  Designing the shape of silicon nanoparticles has been shown to be an
effective approach to increasing overlap between electric and magnetic dipole
resonances thereby achieving directional scattering and decrease of reflection.
Variations of disk diameter and/or height affect resonances differently and can
thus result in resonance overlap. In most of the studies, the disks are
arranged in a periodic array where the periodicity is varied together with disk
diameter, but the role of lattice effect is neglected. Here we theoretically
study a periodic array of disks and show that the contribution of the lattice
effect in shifting resonance positions is comparable to the effect of the
diameter change. We demonstrate that the lattice effect is important even when
the wavelength of diffraction remains on the blue side from electric and
magnetic dipole resonances and there are no additional lattice resonances are
excited. Period and disk dimensions are chosen so that the resonances overlap
in the proximity of the telecommunication wavelength which is of great
practical interest.
