  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 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.
