Quantum Theory of a Resonant Photonic Crystal
Abstract
We present a quantum model of two-level atoms localized in a 3D lattice, based on the Hopfield theory of exciton polaritons. In addition to a polaritonic gap at the exciton energy, a photonic bandgap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the exciton energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of 25 cm-1, up to 105 times the detuned gap size. The dispersion curve contains a branch supporting slow-light modes with vanishing exciton probability density.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.