  We describe applications of two-dimensional subwavelength quantum emitter
arrays as efficient optical elements in the linear regime. For normally
incident light, the cooperative optical response, stemming from emitter-emitter
dipole exchanges, allows the control of the array's transmission, its resonance
frequency, and bandwidth. Operations on fully polarized incident light, such as
generic linear and circular polarizers as well as phase retarders can be
engineered and described in terms of Jones matrices. Our analytical approach
and accompanying numerical simulations identify optimal regimes for such
operations and reveal the importance of adjusting the array geometry and of the
careful tuning of the external magnetic fields amplitude and direction.
