Mechanism of formation and evolution of bound states in the continuum of split-hole all-dielectric metasurface under asymmetric displacement perturbation

Bound states in the continuum (BICs) with ultra-high Q properties have attracted much attention for their perfect localization in the continuous spectral range coexisting with extended waves. In this study, breaking the traditional excitation form of structure breakage or excitation field asymmetry, a monolithic silicon nanodisk array with relative displacement generated by the complete splitting of square nanopores is proposed based on the unique electromagnetic properties of all-dielectric metamaterials. During the introduction of perturbations by asymmetric displacements of splitting holes, it is shown by numerical simulations that two BICs at different wavelengths can be realized. Combined with eigenmodes of group theory, the symmetric matching relationship between the symmetry-protected BICs and the free-space radiation during the evolution process is analytically demonstrated, and the formation mechanism and the evolution law of the BICs excited by this metasurface are deeply investigated. meanwhile, it also provides a theoretical basis for the polarization dependence of quasi-BICs excitation and the ultra-high Q factor expression of BICs. Furthermore, near-field distribution and multipole decomposition show that the field distribution and surface currents support the excitation of BIC-driven toroidal dipole and magnetic quadrupole dual modes. This study not only provides an effective reference for the stability of high-Q resonance wavelengths, but also solves the problem of the lack of universality in analyzing the resonance mechanism based on resonance phenomena, and provides solid theoretical support for the study of displacement-mediated BICs resonance excitation and evolution.