Revisiting the physics of Fano resonances for nanoparticle oligomers

We present a robust approach for interpreting the physics of Fano resonances in planar oligomer structures of both metallic and dielectric nanoparticles. We reveal a key mechanism for Fano resonances by demonstrating that such resonances can be generated purely from the interference of nonorthogonal collective eigenmodes, which are clearly identified based on the coupled-dipole approximation. We prove analytically a general theorem to identify the number of collective eigenmodes that can be excited in ring-type nanoparticle oligomers and further demonstrate that no dark-mode excitation is necessary for the existence of Fano resonances in symmetric oligomers. As a consequence, we unify the understanding of Fano resonances for both plasmonic and all-dielectric oligomers.