  We investigate spontaneous photon emission processes of two-level atoms in
parabolic and ellipsoidal cavities thereby taking into account the full
multimode scenario. In particular, we calculate the excitation probabilities of
the atoms and the energy density of the resulting few-photon electromagnetic
radiation field by using semiclassical methods for the description of the
multimode scenario. Based on this approach photon path representations are
developed for relevant transition probability amplitudes which are valid in the
optical frequency regime where the dipole and the rotating-wave approximations
apply. Comparisons with numerical results demonstrate the quality of these
semiclassical results even in cases in which the wave length of a spontaneously
emitted photon becomes comparable or even larger than characteristic length
scales of the cavity. This is the dynamical regime in which diffraction effects
become important so that geometric optical considerations are typically not
applicable.
