Mode structure and ray dynamics of a parabolic dome microcavity

We consider the wave and ray dynamics of an electromagnetic field in a parabolic dome microcavity. The structure of the fundamental s wave involves a main lobe in which the electromagnetic field is confined around the focal point in an effective volume of the order of a cubic wavelength, while modes with finite angular momentum have a structure that avoids the focal area and have correspondingly larger effective volumes. The ray dynamics indicate that the fundamental s wave is robust with respect to small geometrical deformations of the cavity, while the higher order modes are unstable, giving rise to optical chaos. We discuss the incidence of these results on the modification of the spontaneous emission dynamics of an emitter placed in such a parabolic dome microcavity.