  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.
