  We present all the periodic Green function dyadics that enter a description
of a 2d array of emitters at the level that includes the electric dipole,
magnetic dipole and electric quadrupole moment of each emitter. We find a
concise analytic form for the radiative contributions to the periodic Green
function dyadics that give rise to radiation reaction fields, and we give the
non-radiative contributions that do not affect energy balance in the form of
rapidly converging series. Finally, we present an approximation scheme for
evaluating periodic Green function dyadics at long wavelengths that rigorously
respects energy conservation. The scheme extends the range of validity of the
usual static approximation by the inclusion of a simple dynamic correction.
