  Near-field thermal emission can be engineered by using periodic arrays of
sub-wavelength emitters. The array thermal emission is dependent on the shape,
size, and materials properties of the individual elements as well as the period
of the array. Designing periodic arrays with desired properties requires models
that relate the array geometry and material properties to its near-field
thermal emission. In this study, a periodic method is presented for modeling
two-dimensional periodic arrays of sub-wavelength emitters. This technique only
requires discretizing one period of the array, and thus is computationally
beneficial. In this method, the energy density emitted by the array is
expressed in terms of array's Green's functions. The array Green's functions
are found using the discrete dipole approximation in a periodic manner by
expressing a single point source as a series of periodic arrays of
phase-shifted point sources. The presented method can be employed for modeling
periodic arrays made of inhomogeneous and complex-shape emitters with
non-uniform temperature distribution. The proposed technique is verified
against the non-periodic thermal discrete-dipole-approximation simulations, and
it is demonstrated that this method can serve as a versatile and reliable tool
for studying near-field thermal emission by periodic arrays.
