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

Abstract

We present a detailed analysis of exciton–photon interaction in a microcavity made out of a photonic crystal slab. Here we have analysed a disc-like quantum dot where an exciton is formed. Excitonic eigen functions in addition to their eigen energies are found through direct matrix diagonalization, while wavefunctions corresponding to unbound electron and hole are chosen as the basis set for this procedure. In order to evaluate these wavefunctions precisely, we have used the 6 × 6 Luttinger Hamiltonian in the case of hole while ignoring bands adjacent to the conduction band for electron states. After analysing 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 a finite-difference time-domain method in order to simulate our cavity with sufficient precision. Finally, we formulate the coupling constants for the 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 a strong-coupling regime and Rabi oscillations can occur.