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Monolayers of transition metal dichalcogenides (TMDC) are direct-gapsemiconductors with strong light-matter interactions featuring tightly boundexcitons, while plasmonic crystals (PCs), consisting of metal nanoparticlesthat act as meta-atoms, exhibit collective plasmon modes and allow one totailor electric fields on the nanoscale. Recent experiments show that TMDC-PChybrids can reach the strong-coupling limit between excitons and plasmonsforming new quasiparticles, so-called plexcitons. To describe this couplingtheoretically, we develop a self-consistent Maxwell-Bloch theory for TMDC-PChybrid structures, which allows us to compute the scattered light in the near-and far-field explicitly and provide guidance for experimental studies. Ourcalculations reveal a spectral splitting signature of strong coupling of morethan $100\,$meV in gold-MoSe$_2$ structures with $30\,$nm nanoparticles,manifesting in a hybridization of exciton and plasmon into two effectiveplexcitonic bands. In addition to the hybridized states, we find a remainingexcitonic mode with significantly smaller coupling to the plasmonic near-field,emitting directly into the far-field. Thus, hybrid spectra in the strongcoupling regime can contain three emission peaks.

Strong Coupling of Two-Dimensional Excitons and Plasmonic Photonic Crystals: Microscopic Theory Reveals Triplet Spectra