Exciton-photon interaction in a quantum dot embedded in a photonic microcavity

We present a detailed analysis of exciton-photon interaction in a microcavity made out of a photonic crystal slab. Here we have analyzed a disk-like quantum dot where an exciton is formed. Excitonic eigen-functions in addition to their eigen-energies are found through direct matrix diagonalization, while wave functions corresponding to unbound electron and hole are chosen as the basis set for this procedure. In order to evaluate these wave functions precisely, we have used Luttinger Hamiltonian in the case of hole while ignoring bands adjacent to conduction band for electron states. After analyzing Excitonic states, a photonic crystal based microcavity with a relatively high quality factor mode has been proposed and its lattice constant has been adjusted to obtain the prescribed resonant frequency. We use finite-difference time-domain method in order to simulate our cavity with sufficient precision. Finally, we formulate the coupling constants for exciton-photon interaction both where intra-band and inter-band transitions occur. By evaluating a sample coupling constant, it has been shown that the system can be in strong coupling regime and Rabi oscillations can occur for Excitonic state population.