  We consider light scattering off a two-dimensional (2D) dipolar array and
show how it can be tailored by properly choosing the lattice constant of the
order of the incident wavelength. In particular, we demonstrate that such
arrays can operate as nearly perfect mirrors for a wide range of incident
angles and frequencies close to the individual atomic resonance. These results
can be understood in terms of the cooperative resonances of the surface modes
supported by the 2D array. Experimental realizations are discussed, using
ultracold arrays of trapped atoms and excitons in 2D semiconductor materials,
as well as potential applications ranging from atomically thin metasurfaces to
single photon nonlinear optics and nanomechanics.
