The influence of periodicity on the optical response of cube silicon metasurfaces

•Some radiation phenomena caused by the periodicity of the cube silicon metasurfaces are explored which can be explained by the lattice resonance theory and guided-mode resonance filter theory.•The electromagnetic coupling between array nanoparticles enhances dipole and octupole radiation in the metasurfaces when Mie resonances and guided-mode resonances occur.•The enhanced electric and magnetic octupoles should not always be ignored when analyzing the optical properties of cube silicon metasurfaces via the multipole expansion method.•Guided-mode resonances, which are caused by the periodicity of metasurfaces, can be applied in designing devices. All-dielectric metasurfaces have attracted extensive attention because of their ability to control electromagnetic waves with low loss. However, compared with the research on the physical basis of a single nanoparticle controlling electromagnetic waves, foundational research on the influence of the periodicity of all-dielectric metasurfaces on their control of electromagnetic waves is still insufficient. Thus, the aim of this article is to further explore and emphasize the effect of the periodicity of metasurfaces on their optical performance and their electromagnetic response and coupling, and to describe how the above theoretical exploration can be employed for designing devices. We first explore some optical performance caused by the periodicity of cube silicon metasurfaces in the near-infrared band and reveal that these phenomena cannot be explained by the Mie resonances of the single nanoparticles composing the metasurfaces but by the lattice resonance theory and guided-mode resonance filter theory. Then, the influence of the periodicity on the electromagnetic response and coupling in the metasurfaces are analyzed via the multipole expansion method. We emphasize that the electromagnetic coupling between array nanoparticles enhances dipole and octupole radiation in the metasurfaces and analyze how the radiation is enhanced. We also study some phenomena and applications caused by the guided-mode resonances for future design. The results of this study may have potential applications in lasers, reflectors, absorbers, detectors, and other fields, and provide theoretical basis for the design of specific performance devices by adjusting the size of metasurfaces related to periodicity.