Tunable collective resonances in bi-layer dielectric metasurfaces under mechanical displacement.

Advances in manufacturing technology have recently enabled the realization of multilayer metasurfaces, which are attracting increasing attention due to their additional structural degrees of freedom compared to single-layer designs. Complex resonant phenomena have been reported in closely spaced configurations due to near-field coupling between layers. However, previous studies on coupled multilayer metasurfaces have predominantly focused on dipolar responses, and the role of higher-order multipoles in shaping the optical behavior of such systems has not been systematically investigated. In this work, we investigate a bi-layer all-dielectric metasurface composed of two identical layers, where each individual layer supports electric and magnetic multipoles up to the octupole order. By varying the lateral and vertical displacement between the layers, in-plane and out-of-plane coupling lead to the emergence and tunability of several displacement-induced effects. These include symmetry-protected and accidental bound states in the continuum (BICs), anapole-type BICs, surface lattice resonances (SLRs), lattice Kerker effects, and several collective resonances that remain robust under displacement. We show that interactions beyond the dipolar regime play a fundamental role in the formation of these complex resonance phenomena, and explain their origin via full-wave electromagnetic simulations combined with multipole decomposition. These results provide opportunities for engineering and tuning collective resonances in multilayer metasurfaces for applications in sensing, nonlinear optics, filters, and switching.