Exciton–polaritons of a 2D semiconductor layer in a cylindrical microcavity

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 MoS2 embedded in a Si3N4 cylinder as an example. The calculated results demonstrate a strong enhancement for certain frequencies of the total and local DOS (and, consequently, of the spontaneous emission rate of a nearby point emitter, i.e., the Purcell effect) caused by the presence of the 2D layer.