  To achieve efficient light control at subwavelength dimensions, plasmonic and
all-dielectric nanoparticles have been utilized both as a single element as
well as in the arrays. Here we study 2D periodic nanoparticle arrays
(metasurfaces) that support lattice resonances near the Rayleigh anomaly due to
the electric dipole (ED) and magnetic dipole (MD) resonant coupling between the
nanoparticles. Silicon and core-shell particles are considered. We demonstrate
for the first time that, choosing of lattice periods independently in each
mutual-perpendicular direction, it is possible to achieve a full overlap
between the ED-lattice resonance and MD resonances of nanoparticles in certain
spectral range and to realize the resonant lattice Kerker effect (resonant
suppression of the scattering or reflection). At the effect conditions, the
strong suppression of light reflectance in the structure is appeared due to
destructive interference between electromagnetic waves scattered by ED and MD
moments of every nanoparticle in the backward direction with respect to the
incident light wave. Influence of the array size on the revealed reflectance
and transmittance behavior is discussed. The resonant lattice Kerker effect
based on the overlap of both ED and MD lattice resonances is also demonstrated.
