  We study the optical properties of coupled quantum dot-microcavity systems
with elliptical cross section. First, we develop an analytic model that
describes the spectrum of the cavity modes that are split due to the reduced
symmetry of the resonator. By coupling the QD emission to the polarized
fundamental cavity modes, we observe the vectorial nature of the Purcell
enhancement, which depends on the intrinsic polarization of the quantum dot and
its relative alignment with respect to the cavity axis. The variable
interaction strength of the QD with the polarized cavity modes leads to the
observation of strong and weak coupling. Finally, we demonstrate the capability
of elliptical micropillars to emit single and highly indistinguishable photons
(visibility over 93 \%).
