  Subwavelength particles with hyperbolic light dispersion in the constituent
medium are a promising alternative to plasmonic, high-refractive-index
dielectric, and semiconductor structures in the practical realization of
nanoscale optical elements. Hexagonal boron nitride (hBN) is a layered van der
Waals material with natural hyperbolic properties and low-loss
phonon-polaritons at the same time. In this work, we consider multipole
excitations and antennas properties of hBN particles with an emphasis on the
periodic arrangement and collective array modes. We analyze excitation of
lattice resonances in the antenna array and effect of resonance shifts and
overlap with other multipoles supported by particles in the lattice. A decrease
of reflectance from the array is achieved with appropriate lattice spacing
(periods) where the electric and magnetic multipoles overlap, and the resonance
oscillations are in phase and comparable in magnitude. We theoretical
demonstrate that generalized Kerker condition is satisfied in this case, and
hBN antennas in the array efficiently scatter light in the predominantly
forward direction resulting in near-zero reflectance. The resonant lattice
Kerker effect with hyperbolic-medium antennas can be applied in developing
metasurfaces based on hBN resonators for mid-infrared photonics.
