  We analyze the change in the spontaneous decay rate, or Purcell effect, of an
extended quantum emitter in a structured photonic environment. Based on a
simple theory, we show that the cross-density of states is the central quantity
driving interferences in the emission process. Using numerical simulations in
realistic photonic cavity geometries, we demonstrate that a structured
cross-density of states can induce subradiance or superradiance, and change
subtantially the emission spectrum. Interestingly, the spectral lineshape of
the Purcell effect of an extended source cannot be predicted from the sole
knowledge of the spectral dependence of the local density of states.
