  Inspired by recent advances in the manipulation of atoms trapped near 1D
waveguides and pro- posals to use surface acoustic waves on piezoelectric
substrates for the same purpose, we show the potential of two-dimensional
platforms. We exploit the directional emission of atoms near photonic crystal
slabs with square symmetry to build perfect subradiant states of 2 distant
atoms, possible in 2D only for finite lattices with reflecting boundaries. We
also show how to design massively parallel 1D arrays of atoms above a single
crystal, useful for multi-port output of nonclassical light, by ex- ploiting
destructive interference of guided resonance modes due to finite size effects.
Directionality of the emission is shown to be present whenever a linear
iso-frequency manifold is present in the dispersion relation of the crystal.
Multi-atom radiance properties can be obtained from a simple cross-talk
coefficient of a master equation, which we compare with exact atom-crystal
dynamics, showing its predictive power.
