Mode structure and ray dynamics of a parabolic dome microcavity

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.