Bound states in the continuum (BIC) have been at the forefront of research in optics and photonics over the past decade. It is of great interest to study the effects associated with quasi-BICs in the simplest structures, where quasi-BICs are very pronounced. An example is a dielectric cylinder, and in a number of works, quasi-BICs have been studied both in single cylinders and in structures composed of cylinders. In this work, we studied the properties of quasi-BICs during the transition from a homogeneous dielectric cylinder in an air environment to a ring with narrow walls while increasing the diameter of the inner air cylinder gradually. The results demonstrate the quasi-BIC crossover from the strong-coupling to the weak-coupling regime, which manifests itself in the transition from the avoided crossing of branches to their intersection with the quasi-BIC being preserved on only one straight branch. In the regime of strong-coupling and quasi-BIC, three waves interfere in the far-field zone: two waves corresponding to the resonant modes of the structure and the wave scattered by the structure as a whole. The validity of the Fano resonance concept is discussed since it describes the interference of only two waves under weak coupling conditions.

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Trapping and confining electromagnetic waves is important in both basic research and a variety of applications. For these purposes, various physical mechanisms are exploited including bound states in the continuum, which have been actively investigated recently. Bound states in the continuum have been observed in various objects consisting of both one and a number of dielectric structures. In particular, these photonic states were observed in high-contrast dielectric cylinders in the regime of strong eigenmode coupling, which leads to destructive interference in the far-field zone. In this article, we present the results of a study of bound states in a continuum in a dielectric ring, i.e. cylinder with coaxial air hole. The dependence of the quality factor Q on the normalized diameter of the hole is discussed.