Quantum theory of exciton polaritons in cylindrical semiconductor microcavities

A quantum-mechanical formalism is developed in order to study the interaction between a quantum-well exciton and the electromagnetic (e.m.) field inside a cylindrical microcavity. The cavity modes are evaluated as a function of the radius according to a self-consistent procedure, and are found to be in good agreement with the experiment [J.M. Gerard, D. Barrier, J. Y. Martin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, Appl. Phys. Lett. 69, 449 (1996)]. The cavity polaritons are then evaluated by diagonalizing the total Hamiltonian, which is written in second quantized form and includes also the self-interaction term. The mixed radiation-matter states manifest themselves with the characteristic anticrossing behavior. The Rabi splitting is found to depend on the quantum numbers of the mode and on its polarization: for a large radius of the cavity it approaches the planar cavity limit, and it decreases for decreasing radius. This effect is interpreted in terms of the leakage of the cavity modes in the outside region, which decreases the overlap between the exciton wave function and the e.m. field. Although the interaction between material and radiation excitations with the same quantum numbers still remains the dominant one, different boundary conditions applying to the exciton and to cavity mode wave functions lead to interactions between states with different radial quantum numbers. Removal of the exciton degeneracy is predicted: the large energy separation between radiation modes with different quantum numbers produces an energy splitting of the otherwise degenerate exciton states inside a cylindrical microcavity. [S0163-1829(99)11847-2].