Multipole couplings and resonance shifts in an array of dielectric particles at oblique incidence

In the present paper, we propose a coupled multipole model to treat the mutual interactions between nanoparticles aligned in a periodic array, which may be frequently encountered in designing metasurfaces and other functional electromagnetic structures. Our model is comprehensive in that it takes into account the electric and magnetic multipoles both up to the quadrupole order. Working under Cartesian coordinates, this model can readily give the multipole responses of the particles in an infinite array at both normal and oblique incidence. In particular, we work out the analytical expressions of the cross-multipole coupling tensors, which are much more complicated for oblique incidence than normal incidence. We invoke the Ewald method to efficiently and accurately calculate the involved lattice sum whose convergence is otherwise very slow. By quantifying the contributions from the various couplings, we are able to analyze the mechanisms of new resonances that emerge only at oblique incidence. As a prototypical example, we use this method to give physically clear explanations of and show flexible control on the resonance shifts of the multipoles of an array of silicon spheres. The power of this model makes it very promising for dealing with metasurfaces with extended areas or working at large numerical apertures.