  While metamaterials are often desirable for near-field functions, such as
perfect lensing, or cloaking, they are often quantified by their response to
plane waves from the far field. Here, we present a theoretical analysis of the
local density of states near lattices of discrete magnetic scatterers, i.e.,
the response to near field excitation by a point source. Based on a
point-dipole theory using Ewald summation and an array scanning method, we can
swiftly and semi-analytically evaluate the local density of states (LDOS) for
magnetoelectric point sources in front of an infinite two-dimensional (2D)
lattice composed of arbitrary magnetoelectric dipole scatterers. The method
takes into account radiation damping as well as all retarded electrodynamic
interactions in a self-consistent manner. We show that a lattice of magnetic
scatterers evidences characteristic Drexhage oscillations. However, the
oscillations are phase shifted relative to the electrically scattering lattice
consistent with the difference expected for reflection off homogeneous magnetic
respectively electric mirrors. Furthermore, we identify in which source-surface
separation regimes the metasurface may be treated as a homogeneous interface,
and in which homogenization fails. A strong frequency and in-plane position
dependence of the LDOS close to the lattice reveals coupling to guided modes
supported by the lattice.
