  We study high quality-factor (high Q) resonances supported by periodic arrays
of Mie resonators from the perspectives of both Bloch wave theory and multiple
scattering theory. We reveal that, unlike a common belief, the bound states in
the continuum (BICs) derived by the Bloch-wave theory do not directly determine
the resonance with the highest Q value in large but finite arrays. Higher Q
factors appear to be associated with collective resonances formed by nominally
guided modes below the light line associated with strong effect of both
electric and magnetic multipoles. Our findings offer valuable insights into
accessing the modes with higher Q resonances via bonding modes within finite
metastructures. Our results underpin the pivotal significance of magnetic and
electric multipoles in the design of resonant metadevices and nonlocal
flat-band optics. Moreover, our demonstrations reveal that coupled arrays of
high-Q microcavities do not inherently result in a stronger light-matter
interaction when compared to coupled low-Q nanoresonators. This result
emphasizes the critical importance of the study of multiple light-scattering
effects in cavity-based systems.
