Collective nature of high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Q</mml:mi></mml:math> resonances in finite-size photonic metastructures

We study high-quality factor (high <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>Q</a:mi></a:math>) resonances in periodic and disordered 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>Q</b:mi></b:math> value in large but finite arrays. Higher <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>Q</c:mi></c:math> factors appear to be associated with collective resonances formed by nominally guided modes below the light line associated with strong-coupling effect of both electric and magnetic multipoles. Our findings offer valuable insights into accessing the modes with higher <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>Q</d:mi></d:math> 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-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>Q</e:mi></e:math> microcavities do not inherently result in a stronger light-matter interaction when compared to coupled low-<f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>Q</f:mi></f:math> nanoresonators. This result emphasizes the critical importance of multiple light-scattering effects in cavity-based systems.