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GaAs/AlAs pillar microcavities with elliptical cross section have been fabricated by molecular beam epitaxy, electron-beam lithography, and reactive ion etching. We study their lowest energy confined photonic modes by photoluminescence, using a quantum box array placed inside the cavity as an internal broadband light source. Such an anisotropic cross section allows to split the twofold polarization degenerate fundamental mode of circular micropillars into a pair of orthogonal linearly polarized modes. Their energy splitting, which is well accounted for by a simple perturbative model, is studied experimentally and theoretically as a function of the eccentricity and average radius of the pillars. Splittings as large as 15 meV are observed, which is very encouraging for applications ranging from the improvement of the polarization locking in vertical cavity lasers to the fabrication of light emitting diodes with a better …