Our work allows for the determination and tailoring of light emission characteristics across diverse radiative channels in complex photonic environments.