Light-matter interaction in all-dielectric nanoparticles has attracted more attention because of the abil- ity to control and configure light scattering on high-index nanoparticles. In the framework of the dis- crete dipole approximation, we theoretically applied cartesian multipole expansion to a periodic array of nanoparticles. This allows to analyze the contribution of multipole moments, including toroidal moments, in the scattering spectra of an array of infinite 1D/2D periodic structure of arbitrary shaped nanoparticles. The formulation is based on the Taylor expansion in cartesian coordinate system up to the fifth-order that includes a magnetic 16-pole and an electric 32-pole. Examples of a wide-band reflector and a wide-band transmitter made of silicon nanodisks are studied at IR wavelengths. The results show how constructive and destructive interferences of multipole terms affect the scattering field. The proposed method paves the way to design and analyze novel types of nanoscale subwavelength metasurfaces.

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