  We describe exciton-polariton modes formed by the interaction between
excitons in a 2D layer of a transition metal dichalcogenide embedded in a
cylindrical microcavity and the microcavity photons. For this, an expression
for the excitonic susceptibility of a semiconductor disk placed in the symmetry
plane perpendicular to the axis of the microcavity is derived. Semiclassical
theory provides dispersion relations for the polariton modes, while the
quantum-mechanical treatment of a simplified model yields the Hopfield
coefficients, measuring the degree of exciton-photon mixing in the coupled
modes. The density of states (DOS) and its projection onto the photonic and the
excitonic subspaces are calculated taking monolayer MoS 2 embedded in a Si 3 N
4 cylinder as an example. The calculated results demonstrate a strong
enhancement, for certain frequencies, of the total and local DOS (Purcell
effect) caused by the presence of the 2D layer.
