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 MoS ₂ embedded in a Si ₃N ₄ 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.