  We consider the wave and ray dynamics of the 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 the modes with
finite angular momentum have a structure that avoids the focal area and have
correspondingly larger effective volume. The ray dynamics indicates that the
fundamental s-wave is robust with respect to small geometrical deformations of
the cavity, while the higher order modes are associated with ray chaos and
short-lived. 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.
