  The optical properties of periodic arrays of plasmonic nanoantennas are
strongly affected by coherent multiple scattering in the plane of the array,
which leads to sharp spectral resonances in both transmission and reflection
when the wavelength is commensurate with the period. We demonstrate that the
presence of a substrate (i.e., an asymmetric refractive-index environment) can
inhibit long-range coupling between the particles and suppress lattice
resonances, in agreement with recent experimental results. We find the
substrate-to-superstrate index contrast and the distance between the array and
the interface to be critical parameters determining the strength of diffractive
coupling. Our rigorous electromagnetic simulations are well reproduced by a
simple analytical model. These findings are important in the design of periodic
structures and in the assessment of their optical resonances for potential use
in sensing and other photonic technologies.
