A comprehensive design framework for all-dielectric metasurfaces by harnessing the interplay of controlled multiple multipole excitation, Rayleigh anomaly, Mie and lattice resonances.

Dielectric metasurfaces have emerged as promising candidates for controlling electromagnetic (EM) multipoles, crucial for precise manipulation of associated light-matter interactions, particularly for multifunctionality in photonics technologies spanning across structural scales and the EM spectrum. Each multipole with a given nature (electric-E, magnetic-H) and order (dipole-D, quadrupole-Q) has specific functionality with implications on resonance types (fundamental as well as collective), their coupling and hybridization. By using geometrical dimensions as the primary design parameters, only a few multipoles have been reported to be excited simultaneously. Moreover, an understanding of the relationship among meta-atom Mie resonances, lattice periodicity, and lattice resonances is still lacking. The local field distribution due to spatial hybridization with neighboring meta-atoms is also unknown for finite metasurfaces. We have developed a comprehensive design framework to maximize resonance strength by controlled multipole excitation, overlap, and coupling among different resonance types, including Mie, lattice, Rayleigh anomaly, and local fields in metasurfaces, using numerical simulations. The simultaneous spectral overlap of four multipoles (ED, MD, EQ, and MQ) is demonstrated when the meta-atom height exceeds the excitation wavelength. As periodicity matches both the Mie and Rayleigh anomaly wavelengths, the resulting metasurface resonance attains a high