  Higher-order topological insulators(HOTIs) is an exciting topic. We
constructed a square lattice dipole arrays, it supports out-of-plane and
in-plane modes by going beyond conventional scalar coupling. In-plane modes
naturally break $\mathrm C_{4}$ symmetry, we only studied the out-of-plane
modes that maintain $\mathrm C_{4}$ symmetry. Due to the slowly decaying
long-range coupling, we consider its fully coupled interactions by using the
lattice sums technique and combined with the coupled dipole method (CDM) to
study its topological properties in detail. Interestingly, even when the full
coupling is considered, the topological properties of the system remain similar
to those of the 2D Su-Schrieffer-Heeger(SSH) model, but very differently, it
supports robust zero-energy corner states (ZECSs) with $\mathrm C_{4}$
symmetry, we calculate the bulk polarization and discuss in detail the
topological origin of the ZECSs. The lattice sums technique in the article can
be applied to arbitrary fully coupled 2D dipole arrays. The materials we used
can be able to confine light into the deep subwavelength scale, it has a great
potential in enhancing light-matter interactions in the terahertz (THz) range.
