  We present a detailed experimental characterization of the spectral and
spatial structure of the confined optical modes for oxide-apertured micropillar
cavities, showing good-quality Hermite-Gaussian profiles, easily mode-matched
to external fields. We further derive a relation between the frequency
splitting of the transverse modes and the expected Purcell factor. Finally, we
describe a technique to retrieve the profile of the confining refractive index
distribution from the spatial profiles of the modes.
