Group theory based formation mechanism and evolution of multiple Fano resonances in dielectric nanoholearrays with lattice-perturbed

Based on the electromagnetic properties of all-dielectric optical metamaterial, an all-dielectric metasurfaceof lattice-perturbed nanohole array is proposed to excite a multiple Fano resonance in the near-infrared region.Combined with the group theory, the formation mechanism and evolution law of multiple Fano resonances inthis structure when its unit cell is a square lattice configuration and the square lattice symmetry is broken areexplored in depth. The results show that double degenerate mode directly excited by the normal incident planewave is coupled to vertical free-space radiation continuum to form double Fano resonance when unit cell issymmetrical, while the uncoupled non-degenerate modes excited by the normal incident plane wave is coupledto vertical free-space radiation continuum to form triple Fano resonance with higher Q factor when thesymmetry is broken. Numerical simulation is used to explore the influences of x-polarized and y-polarized planewave on the above Fano resonances, and the results show that the Fano resonance of double degenerateresonance is polarization independent, while the non-degenerate resonance is polarization dependent. Thefindings in this work can provide an effective theoretical reference for designing other square lattice metasurfaceto realize the excitation and evolution of multiple Fano resonances