Monolayers of transition
metal dichalcogenides (TMDCs)
are direct-gap
semiconductors with strong light–matter interactions featuring
tightly bound excitons, while plasmonic crystals (PCs), consisting
of metal nanoparticles that act as meta-atoms, exhibit collective
plasmon modes and allow one to tailor electric fields on the nanoscale.
Recent experiments show that TMDC-PC hybrids can reach the strong-coupling
limit between excitons and plasmons, forming new quasiparticles, so-called
plexcitons. To describe this coupling theoretically, we develop a
self-consistent Maxwell-Bloch theory for TMDC-PC hybrid structures,
which allows us to compute the scattered light in the near- and far-fields
explicitly and provide guidance for experimental studies. One of the
key findings of the developed theory is the necessity to differentiate
between bright and originally momentum-dark excitons. Our calculations
reveal a spectral splitting signature of strong coupling of more than
100 meV in gold-MoSe2 structures with 30 nm nanoparticles,
manifesting in a hybridization of the plasmon mode with momentum-dark
excitons into two effective plexcitonic bands. The semianalytical
theory allows us to directly infer the characteristic asymmetric line
shape of the hybrid spectra in the strong coupling regime from the
energy distribution of the momentum-dark excitons. In addition to
the hybridized states, we find a remaining excitonic mode with significantly
smaller coupling to the plasmonic near-field, emitting directly into
the far-field. Thus, hybrid spectra in the strong coupling regime
can contain three emission peaks.