  We study the spontaneous decay of an impurity coupled to a linear array of
bosonic cavities forming a single-band photonic waveguide. The average
frequency of the emitted photon is different from the frequency for
single-photon resonant scattering, which perfectly matches the bare frequency
of the excited state of the impurity. We study how the energy of the excited
state of the impurity influences the spatial profile of the emitted photon. The
farther the energy is from the middle of the photonic band, the farther the
wave packet is from the causal limit. In particular, if the energy lies in the
middle of the band, the wave packet is localized around the causal limit.
Besides, the occupation of the excited state of the impurity presents a rich
dynamics: it shows an exponential decay up to intermediate times, this is
followed by a power-law tail in the long-time regime, and it finally reaches an
oscillatory stationary regime. Finally, we show that this phenomenology is
robust under the presence of losses, both in the impurity and the cavities.
