A theoretical description of the interaction between confined excitons and
photonic modes in pillar microcavities is given. For quantum-well excitons
in the strong coupling regime, the Rabi splitting is reduced compared to th
e reference planar cavity and a radiative splitting of exciton states coupl
ed to cavity modes with different symmetries is found. In the case of zero-
dimensional excitations, the conditions for achieving the strong-coupling r
egime are determined. For InAs quantum dots the oscillator strength is too
low to yield a vacuum-field Rabi splitting, while excitons bound to monolay
er fluctuations in quantum wells behave as quantum dots with a large oscill
ator strength and can more easily be in the strong-coupling regime.