  The interaction of quantum emitters with structured baths modifies both their
individual and collective dynamics. In Gonz\'alez-Tudela \emph{et al} we show
how exotic quantum dynamics emerge when QEs are spectrally tuned around the
middle of the band of a two-dimensional structured reservoir, where we predict
the failure of perturbative treatments, anisotropic interactions and novel
super and subradiant behaviour. In this work, we provide further analysis of
that situation, together with a complete analysis for the quantum emitter
dynamics in spectral regions different from the center of the band.
